DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claim 1-32 are rejected under 35 U.S.C. 101 because the claimed invention are directed to abstract ideas without significantly more.
Regarding Claim 1:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim recites the abstract ideas:
estimating, by the at least one digital processor, a gradient of the objective function based on a current value of the at least one optimizable parameter and the set of samples from the probability distribution generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as the process of estimating the gradient of the objective function consists of mathematical calculations, therefore, this limitation amounts to mathematical concepts;
determining, by the at least one digital processor, first and second order moments based on the estimated gradient: - This limitation recites the abstract idea of mathematical concepts, as when given the broadest reasonable interpretation in light of the specification, the determining of the first and second order moments are calculated using a gradient estimation technique requiring only two function evaluations, therefore, this limitation amounts to mathematical process;
evaluating, by the at least one digital processor, the objective function using updated values of the one or more optimizable parameters: - This limitation is directed to the abstract idea of a mental process, as the process of evaluating the objective function using updated values of the optimizable parameters is a thought process that can be performed in a human mind by observing and judging (concepts performed in the human mind (including an observation, evaluation, judgment, opinion) (see MPEP § 2106.04(a)(2), subsection III)).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
initializing, by the at least one digital processor, a set of parameters including the one or more optimizable parameters and an objective function: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g));
until the objective function converges: - This limitation is simply manipulating data on iterative manner which does not impose a meaningful limit on the claim, being insignificant as extra solution activity;
receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application;
updating, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments: - This limitation invokes the digital processor merely as a tool for performing an abstract idea (see MPEP 2106.05(f)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
initializing, by the at least one digital processor, a set of parameters including the one or more optimizable parameters and an objective function: - This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii));
until the objective function converges: - This limitation is directed to performing repetitive calculations (see MPEP 2106.05(d)(II)(ii)), therefore, fails to amount to significantly more than the judicial exception;
receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II);
updating, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments: - This limitation invokes the digital processor merely as a tool for performing an abstract idea (see MPEP 2106.05(f)) and therefore fails to amount to significantly more than the judicial exception.
Regarding Claim 2:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 1 which included an abstract idea (see rejection for claim 1). Additionally, claim 2 recites the abstract ideas:
estimating the gradient based on the current value of the at least one optimizable parameter and the array of random directions: - This limitation recites the abstract idea of mathematical concepts, as the process of estimating the gradient is done using mathematical calculations, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
generating an array of random directions based on the set of samples generated from the probability distribution by the quantum processor: - This limitation is selecting a particular data source or type of data to be manipulated as it is merely adding data to the training set, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
generating an array of random directions based on the set of samples generated from the probability distribution by the quantum processor: - This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 3:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 1 which included an abstract idea (see rejection claim 1). Additionally, claim 3 recites the abstract ideas:
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction to obtain a first objective function value: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function is done using mathematical calculations, therefore, this limitation amounts to mathematical concepts;
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function is done using mathematical calculations, therefore, this limitation amounts to mathematical concepts;
determining a rate of change between the first and the second objective function values: - This claim is directed to a mathematical concept, as the process of determining a rate of change is a step of “determining” a variable or number using mathematical method (see MPEP 2106.04(a)(2) subsection C).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 4:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 3 which included an abstract idea (see rejection claim 3). Additionally, claim 4 recites the abstract ideas:
determining the perturbation parameter based on a normalized perturbation strength and the set of samples from the probability distribution generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as when giving the broadest interpretation in the light of the specification, the determining the perturbation parameter is a product of the array of random directions and the normalized perturbation strength, which is a mathematical calculation, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 5:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 4 which included an abstract idea (see rejection claim 4). Additionally, claim 5 recites the abstract ideas:
determining the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution generated by the quantum processor comprises: determining the normalized perturbation strength based on the initial perturbation strength and a current perturbation strength decay: - This limitation recites the abstract idea of mathematical concepts, as when giving the broadest interpretation in the light of the specification, determining the normalized perturbation strength is the quotient of the initial perturbation strength and the current value of the timestep counter t experiencing exponential decay at a rate, which is a mathematical calculation, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
initializing the set of parameters comprises receiving an initial perturbation strength: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
initializing the set of parameters comprises receiving an initial perturbation strength: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 6:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 1 which included an abstract idea (see rejection claim 1).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein, prior to receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor, the method comprises: instructing the quantum processor to generate the set of samples from the probability distribution: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein, prior to receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor, the method comprises: instructing the quantum processor to generate the set of samples from the probability distribution: - This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 7:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 6 which included an abstract idea (see rejection claim 6).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
the quantum processor comprises a plurality of qubits: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f));
instructing the quantum processor to generate the set of samples from the probability distribution comprises: programming the quantum processor to have the probability distribution over the plurality of qubits, and instructing the quantum processor to perform quantum evolution using the plurality of qubits: - This limitation recites the use of performing quantum evolution using the plurality of qubits for the purpose of instructing the quantum processor, therefore, this limitation merely indicates a field of use or technological environment such as programming the quantum processor. Therefore, it fails to integrate the judicial exception into a practical application (see MPEP 2106.05(h));
receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
the quantum processor comprises a plurality of qubits: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f));
instructing the quantum processor to generate the set of samples from the probability distribution comprises: programming the quantum processor to have the probability distribution over the plurality of qubits, and instructing the quantum processor to perform quantum evolution using the plurality of qubits: - This limitation recites the use of performing quantum evolution using the plurality of qubits for the purpose of instructing the quantum processor, therefore, this limitation merely indicates a field of use or technological environment such as programming the quantum processor. Therefore, it fails to amount to significantly more than the judicial exception (see MPEP 2106.05(h));
receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 8:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 1 which included an abstract idea (see rejection claim 1).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 9:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim recites the abstract ideas:
generating, by the at least one digital processor, a training model associated with the machine learning model, the training model having an objective function: - This limitation recites the abstract idea of mathematical concepts, as when giving the broadest interpretation in the light of the specification, the training model associated with the machine learning model is the Boltzmann machine of the QBM described by a transverse Ising Hamiltonian, thus, generating the training model consists of mathematical calculations, therefore, this limitation amounts to mathematical concepts;
using the training model, by the at least one digital processor, to optimize the at least one optimizable parameter of the machine learning model, wherein using the training model includes estimation of a gradient of the objective function using a current value of the at least one optimizable parameter and a perturbation parameter based on the set of samples generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as the estimation of the gradient of the objective function consists of mathematical calculations, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
receiving, by the at least one digital processor, a training data set: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application;
initializing, by the at least one digital processor, training model parameters, the training model parameters including at least one optimizable parameter of the machine learning model: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g));
receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application;
returning, to the machine learning model, the training model with an optimized value of the at least one optimizable parameter: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
receiving, by the at least one digital processor, a training data set: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II);
initializing, by the at least one digital processor, training model parameters, the training model parameters including at least one optimizable parameter of the machine learning model: - This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii));
receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II);
returning, to the machine learning model, the training model with an optimized value of the at least one optimizable parameter: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 10:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9). Additionally, claim 10 recites the abstract ideas:
determining a first order moment and a second order moment using the gradient of the objective function that is estimated based on the set of samples from the probability distribution generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as when given the broadest reasonable interpretation in light of the specification, the determining of the first and second order moments are calculated using a gradient estimation technique requiring only two function evaluations, therefore, this limitation amounts to mathematical process;
determining an updated value of the at least one optimizable parameter of the training model based on the first order moment and the second order moment: - This claim is directed to a mathematical concept, as the process of determining the updated value is a step of “determining” a variable or number using mathematical method (see MPEP 2106.04(a)(2) subsection C);
evaluating the objective function using the updated value of the at least one optimizable parameter: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function consists of mathematical calculations, therefore, this limitation amounts to mathematical process.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein returning, to the machine learning model, the training model with the optimized value of the at least one optimizable parameter includes: returning the updated value of the at least one optimizable parameter once the objective function converges: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein returning, to the machine learning model, the training model with the optimized value of the at least one optimizable parameter includes: returning the updated value of the at least one optimizable parameter once the objective function converges: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 11:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9). Additionally, claim 11 recites the abstract ideas:
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a first direction to obtain a first objective function value: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function consists of mathematical calculations, therefore, this limitation amounts to mathematical process;
evaluating the objective function with the current value of the at least one optimizable parameter perturbed the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function consists of mathematical calculations, therefore, this limitation amounts to mathematical process;
determining a rate of change between the first and the second objective function values: - This claim is directed to a mathematical concept, as the process of determining a rate of change is a step of “determining” a variable or number using mathematical method (see MPEP 2106.04(a)(2) subsection C).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 12:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9). Additionally, claim 12 recites the abstract ideas:
determining a normalized perturbation strength, wherein the perturbation parameter is a product of the array of random directions and the normalized perturbation strength: - This limitation recites the abstract idea of mathematical concepts, as the process of determining the perturbation parameter is a product of the array of random directions and the normalized perturbation strength, thus, the determining the normalized perturbation strength consists of mathematical calculation, therefore, this limitation amounts to mathematical process.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
generating an array of random directions using the set of samples generated by the quantum processor as an array of random binary variables: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
generating an array of random directions using the set of samples generated by the quantum processor as an array of random binary variables: - This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 13:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9). Additionally, claim 13 recites the abstract ideas:
wherein generating the training model associated with the machine learning model includes: generating at least a training model associated with a generative machine learning model: - This limitation recites the abstract idea of mathematical concepts, as when giving the broadest interpretation in the light of the specification, the training model associated with the machine learning model is the Boltzmann machine of the QBM described by a transverse Ising Hamiltonian, thus, generating the training model consists of mathematical calculations, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 14:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein generating the training model comprises: generating a quantum Boltzmann machine: - This limitation recites the use of the training model for the purpose of generating a quantum Boltzmann machine, therefore, this limitation merely indicates a field of use or technological environment such as generating a quantum machine. Therefore, it fails to integrate the judicial exception into a practical application (see MPEP 2106.05(h));
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein generating the training model comprises: generating a quantum Boltzmann machine.: - - This limitation recites the use of the training model for the purpose of generating a quantum Boltzmann machine, therefore, this limitation merely indicates a field of use or technological environment such as generating a quantum machine. Therefore, it fails to amount to significantly more than the judicial exception (see MPEP 2106.05(h)).
Regarding Claim 15:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9). Additionally, claim 15 recites the abstract ideas:
generating the training model comprises generating a model described by a transverse Ising Hamiltonian, and the at least one optimizable parameter comprises at least one Hamiltonian parameter: - This limitation recites the abstract idea of mathematical concepts, as the transverse Ising Hamiltonian consists of mathematical calculations, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 16:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein the objective function is a loss function, and using the training model to optimize the at least one optimizable parameter of the machine learning model comprises: minimizing the loss function describing a difference between data belonging to the training data set and the set of samples generated by the quantum processor, and estimating a gradient of the objective function comprises estimating a gradient of the loss function: - This limitation does not integrate a judicial exception into a practical application as the training model is recited at a high level of generality, therefore this amounts to mere instructions to implement an abstract idea 2106.05(f).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein the objective function is a loss function, and using the training model to optimize the at least one optimizable parameter of the machine learning model comprises: minimizing the loss function describing a difference between data belonging to the training data set and the set of samples generated by the quantum processor, and estimating a gradient of the objective function comprises estimating a gradient of the loss function: - This limitation does not amount to significantly more than the judicial exception as the training model is recited at a high level of generality, therefore this amounts to mere instructions to implement an abstract idea 2106.05(f).
Regarding Claim 17:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein prior to receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor, the method comprises: instructing the quantum processor to generate the set of samples from the probability distribution: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein prior to receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor, the method comprises: instructing the quantum processor to generate the set of samples from the probability distribution: This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 18:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 17 which included an abstract idea (see rejection claim 17).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
the quantum processor comprises a plurality of qubits: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f));
instructing the quantum processor to generate the set of samples from the probability distribution comprises: programming the quantum processor to have the probability distribution over the plurality of qubits, and instructing the quantum processor to perform quantum evolution using the plurality of qubits: - This limitation recites the use of performing quantum evolution using the plurality of qubits for the purpose of instructing the quantum processor, therefore, this limitation merely indicates a field of use or technological environment such as programming the quantum processor. Therefore, it fails to integrate the judicial exception into a practical application (see MPEP 2106.05(h));
receiving, by the at least one digital processor, the set of samples having the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application;
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
the quantum processor comprises a plurality of qubits: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f));
instructing the quantum processor to generate the set of samples from the probability distribution comprises: programming the quantum processor to have the probability distribution over the plurality of qubits, and instructing the quantum processor to perform quantum evolution using the plurality of qubits: - This limitation recites the use of performing quantum evolution using the plurality of qubits for the purpose of instructing the quantum processor, therefore, this limitation merely indicates a field of use or technological environment such as programming the quantum processor. Therefore, it fails to amount to significantly more than the judicial exception (see MPEP 2106.05(h));
receiving, by the at least one digital processor, the set of samples having the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 19:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving, from the quantum processor, samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving, from the quantum processor, samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound: This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 20:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 9 which included an abstract idea (see rejection claim 9).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving samples obtained in a coherent regime when the quantum processor exhibits non-equilibrium dynamics: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving samples obtained in a coherent regime when the quantum processor exhibits non-equilibrium dynamics: This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II).
Regarding Claim 21:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a non-transitory processor-readable medium.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim recites the abstract ideas:
estimate, by the at least one digital processor, a gradient of the objective function based on a current value of the at least one optimizable parameter and the set of samples from the probability distribution generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as the process of estimating the gradient of the objective function consists of mathematical calculations, therefore, this limitation amounts to mathematical process;
determine, by the at least one digital processor, first and second order moments based on the estimated gradient: - This limitation recites the abstract idea of mathematical concepts, as when given the broadest reasonable interpretation in light of the specification, the determining of the first and second order moments are calculated using a gradient estimation technique requiring only two function evaluations, therefore, this limitation amounts to mathematical process.
evaluate, by the at least one digital processor, the objective function using updated values of the one or more optimizable parameters: - This limitation is directed to the abstract idea of a mental process, as the process of evaluating the objective function using updated values of the optimizable parameters is a thought process that can be performed in a human mind by observing and judging (concepts performed in the human mind (including an observation, evaluation, judgment, opinion) (see MPEP § 2106.04(a)(2), subsection III)).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
initialize a set of parameters, including one or more optimizable parameters and an objective function: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g));
until the objective function converges: - This limitation is simply manipulating data on iterative manner which does not impose a meaningful limit on the claim, being insignificant as extra solution activity;
receive, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor,: - This limitation is directed to mere data gathering and outputting. The courts (as per Ultramercial, 772 F.3d at 715, 112 USPQ2d at 1754) have recognized mere data gathering and outputting as insignificant extra-solution activity (see MPEP 2106.05(g)(3)) and therefore fails to integrate the exception into a practical application;
update, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments: - This limitation invokes the digital processor merely as a tool for performing an abstract idea (see MPEP 2106.05(f)) and therefore fails to integrate the exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
initialize a set of parameters, including one or more optimizable parameters and an objective function: - This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii));
until the objective function converges: - This limitation is directed to performing repetitive calculations (see MPEP 2106.05(d)(II)(ii)), therefore, fails to amount to significantly more than the judicial exception;
receive, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor: - This limitation is directed to receiving or transmitting data over a network. The courts (as per Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362) have recognized receiving or transmitting data over a network as well-understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) (see MPEP 2106.05(d) II);
update, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments: - This limitation invokes the digital processor merely as a tool for performing an abstract idea (see MPEP 2106.05(f)) and therefore fails to amount to significantly more than the judicial exception.
Regarding Claim 22:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein the quantum processor comprises a plurality of qubits: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein the quantum processor comprises a plurality of qubits: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f)).
Regarding Claim 23:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 22 which included an abstract idea (see rejection claim 22).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein each sample of the set of samples is a set of states of the plurality of qubits of the quantum processor: - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein each sample of the set of samples is a set of states of the plurality of qubits of the quantum processor: This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 24:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein the quantum processor is a quantum annealer or an adiabatic quantum processor: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein the quantum processor is a quantum annealer or an adiabatic quantum processor: - These generic computer components are recited at a high level of generality such that it amounts no more than mere instructions to apply the judicial exception using a computer (see MPEP 2106.05(f)).
Regarding Claim 25:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21). Additionally, claim 25 recites the abstract ideas:
wherein, the gradient is based on the current value of the at least one optimizable parameter and an array of random directions, wherein the array of random directions is based on the set of samples generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as the process of estimating the gradient is done using mathematical calculations, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 26:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21). Additionally, claim 26 recites the abstract ideas:
the gradient is based on a rate of change between a first objective function value and a second objective function value: - This claim is directed to a mathematical concept, as the process of determining a rate of change is a step of “determining” a variable or number using mathematical method (see MPEP 2106.04(a)(2) subsection C);
the first objective function value is an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function is done using mathematical calculations, therefore, this limitation amounts to mathematical concepts;
the second objective function value is an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction: - This limitation recites the abstract idea of mathematical concepts, as the process of evaluating the objective function is done using mathematical calculations, therefore, this limitation amounts to mathematical concepts;
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 27:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 26 which included an abstract idea (see rejection claim 26). Additionally, claim 27 recites the abstract ideas:
wherein the perturbation parameter is based on a normalized perturbation strength and the set of samples generated by the quantum processor: - This limitation recites the abstract idea of mathematical concepts, as when giving the broadest interpretation in the light of the specification, the perturbation parameter is a product of the array of random directions and the normalized perturbation strength, which is a mathematical calculation, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 28:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 27 which included an abstract idea (see rejection claim 27). Additionally, claim 28 recites the abstract ideas:
wherein the normalized perturbation strength is based on a perturbation strength and a current perturbation strength decay: - This limitation recites the abstract idea of mathematical concepts, as when giving the broadest interpretation in the light of the specification, determining the normalized perturbation strength is the quotient of the initial perturbation strength and the current value of the timestep counter t experiencing exponential decay at a rate, which is a mathematical calculation, therefore, this limitation amounts to mathematical concepts.
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 29:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein the set of samples generated by the quantum processor are samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound: - - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein the set of samples generated by the quantum processor are samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound: This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 30:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein the set of samples generated by the quantum processor are samples obtained when the quantum processor exhibits non-equilibrium dynamics in a coherent regime: - - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein the set of samples generated by the quantum processor are samples obtained when the quantum processor exhibits non-equilibrium dynamics in a coherent regime: This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding Claim 31:
Step 1 - Is the claim directed to a process, a machine, manufacture or composition of matter? - Yes, the claim is directed to a process.
Step 2A - Prong 1 - Does the claim recite an abstract idea, law of nature, or natural phenomenon? - Yes, the claim is dependent on claim 21 which included an abstract idea (see rejection claim 21).
Step 2A - Prong 2 - Does the claim recite additional elements that integrate the judicial exception into a practical application? - No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
wherein prior to receipt of the set of samples from the quantum processor, the at least one digital processor is to instruct the quantum processor to generate the set of samples from the probability distribution: - - This limitation is directed to selection of a particular data source or type of data to be manipulated as it is merely adding data, being insignificant extra-solution activity (see MEPEP n2106.05(g)).
Step 2B - Does the claim recite additional elements that amount to significantly more than the judicial exception? - No, there are no additional elements that amount to significantly more than the judicial exception. The additional elements:
wherein prior to receipt of the set of samples from the quantum processor, the at least one digital processor is to instruct the quantum processor to generate the set of samples from the probability distribution: This limitation is analogous to electronic recordkeeping because it’s adding data to the training set and keeping record of it (see MPEP 2106.05(d) II (iii)).
Regarding independent Claim 32, this claim is directed to a non-transitory processor-readable medium and is rejected on the same basis as independent claim 9 since they are analogous claims.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
This application currently names joint inventors. In considering patentability of the claims the examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the examiner to consider the applicability of 35 U.S.C. 102(b)(2)(C) for any potential 35 U.S.C. 102(a)(2) prior art against the later invention.
Claims 1, 6 are rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang).
Referring to Claim 1, Wiebe teaches:
initializing, by the at least one digital processor, a set of parameters including the one or more optimizable parameters and an objective function (see Wiebe at Cl. 15 Ln. 64-67 and Cl. 16 Ln. 1-14: “With reference to FIG. 2, a method 200 of training a Boltzmann machine includes providing training data and initializing at 202. At 204, a gradient of an objective function is determined with a quantum computer, and at 206, gradient ascent is used to refine the Boltzmann machine. If a local optimum is reached as determined at 208, an optimized Boltzmann machine specification is returned at 210. Otherwise, additional quantum processing is executed at 204. A method 300 of gradient calculation is illustrated in FIG. 3. At 302, training data and an initial Boltzmann machine specification (such as numbers of layers, and numbers of units in each layer) are provided. At 304, a quantum-based sampling algorithm (such as that of Table 1 or Table 2 for example) is carried out for the selected model and data expectation using a training vector. At 306, visible unit and hidden unit values (vi,hj) are determined for each edge specified by (i,j) for a model average and a data average. At 308, the result vectors are subtracted, and the result returned”. Examiner interpreted the combination of the following passages: providing data set and initializing; determining the gradient of the objective function; providing the initial Boltzmann machine specification such as numbers of layers, and numbers of units in each layer; to be equivalent as the claimed “initializing, by the at least one digital processor, a set of parameters including the one or more optimizable parameters and an objective function”);
until the objective function converges (see Wiebe at Cl. 15 Ln. 64-67 and Cl. 16 Ln. 1-14: “With reference to FIG. 2, a method 200 of training a Boltzmann machine includes providing training data and initializing at 202. At 204, a gradient of an objective function is determined with a quantum computer, and at 206, gradient ascent is used to refine the Boltzmann machine. If a local optimum is reached as determined at 208, an optimized Boltzmann machine specification is returned at 210. Otherwise, additional quantum processing is executed at 204. A method 300 of gradient calculation is illustrated in FIG. 3. At 302, training data and an initial Boltzmann machine specification (such as numbers of layers, and numbers of units in each layer) are provided. At 304, a quantum-based sampling algorithm (such as that of Table 1 or Table 2 for example) is carried out for the selected model and data expectation using a training vector. At 306, visible unit and hidden unit values (vi,hj) are determined for each edge specified by (i,j) for a model average and a data average. At 308, the result vectors are subtracted, and the result returned”. Examiner interprets the local optimum being reached to be equivalent as the claimed “until the objective function converges”);
receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor (see Wiebe at Cl. 6 Ln. 18-39: “Quantum computers can draw unbiased samples from the Gibbs distribution, thereby allowing probabilities to be computed by sampling (or by quantum sampling). As disclosed herein, a quantum distribution is prepared that approximates the ideal probability distribution over the model or data. This approximate distribution is then refined by rejection sampling into a quantum distribution that is, to within numerical error, the target probability distribution. Layer by layer training is unnecessary, and approximations required in conventional methods can be avoided. Beginning with a uniform prior over the amplitudes of the Gibbs state, preparing the state via quantum rejection sampling is likely to be inefficient. This is because the success probability depends on a ratio of the partition functions of the initial state and the Gibbs state which is generally exponentially small for machine learning problems. In some examples, a mean-field approximation is used over the joint probabilities in the Gibbs state, rather than a uniform prior. This additional information can be used to boost the probability of success to acceptable levels for numerically tractable examples”. Examiner interprets the quantum computers can draw unbiased samples from the Gibbs distribution, thereby allowing probabilities to be computed by sampling; to be equivalent as the claimed “receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor”);
estimating, by the at least one digital processor, a gradient of the objective function based on a current value of the at least one optimizable parameter and the set of samples from the probability distribution generated by the quantum processor (see Wiebe at Cl. 15 Ln. 64-67 and Cl. 16 Ln. 1-14: “With reference to FIG. 2, a method 200 of training a Boltzmann machine includes providing training data and initializing at 202. At 204, a gradient of an objective function is determined with a quantum computer, and at 206, gradient ascent is used to refine the Boltzmann machine. If a local optimum is reached as determined at 208, an optimized Boltzmann machine specification is returned at 210. Otherwise, additional quantum processing is executed at 204. A method 300 of gradient calculation is illustrated in FIG. 3. At 302, training data and an initial Boltzmann machine specification (such as numbers of layers, and numbers of units in each layer) are provided. At 304, a quantum-based sampling algorithm (such as that of Table 1 or Table 2 for example) is carried out for the selected model and data expectation using a training vector. At 306, visible unit and hidden unit values (vi,hj) are determined for each edge specified by (i,j) for a model average and a data average. At 308, the result vectors are subtracted, and the result returned”. Examiner interprets the initial Boltzmann machine specification; the quantum-based sampling algorithm being carried out; the gradient of the objective function being determined and the result vectors being extracted; to be equivalent as the claimed “based on a current value of the at least one optimizable parameter”, “the set of samples from the probability distribution generated by the quantum processor” and “estimating a gradient of the objective function” respectively).
However, Wiebe fails to teach:
determining, by the at least one digital processor, first and second order moments based on the estimated gradient;
updating, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments;
evaluating, by the at least one digital processor, the objective function using updated values of the one or more optimizable parameters;
Huang teaches, in analogous system,
determining, by the at least one digital processor, first and second order moments based on the estimated gradient (see Huang at Page 2: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value”. Examiner interprets estimating the first-order moment and second-order moment of each parameter gradient according to the loss function to be equivalent as the claimed “determining, by the at least one digital processor, first and second order moments based on the estimated gradient”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe with the above teachings of Huang by estimating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe, and to determine the first and second order moments based on the estimated gradient, as taught by Huang. The modification would have been obvious because one of ordinary skill in the art would be motivated to use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the model (as suggested by Huang at Page 2: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value”).
updating, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments (see Huang at Page 2: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value”. Examiner interprets continuously update the weight of the neural network model and the first and second moments being calculated to be equivalent as the claimed “updating, by the at least one digital processor, the one or more optimizable parameters based on the first and the second order moments”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe with the above teachings of Huang by estimating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe, and to update the optimizable parameters based on the first and the second order moments, as taught by Huang. The modification would have been obvious because one of ordinary skill in the art would be motivated to use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the model (as suggested by Huang at Page 2: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value”).
evaluating, by the at least one digital processor, the objective function using updated values of the one or more optimizable parameters (see Huang at Page 2: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value”. Examiner interprets determining the distance moved in the opposite direction of the gradient each time, and continuously updating the weight of the neural network model until the loss function (interpreted as objective function) tends to a stable value, to be equivalent as the claimed “evaluating, by the at least one digital processor, the objective function using updated values of the one or more optimizable parameters”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe with the above teachings of Huang by estimating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe, and to evaluate objective function using updated values of the optimizable parameters, as taught by Huang. The modification would have been obvious because one of ordinary skill in the art would be motivated to use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the model (as suggested by Huang at Page 2: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value”).
Referring to Claim 6, Wiebe – Huang teaches the method of claim 1, Wiebe further teaches:
wherein, prior to receiving, by the at least one digital processor, a set of samples from a probability distribution generated by the quantum processor, the method comprises: instructing the quantum processor to generate the set of samples from the probability distribution (see Wiebe at Cl. 3 Ln. 40-53: “The methods and apparatus described herein generally use a classical computer coupled to a quantum computer to train a deep Boltzmann machine. In order for the classical computer to update a model for the deep Boltzmann machine given training data, certain expectation values are computed. A quantum computer is arranged to accelerate this process. In typical examples, a classically tractable approximation to the state provided by a mean field approximation, or a related approximation, is used to prepare a quantum state that is close to the distribution that yields the desired expectation values. The quantum computer is then used to efficiently refine this approximation into precisely the desired distribution. The required expectation values are then learned by sampling from this quantum distribution”. Examiner interprets the required expectation values being learned by sampling from this quantum distribution; to be equivalent as the claimed “instructing the quantum processor to generate the set of samples from the probability distribution”).
Claims 2-3 are rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Liu et al. (US-20200279155-A1- hereinafter Liu).
Referring to Claim 2, Wiebe – Huang teaches the method of claim 1.
However, Wiebe – Huang fails to teach:
generating an array of random directions based on the set of samples generated from the probability distribution by the quantum processor;
estimating the gradient based on the current value of the at least one optimizable parameter and the array of random directions;
Liu teaches, in analogous system,
generating an array of random directions based on the set of samples generated from the probability distribution by the quantum processor (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3), where x=xk in Algorithm 1,
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|=bi{ui,j}j=1 q are independent and identically distributed (i.i.d.) random directions drawn from a uniform distribution over a unit sphere, and {circumflex over (∇)}ƒi(xiui,j) gives a conventional two-point based random gradient estimate with direction ui,j and smoothing parameter μ>0”. Examiner interprets q directional vectors ui,j being independently and identically drawn from a uniform distribution over a unit sphere to be equivalent as the claimed “generating an array of random directions based on the set of samples generated from the probability distribution”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to generate the array of random directions based on the set of samples generated from the probability distribution, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
estimating the gradient based on the current value of the at least one optimizable parameter and the array of random directions (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3), where x=xk in Algorithm 1,
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|=bi{ui,j}j=1 q are independent and identically distributed (i.i.d.) random directions drawn from a uniform distribution over a unit sphere, and {circumflex over (∇)}ƒi(xiui,j) gives a conventional two-point based random gradient estimate with direction ui,j and smoothing parameter μ>0”. Examiner interprets the gradient estimate being constructed through the forward difference of two function values; and the algorithm having only access to function values of {ƒi(x)} given a query point x (x interpreted as on the current value of the optimizable parameter); as well as q directional vectors ui,j being independently and identically drawn from a uniform distribution over a unit sphere; to be equivalent as the claimed “estimating the gradient based on the current value of the at least one optimizable parameter and the array of random directions”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to estimate the gradient based on the current value of the at least one optimizable parameter and the array of random directions, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
Referring to Claim 3, Wiebe – Huang teaches the method of claim 1.
However, Wiebe – Huang fails to teach:
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction to obtain a first objective function value;
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value;
determining a rate of change between the first and the second objective function values;
Liu teaches, in analogous system,
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction to obtain a first objective function value (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3):
∇
^
f
i
x
;
u
=
d
μ
f
i
x
+
μ
u
-
f
i
x
⋅
u
“. Examiner interprets fi(x;u) to be equivalent as the claimed “evaluating the objective function”; the given query point x is interpreted to be equivalent as the claimed “the current value of the at least one optimizable parameter”; μ is interpreted to be equivalent as the claimed “perturbation parameter”; u is interpreted as the first direction vector; fi(x + μu) is interpreted as the first objective function value).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to evaluate the objective function with the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction to obtain a first objective function value, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value (see Liu at Pg. 54: “Next, two variants of ZO-signSGD are shown, where the gradient will be estimated using the central difference of function values or the signs of ZO gradient estimates with majority vote. That is:
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“. Examiner interprets the central difference of function values as perturbing the parameter in two opposing directions; x is interpreted to be equivalent as the claimed “the current value of the at least one optimizable parameter”; +μui,j is interpreted as perturbation parameter perturbing the vector in the first direction; -μui,j is interpreted as perturbation parameter perturbing the vector in the opposite second direction; fi(x + μui,j) is interpreted as the first objective function; fi(x - μui,j) is interpreted as the second objective function).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to evaluate the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
determining a rate of change between the first and the second objective function values (see Liu at Pg. 54: “see Liu at Pg. 54: “Next, two variants of ZO-signSGD are shown, where the gradient will be estimated using the central difference of function values or the signs of ZO gradient estimates with majority vote. That is:
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“. Examiner interprets the quotient obtained when the result of subtracting the two objective functions is divided by (2μ):
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to be equivalent as the claimed “determining a rate of change between the first and the second objective function values”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to determine the rate of change between the first and the second objective function values, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
Claims 4 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Liu et al. (US-20200279155-A1- hereinafter Liu) and in further view of Brendel et al. (NPL: “Decision-based adversarial attacks: reliable attacks against black-box machine learning models” - hereinafter Brendel).
Referring to Claim 4, Wiebe – Huang - Liu teaches the method of claim 3.
However, Wiebe – Huang – Liu fails to teach:
wherein evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter comprises: determining the perturbation parameter based on a normalized perturbation strength and the set of samples from the probability distribution generated by the quantum processor;
Brendel teaches, in analogous system,
wherein evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter comprises: determining the perturbation parameter based on a normalized perturbation strength and the set of samples from the probability distribution generated by the quantum processor (see Brendel at Page 4: “The efficiency of the algorithm crucially depends on the proposal distribution P, i.e. which random directions are explored in each step of the algorithm. The optimal proposal distribution will generally depend on the domain and / or model to be attacked, but for all vision-related problems tested here a very simple proposal distribution worked surprisingly well. The basic idea behind this proposal distribution is as follows: in the k-th step we want to draw perturbations ηk from a maximum entropy distribution subject to the following constraints:
1. The perturbed sample lies within the input domain,
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2. The perturbation has a relative size of δ,
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3. The perturbation reduces the distance of the perturbed image towards the original input by a relative amount
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“. Examiner interprets the perturbation vector ηk at step k to be equivalent as the claimed “perturbation parameter”, the perturbation δ having a relative size is interpreted to be equivalent as the claimed “normalized perturbation strength”, drawing perturbations ηk from a maximum entropy distribution is interpreted as based on the set of samples from the probability distribution).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe, Huang and Liu with the above teachings of Brendel by estimating, updating and evaluating the gradient of the objective function and determining the rate of change between the first and the second objective function values, as taught by Wiebe, Huang and Liu, and to determine the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution, as taught by Brendel. The modification would have been obvious because one of ordinary skill in the art would be motivated to reduce the distance of the perturbed image towards the original input (as suggested by Brendel at Page 4: “3. The perturbation reduces the distance of the perturbed image towards the original input by a relative amount
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”).
Claims 5 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Liu et al. (US-20200279155-A1- hereinafter Liu) and in further view of Brendel et al. (NPL: “Decision-based adversarial attacks: reliable attacks against black-box machine learning models” - hereinafter Brendel) and in further view of Baumann et al. (NPL: “Estimation of the maximal Lyapunov exponent of nonsmooth systems using chaos synchronization” - hereinafter Baumann).
Referring to Claim 5, Wiebe – Huang – Liu - Brendel teaches the method of claim 4.
However, Wiebe – Huang – Liu – Brendel fails to teach:
initializing the set of parameters comprises receiving an initial perturbation strength;
determining the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution generated by the quantum processor comprises: determining the normalized perturbation strength based on the initial perturbation strength and a current perturbation strength decay;
Baumann teaches, in analogous system,
initializing the set of parameters comprises receiving an initial perturbation strength (see Baumann at Page 2: “The dynamics of a smooth system is given by
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where the vector field
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→ℝ𝑛 is continuously differentiable in its first argument and continuous in its second argument. We denote the solution of (1) for the initial conditions
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) obtained using the perturbed initial conditions
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𝒆 with
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‖
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= 1 and
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>0 small. The dynamics of the perturbation
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Δ
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) is obtained as”. Examiner interprets the perturbed initial conditions
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𝒆 to be equivalent as the claimed “initializing the set of parameters comprises receiving an initial perturbation strength”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe, Huang, Liu and Brendel with the above teachings of Baumann by estimating, updating and evaluating the gradient of the objective function and determining the rate of change as well as determining the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution, as taught by Wiebe, Huang, Liu and Brendel, and to initialize the set of parameters comprises receiving an initial perturbation strength, as taught by Baumann. The modification would have been obvious because one of ordinary skill in the art would be motivated to capture the sensitivity of solutions with respect to initial conditions (as suggested by Baumann at Page 1: “The spectrum of Lyapunov exponents is an important characteristic of limit sets. It measures the exponential convergence or divergence of nearby trajectories, thereby capturing the sensitivity of solutions with respect to initial conditions. An infinitesimal sphere of perturbed initial conditions will deform into an ellipsoid under the flow of a smooth dynamical system. The Lyapunov exponents capture the average exponential growth or decay rate of the principal axes of the ellipsoid and the maximal Lyapunov exponent captures the long-term behavior of the dominating direction. For example, an attractive limit cycle has only negative Lyapunov exponents (except possibly one at zero corresponding to the freedom of phase [20]). A positive maximal Lyapunov exponent implies instability of the limit set (i.e., equilibrium, limit cycle, periodic or quasi-periodic solution) or it can be an indication for a chaotic attractor”).
determining the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution generated by the quantum processor comprises: determining the normalized perturbation strength based on the initial perturbation strength and a current perturbation strength decay (see Baumann at Page 3: “The error
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z is of the order of the initial error z0, which itself is proportional to 𝜅. Analogously to the normalized perturbation 𝝃, we define the normalized synchronization error as
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∶
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= lim𝜅→0
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𝒛/𝜅. Taking the limit
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→
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0 of (7), divided by 𝜅, and using
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) yields d𝜻/d𝑡=𝑨(𝑡)𝜻−𝑘𝜻.(8). By comparing (3) and (8), we find that 𝜻=𝜱(𝑡,𝑡0)𝑒−𝑘(𝑡−𝑡0)𝒆=𝝃𝑒−𝑘(𝑡−𝑡0). (9)”. Examiner interprets the normalized synchronization error 𝜻 to be equivalent as the claimed “the normalized perturbation strength”, the term 𝒆 is interpreted to be equivalent as the claimed “initial perturbation strength”, 𝝃 = 𝜱(𝑡,𝑡0)𝒆 is interpreted to be equivalent as the claimed “current perturbation strength”, the term 𝑒−𝑘(𝑡−𝑡0) is interpreted as the decaying factor).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe, Huang, Liu and Brendel with the above teachings of Baumann by estimating, updating and evaluating the gradient of the objective function and determining the rate of change as well as determining the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution, as taught by Wiebe, Huang, Liu and Brendel, and to determine the normalized perturbation strength based on the initial perturbation strength and the current perturbation strength decay, as taught by Baumann. The modification would have been obvious because one of ordinary skill in the art would be motivated to capture the average exponential growth or decay rate (as suggested by Baumann at Page 1: “The spectrum of Lyapunov exponents is an important characteristic of limit sets. It measures the exponential convergence or divergence of nearby trajectories, thereby capturing the sensitivity of solutions with respect to initial conditions. An infinitesimal sphere of perturbed initial conditions will deform into an ellipsoid under the flow of a smooth dynamical system. The Lyapunov exponents capture the average exponential growth or decay rate of the principal axes of the ellipsoid and the maximal Lyapunov exponent captures the long-term behavior of the dominating direction. For example, an attractive limit cycle has only negative Lyapunov exponents (except possibly one at zero corresponding to the freedom of phase [20]). A positive maximal Lyapunov exponent implies instability of the limit set (i.e., equilibrium, limit cycle, periodic or quasi-periodic solution) or it can be an indication for a chaotic attractor”).
Claims 7 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Horii et al. (US-20210383267-A1- hereinafter Horii).
Referring to Claim 7, Wiebe – Huang teaches the method of claim 6, Wiebe further teaches:
the quantum processor comprises a plurality of qubits (see Wiebe at Cl. 16 Ln. 16-23: “Referring to FIG. 4, a method 400 of establishing and sampling a model average includes receiving a Boltzmann machine specification at 402 and computing a mean field approximation to a Gibbs state at 404. At 406, the mean-field values are used to prepare a mean-field state on qubits in a quantum computer and at 408, a qubit string is prepared that stores energy of each configuration (v,h)”. Examiner interprets preparing a mean-field state on qubits in a quantum computer to be equivalent as the claimed “the quantum processor comprises a plurality of qubits”);
instructing the quantum processor to generate the set of samples from the probability distribution comprises: programming the quantum processor to have the probability distribution over the plurality of qubits (see Wiebe at Cl. 6 Ln. 46-54: “Disclosed below are methods by which an initial quantum distribution is refined into a quantum coherent Gibbs state (often called a coherent thermal state or CTS). Mean-field approaches or generalizations thereof can be used to provide suitable initial states for the quantum computer to refine into the CTS. All units are assumed to be binary-valued in the following examples, but other units (such as Gaussian units) can be approximated within this framework by forming a single unit out of a string of several qubits”. Examiner interprets providing suitable initial states for the quantum computer to refine into the CTS to be equivalent as the claimed “programming the quantum processor”; initial quantum distribution being refined into a quantum coherent Gibbs state is interpreted to be equivalent as the claimed “to have the probability distribution”; forming a single unit out of a string of several qubits is interpreted to be equivalent as the claimed “over the plurality of qubits”).
However, Wiebe – Huang fails to teach:
instructing the quantum processor to generate the set of samples from the probability distribution comprises: instructing the quantum processor to perform quantum evolution using the plurality of qubits;
receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution;
Horii teaches, in analogous system,
instructing the quantum processor to generate the set of samples from the probability distribution comprises: instructing the quantum processor to perform quantum evolution using the plurality of qubits (see Horii at Pg. 54: “System 300 depicted in FIG. 3 can comprise an illustration of an example quantum system (e.g., a superconducting system) that can comprise a quantum circuit 302 (denoted as Circuit in FIG. 3). Quantum circuit 302 can comprise an algorithm (e.g., a quantum-based algorithm) that can comprise one or more operators 304 a, 304 b, and/or 304 c (denoted as Kraus 1, Kraus2, and Kraus3, respectively, in FIG. 3). Although operators 304 a, 304 b, 304 c are depicted in FIG. 3 as Kraus operators, it should be appreciated that such operators 304 a, 304 b, 304 c can comprise one or more other operators such as, for instance, conditional operators. When executed, operators 304 a, 304 b, 304 c can respectively yield a probability distribution and/or a quantum state associated with quantum circuit 302 and/or with one or more quantum bits (qubits) of quantum circuit 302. In the example embodiment illustrated in FIG. 3, execution of quantum circuit 302 and/or operators 304 a, 304 b, 304 c is depicted as one or more shots 306 a, 306 b, 306 c, 306 d, 306 e, and/or 306 n (denoted as shot1, shot2, shot3, shot4, shot5, and shotn, respectively, in FIG. 3, where n represents a total quantity of shots). As referenced herein, a shot can denote a single algorithm execution instance that can yield a probability range (also referred to herein as a probability distribution or a probability amplitude) associated with a result”. Examiner interprets executing operators respectively yield the probability distribution and/or the quantum state associated with quantum circuit and/or with one or more quantum bits (qubits) of quantum circuit; to be equivalent as the claimed “instructing the quantum processor to perform quantum evolution using the plurality of qubits”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Horii by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to instruct the quantum processor to perform quantum evolution using the plurality of qubits, as taught by Horii. The modification would have been obvious because one of ordinary skill in the art would be motivated to facilitate sampling of an operator in a quantum system (as suggested by Horii at Pg. 53: “FIGS. 3-9 illustrate block diagrams of example, non-limiting systems 300, 400, 500, 600, 700, 800, and 900, respectively, that can facilitate sampling of an operator in a quantum system in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity”).
receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution (see Horii at Pg. 54: “System 300 depicted in FIG. 3 can comprise an illustration of an example quantum system (e.g., a superconducting system) that can comprise a quantum circuit 302 (denoted as Circuit in FIG. 3). Quantum circuit 302 can comprise an algorithm (e.g., a quantum-based algorithm) that can comprise one or more operators 304 a, 304 b, and/or 304 c (denoted as Kraus 1, Kraus2, and Kraus3, respectively, in FIG. 3). Although operators 304 a, 304 b, 304 c are depicted in FIG. 3 as Kraus operators, it should be appreciated that such operators 304 a, 304 b, 304 c can comprise one or more other operators such as, for instance, conditional operators. When executed, operators 304 a, 304 b, 304 c can respectively yield a probability distribution and/or a quantum state associated with quantum circuit 302 and/or with one or more quantum bits (qubits) of quantum circuit 302. In the example embodiment illustrated in FIG. 3, execution of quantum circuit 302 and/or operators 304 a, 304 b, 304 c is depicted as one or more shots 306 a, 306 b, 306 c, 306 d, 306 e, and/or 306 n (denoted as shot1, shot2, shot3, shot4, shot5, and shotn, respectively, in FIG. 3, where n represents a total quantity of shots). As referenced herein, a shot can denote a single algorithm execution instance that can yield a probability range (also referred to herein as a probability distribution or a probability amplitude) associated with a result”. Examiner interprets the combination of the following passages: quantum system executing quantum circuit which comprises operators (executing quantum circuit and operators is interpreted as quantum evolution); executing operators respectively yield the probability distribution and/or the quantum state associated with quantum circuit and/or with one or more quantum bits (qubits) of quantum circuit; execution of quantum circuit and/or operators is depicted as one or more shots (interpreted as samples); to be equivalent as the claimed “receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Horii by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to receive a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution, as taught by Horii. The modification would have been obvious because one of ordinary skill in the art would be motivated to facilitate sampling of an operator in a quantum system (as suggested by Horii at Pg. 53: “FIGS. 3-9 illustrate block diagrams of example, non-limiting systems 300, 400, 500, 600, 700, 800, and 900, respectively, that can facilitate sampling of an operator in a quantum system in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity”).
Claims 8 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang).
Referring to Claim 8, Wiebe – Huang teaches the method of claim 1.
However, Wiebe – Huang fails to teach:
wherein receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound;
Wang teaches, in analogous system,
wherein receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor comprises: receiving a set of samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound (see Wang at Page 2: “A good choice for ∆ni is the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5. Other choices are possible too, but note that the uniform and normal distributions cannot be used because they do not satisfy the finite inverse moment conditions”. Examiner interprets choosing ∆ni as the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5 and ∆ni satisfying the finite inverse moment conditions; to be equivalent as the claimed “receiving a set of samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Wang by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and to receive a set of samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound, as taught by Wang. The modification would have been obvious because one of ordinary skill in the art would be motivated to satisfy the finite inverse moment conditions (as suggested by Wang at Pg. 2: “A good choice for ∆ni is the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5. Other choices are possible too, but note that the uniform and normal distributions cannot be used because they do not satisfy the finite inverse moment conditions”).
Claims 9, 13-14, 17, 19, 32 are rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang).
Referring to Claim 9, Wiebe teaches:
receiving, by the at least one digital processor, a training data set (see Wiebe at Cl. 3 Ln. 61-67 and Cl. 4 Ln. 1-4: “The Boltzmann machine is a powerful paradigm for machine learning in which the problem of training a system to classify or generate examples of a set of training vectors is reduced to the problem of energy minimization of a spin system. The Boltzmann machine consists of several binary units that are split into two categories: (a) visible units and (b) hidden units. The visible units are the units in which the inputs and outputs of the machine are given. For example, if a machine is used for classification, then the visible units will often be used to hold training data as well as a label for that training data”. Examiner interprets the visible units being used to hold training data to be equivalent as the claimed “receiving, by the at least one digital processor, a training data set”);
generating, by the at least one digital processor, a training model associated with the machine learning model, the training model having an objective function (see Wiebe at Cl. 4 Ln. 21-58: “Formally, the Boltzmann machine models the probability of a given configuration (v, h) of hidden and visible units via the Gibbs distribution:P(v,h)=e −E(v,h) /Z wherein Z is a normalizing factor known as the partition function, and v,h refer to visible and hidden unit values, respectively. The energy E of a given configuration of hidden and visible units is of the form:
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wherein vectors v and h are visible and hidden unit values, vectors b and d are biases that provide an energy penalty for a hit taking a value of 1 and wi,j is a weight that assigns an energy penalty for the hidden and visible units both taking on a value of 1. Training a Boltzmann machine reduces to estimating these biases and weights by maximizing the log-likelihood of the training data. A Boltzmann machine for which the biases and weights have been determined is referred to as a trained Boltzmann machine. A so-called L2-regularization term can be added in order to prevent overfitting, resulting in the following form of an objective function:
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This objective function is referred to as a maximum likelihood-objective (ML-objective) function and λ represents the regularization term. Gradient descent provides a method to find a locally optimal value of the ML-objective function”. Examiner interprets the Boltzmann machine to be equivalent as the claimed “the machine learning model”; when biases and weights have been determined it yielded the trained Boltzmann machine interpreted as the generated model; the resulting objective function is interpreted as the training model having an objective function);
initializing, by the at least one digital processor, training model parameters, the training model parameters including at least one optimizable parameter of the machine learning model (see Wiebe at Cl. 4 Ln. 21-58: “Formally, the Boltzmann machine models the probability of a given configuration (v, h) of hidden and visible units via the Gibbs distribution:P(v,h)=e −E(v,h) /Z wherein Z is a normalizing factor known as the partition function, and v,h refer to visible and hidden unit values, respectively. The energy E of a given configuration of hidden and visible units is of the form:
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wherein vectors v and h are visible and hidden unit values, vectors b and d are biases that provide an energy penalty for a hit taking a value of 1 and wi,j is a weight that assigns an energy penalty for the hidden and visible units both taking on a value of 1. Training a Boltzmann machine reduces to estimating these biases and weights by maximizing the log-likelihood of the training data. A Boltzmann machine for which the biases and weights have been determined is referred to as a trained Boltzmann machine. A so-called L2-regularization term can be added in order to prevent overfitting, resulting in the following form of an objective function:
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This objective function is referred to as a maximum likelihood-objective (ML-objective) function and λ represents the regularization term. Gradient descent provides a method to find a locally optimal value of the ML-objective function”. Examiner interprets the vectors b and d being biases and wi,j being a weight and all three taking the value of 1 to be equivalent as the claimed “initializing, by the at least one digital processor, training model parameters”; training a Boltzmann machine to estimate these biases and weights by maximizing the log-likelihood of the training data is interpreted to be equivalent as the claimed “the training model parameters including at least one optimizable parameter of the machine learning model”);
receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor (see Wiebe at Cl. 3 Ln. 40-53: “The methods and apparatus described herein generally use a classical computer coupled to a quantum computer to train a deep Boltzmann machine. In order for the classical computer to update a model for the deep Boltzmann machine given training data, certain expectation values are computed. A quantum computer is arranged to accelerate this process. In typical examples, a classically tractable approximation to the state provided by a mean field approximation, or a related approximation, is used to prepare a quantum state that is close to the distribution that yields the desired expectation values. The quantum computer is then used to efficiently refine this approximation into precisely the desired distribution. The required expectation values are then learned by sampling from this quantum distribution”. Examiner interprets the quantum computer being used to efficiently refine this approximation into precisely the desired distribution and the required expectation values being learned by sampling from this quantum distribution, to be equivalent as the claimed “receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor”);
returning, to the machine learning model, the training model with an optimized value of the at least one optimizable parameter (see Wiebe at Cl. 15 Ln. 64-67 and Cl. 16 Ln. 1-4: “With reference to FIG. 2, a method 200 of training a Boltzmann machine includes providing training data and initializing at 202. At 204, a gradient of an objective function is determined with a quantum computer, and at 206, gradient ascent is used to refine the Boltzmann machine. If a local optimum is reached as determined at 208, an optimized Boltzmann machine specification is returned at 210. Otherwise, additional quantum processing is executed at 204”. Examiner interprets the local optimum being reached and the optimized Boltzmann machine specification being returned as well as gradient ascent being used to refine the Boltzmann machine, to be equivalent as the claimed “returning, to the machine learning model, the training model with an optimized value of the at least one optimizable parameter”).
However, Wiebe fails to teach:
using the training model, by the at least one digital processor, to optimize the at least one optimizable parameter of the machine learning model, wherein using the training model includes estimation of a gradient of the objective function using a current value of the at least one optimizable parameter and a perturbation parameter based on the set of samples generated by the quantum processor;
Wang teaches, in analogous system,
using the training model, by the at least one digital processor, to optimize the at least one optimizable parameter of the machine learning model, wherein using the training model includes estimation of a gradient of the objective function using a current value of the at least one optimizable parameter and a perturbation parameter based on the set of samples generated by the quantum processor (see Wang at Page 2: “Let's denote the sample of
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) to be
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), and assume 𝜃 is a 𝑁-dimensional vector. We also denote the 𝑁-dimensional noisy gradient of
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). In KW algorithm, noisy gradient estimator
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𝜃
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) requires 2𝑁 noisy samples of 𝑓 with each dimension
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𝑔̂𝑖
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(
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) equals
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where 𝑒𝑖 is the unit vector with a 1 in the 𝑖th place, and 𝑐𝑛 is a small positive number that decreases with 𝑛. It is apparently that with the dimension 𝑁 of 𝜃 getting large, KW algorithmic type estimator of the noisy gradient of
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E
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(
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𝑓
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(
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)
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) is getting very inefficient. Simultaneous perturbation stochastic approximation method is achieved by introducing a perturbation vector Δ𝑛 and apply it on each dimension of
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𝑔̂
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(
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𝜃
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). In another words, on SPSA setting, 𝑔̂
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(
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𝜃
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)𝑖 equals
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Note that SPSA essentially apply one numerator on all the dimensions of the quotient estimator of
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𝑔̂
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(
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𝜃
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). Henceforth, KW estimator perturbs only one direction at a time, while the SPSA estimator disturbs all directions at the same time (the numerator is identical in all 𝑝 components). The number of loss function measurements needed in the SPSA method for each
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𝑔̂
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(
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𝜃
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) is always 2, independent of the dimension of theta 𝑁. Thus, SPSA uses 𝑁 times fewer function evaluations than KW estimator, which makes it a lot more efficient. A good choice for Δ𝑛𝑖 is the Rademacher distribution, i.e. Bernoulli ±1 with probability 0.5. Other choices are possible too, but note that the uniform and normal distributions cannot be used because they do not satisfy the finite inverse moment conditions. Since the SPSA gradient estimator can be proved to be an unbiased estimator of the gradient
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𝑔
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(
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), the SPSA optimization algorithm can be proved to be converging to the optimal point of the function
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E
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(
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𝑓
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(
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𝜃
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)
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) under certain differentiable conditions of
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E
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(
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𝑓
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(
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)
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). One example work of convergence proof of SPSA algorithm can be found in. Mayak and Chen [4] denotes
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𝐉
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(
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𝜃
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) as
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E
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(
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𝑓
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(
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)
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), it assume that
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𝐉
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(
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𝜃
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) is twice differentiable and individual elements of the third derivative must be bounded. Additionally,
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∇
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𝐉 must be Lipschitz continuous, bounded and the ODE
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𝜃̇
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= 𝑔
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(
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𝜃
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) must have a unique solution for each initial condition. Under these conditions and a few others, SPSA algorithm will converge in probability to the set of global minima of
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𝐉
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(
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)”. Examiner interprets the formula (3)
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to be equivalent as the claimed “estimation of a gradient of the objective function using a current value of the at least one optimizable parameter and a perturbation parameter based on the set of samples”; 𝑔̂
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(
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𝜃
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) is interpreted as the gradient of the objective function; 𝜃 is interpreted as the current value of the at least one optimizable parameter; 𝑐𝑛 and ∆n are interpreted as permutation parameters; 𝑓̂
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(θ + cn∆n) and 𝑓̂
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(θ + cn∆n) are interpreted as set of samples; 𝑓̂
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is interpreted as the objective function).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe with the above teachings of Wang by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters, as taught by Wiebe, and to estimate the gradient of the objective function using the current value of the optimizable parameter and the perturbation parameter based on the set of samples, as taught by Wang. The modification would have been obvious because one of ordinary skill in the art would be motivated to use N times fewer function evaluations and improve efficient (as suggested by Wang at Page 2: “Note that SPSA essentially apply one numerator on all the dimensions of the quotient estimator of
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𝑔̂
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(
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𝜃
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). Henceforth, KW estimator perturbs only one direction at a time, while the SPSA estimator disturbs all directions at the same time (the numerator is identical in all 𝑝 components). The number of loss function measurements needed in the SPSA method for each
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𝑔̂
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(
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𝜃
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) is always 2, independent of the dimension of theta 𝑁. Thus, SPSA uses 𝑁 times fewer function evaluations than KW estimator, which makes it a lot more efficient”).
Referring to Claim 13, Wiebe – Wang teaches the method of 9, Wiebe further teaches:
wherein generating the training model associated with the machine learning model includes: generating at least a training model associated with a generative machine learning model (see Wiebe at Cl. 4 Ln. 21-58: “Formally, the Boltzmann machine models the probability of a given configuration (v, h) of hidden and visible units via the Gibbs distribution:P(v,h)=e −E(v,h) /Z wherein Z is a normalizing factor known as the partition function, and v,h refer to visible and hidden unit values, respectively. The energy E of a given configuration of hidden and visible units is of the form:
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wherein vectors v and h are visible and hidden unit values, vectors b and d are biases that provide an energy penalty for a hit taking a value of 1 and wi,j is a weight that assigns an energy penalty for the hidden and visible units both taking on a value of 1. Training a Boltzmann machine reduces to estimating these biases and weights by maximizing the log-likelihood of the training data. A Boltzmann machine for which the biases and weights have been determined is referred to as a trained Boltzmann machine. A so-called L2-regularization term can be added in order to prevent overfitting, resulting in the following form of an objective function:
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This objective function is referred to as a maximum likelihood-objective (ML-objective) function and λ represents the regularization term. Gradient descent provides a method to find a locally optimal value of the ML-objective function”. Examiner interprets the Boltzmann machine to be equivalent as the claimed “the machine learning model”; when biases and weights have been determined it yielded the trained Boltzmann machine interpreted as the generated model).
Referring to Claim 14, Wiebe – Wang teaches the method of 9, Wiebe further teaches:
wherein generating the training model comprises: generating a quantum Boltzmann machine (see Wiebe at Cl. 4 Ln. 21-58: “Formally, the Boltzmann machine models the probability of a given configuration (v, h) of hidden and visible units via the Gibbs distribution:P(v,h)=e −E(v,h) /Z wherein Z is a normalizing factor known as the partition function, and v,h refer to visible and hidden unit values, respectively. The energy E of a given configuration of hidden and visible units is of the form:
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wherein vectors v and h are visible and hidden unit values, vectors b and d are biases that provide an energy penalty for a hit taking a value of 1 and wi,j is a weight that assigns an energy penalty for the hidden and visible units both taking on a value of 1. Training a Boltzmann machine reduces to estimating these biases and weights by maximizing the log-likelihood of the training data. A Boltzmann machine for which the biases and weights have been determined is referred to as a trained Boltzmann machine. A so-called L2-regularization term can be added in order to prevent overfitting, resulting in the following form of an objective function:
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This objective function is referred to as a maximum likelihood-objective (ML-objective) function and λ represents the regularization term. Gradient descent provides a method to find a locally optimal value of the ML-objective function”. Examiner interprets the yielded trained Boltzmann machine to be equivalent as the claimed “generating a quantum Boltzmann machine”).
Referring to Claim 17, Wiebe – Wang teaches the method of 9, Wiebe further teaches:
wherein prior to receiving, by the at least one digital processor, the set of samples from the probability distribution generated by the quantum processor, the method comprises: instructing the quantum processor to generate the set of samples from the probability distribution (see Wiebe at Cl. 3 Ln. 40-53: “The methods and apparatus described herein generally use a classical computer coupled to a quantum computer to train a deep Boltzmann machine. In order for the classical computer to update a model for the deep Boltzmann machine given training data, certain expectation values are computed. A quantum computer is arranged to accelerate this process. In typical examples, a classically tractable approximation to the state provided by a mean field approximation, or a related approximation, is used to prepare a quantum state that is close to the distribution that yields the desired expectation values. The quantum computer is then used to efficiently refine this approximation into precisely the desired distribution. The required expectation values are then learned by sampling from this quantum distribution”. Examiner interprets the required expectation values being learned by sampling from this quantum distribution; to be equivalent as the claimed “instructing the quantum processor to generate the set of samples from the probability distribution”).
Referring to Claim 19, Wiebe – Wang teaches the method of 9.
However, Wiebe – Wang fails to teach:
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving, from the quantum processor, samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound;
Wang teaches, in analogous system,
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving, from the quantum processor, samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound (see Wang at Page 2: “A good choice for ∆ni is the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5. Other choices are possible too, but note that the uniform and normal distributions cannot be used because they do not satisfy the finite inverse moment conditions”. Examiner interprets choosing ∆ni as the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5 and ∆ni satisfying the finite inverse moment conditions; to be equivalent as the claimed “receiving, from the quantum processor, samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe with the above teachings of Wang by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters, as taught by Wiebe, and to receive samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound, as taught by Wang. The modification would have been obvious because one of ordinary skill in the art would be motivated to use N times fewer function evaluations and improve efficient (as suggested by Wang at Page 2: “Note that SPSA essentially apply one numerator on all the dimensions of the quotient estimator of
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𝑔̂
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(
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𝜃
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). Henceforth, KW estimator perturbs only one direction at a time, while the SPSA estimator disturbs all directions at the same time (the numerator is identical in all 𝑝 components). The number of loss function measurements needed in the SPSA method for each
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𝑔̂
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(
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) is always 2, independent of the dimension of theta 𝑁. Thus, SPSA uses 𝑁 times fewer function evaluations than KW estimator, which makes it a lot more efficient”).
Referring to independent Claim 32, this claim is rejected on the same basis as independent claim 9 since they are analogous claims.
Claims 10 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang) and in further view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Liu et al. (US-20200279155-A1 - hereinafter Liu).
Referring to Claim 10, Wiebe – Wang teaches the method of claim 9, Wiebe further teaches:
wherein returning, to the machine learning model, the training model with the optimized value of the at least one optimizable parameter includes: returning the updated value of the at least one optimizable parameter once the objective function converges (see Wiebe at Cl. 15 Ln. 64-67 and Cl. 16 Ln. 1-4: “With reference to FIG. 2, a method 200 of training a Boltzmann machine includes providing training data and initializing at 202. At 204, a gradient of an objective function is determined with a quantum computer, and at 206, gradient ascent is used to refine the Boltzmann machine. If a local optimum is reached as determined at 208, an optimized Boltzmann machine specification is returned at 210. Otherwise, additional quantum processing is executed at 204”. Examiner interprets the local optimum being reached to be equivalent as the claimed “once the objective function converges”; the optimized Boltzmann machine specification being returned is interpreted as “returning the updated value of the at least one optimizable parameter”).
However, Wiebe – Wang fails to teach:
determining a first order moment and a second order moment using the gradient of the objective function that is estimated based on the set of samples from the probability distribution generated by the quantum processor;
determining an updated value of the at least one optimizable parameter of the training model based on the first order moment and the second order moment;
Huang teaches, in analogous system,
determining a first order moment and a second order moment using the gradient of the objective function that is estimated based on the set of samples from the probability distribution generated by the quantum processor (see Huang at Page 6: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value. The loss function uses the mean square error MSE to evaluate the model performance, and the number of samples taken in one training is set to 270”. Examiner interprets the estimate of the first-order moment and second-order moment of each parameter gradient according to the loss function, and the number of samples taken in one training is set to 270, to be equivalent as the claimed “determining a first order moment and a second order moment using the gradient of the objective function that is estimated based on the set of samples from the probability distribution”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Huang by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to determine the first order moment and the second order moment using the gradient of the objective function that is estimated based on the set of samples from the probability distribution, as taught by Huang. The modification would have been obvious because one of ordinary skill in the art would be motivated to adapt the moment estimation (as suggested by Huang at Page 6: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value. The loss function uses the mean square error MSE to evaluate the model performance, and the number of samples taken in one training is set to 270”);
determining an updated value of the at least one optimizable parameter of the training model based on the first order moment and the second order moment (see Huang at Page 6: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value. The loss function uses the mean square error MSE to evaluate the model performance, and the number of samples taken in one training is set to 270”. Examiner interprets continuously updating the weight of the neural network model and estimating the first-order moment and second-order moment of each parameter gradient according to the loss function; to be equivalent as the claimed “determining an updated value of the at least one optimizable parameter of the training model based on the first order moment and the second order moment”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Huang by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to determine the updated value of the optimizable parameter of the training model based on the first order moment and the second order moment, as taught by Huang. The modification would have been obvious because one of ordinary skill in the art would be motivated to adapt the moment estimation (as suggested by Huang at Page 6: “Step 6: Use the stochastic gradient optimization algorithm to adapt the moment estimation Adam and the error back propagation algorithm to train the TEC short-term forecast model, that is, train all samples in batches, and estimate the first-order moment and second-order moment of each parameter gradient according to the loss function. Estimate the learning rate and learning step size of the dynamically adjusted parameters, determine the distance moved in the opposite direction of the gradient each time, and continuously update the weight of the neural network model until the loss function tends to a stable value. The loss function uses the mean square error MSE to evaluate the model performance, and the number of samples taken in one training is set to 270”).
However, Wiebe – Wang fails to teach:
evaluating the objective function using the updated value of the at least one optimizable parameter;
Liu teaches, in analogous system,
evaluating the objective function using the updated value of the at least one optimizable parameter (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3):
∇
^
f
i
x
;
u
=
d
μ
f
i
x
+
μ
u
-
f
i
x
⋅
u
“. Examiner interprets fi(x;u) to be equivalent as the claimed “evaluating the objective function”; the given query point x is interpreted to be equivalent as the claimed “the updated value of the at least one optimizable parameter”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Liu by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to evaluate the objective function using the updated value of the at least one optimizable parameter, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
Claims 11 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang) and in further view of Liu et al. (US-20200279155-A1 - hereinafter Liu).
Referring to Claim 11, Wiebe – Wang teaches the method of claim 9.
However, Wiebe – Wang fails to teach:
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a first direction to obtain a first objective function value;
evaluating the objective function with the current value of the at least one optimizable parameter perturbed the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value;
determining a rate of change between the first and the second objective function values;
Liu teaches, in analogous system,
evaluating the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a first direction to obtain a first objective function value (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3):
∇
^
f
i
x
;
u
=
d
μ
f
i
x
+
μ
u
-
f
i
x
⋅
u
“. Examiner interprets fi(x;u) to be equivalent as the claimed “evaluating the objective function”; the given query point x is interpreted to be equivalent as the claimed “the current value of the at least one optimizable parameter”; μ is interpreted to be equivalent as the claimed “perturbation parameter”; u is interpreted as the first direction vector; fi(x + μu) is interpreted as the first objective function value).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Liu by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to evaluate the objective function with the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a first direction to obtain a first objective function value, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”);
evaluating the objective function with the current value of the at least one optimizable parameter perturbed the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value (see Liu at Pg. 54: “Next, two variants of ZO-signSGD are shown, where the gradient will be estimated using the central difference of function values or the signs of ZO gradient estimates with majority vote. That is:
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“. Examiner interprets the central difference of function values as perturbing the parameter in two opposing directions; x is interpreted to be equivalent as the claimed “the current value of the at least one optimizable parameter”; +μui,j is interpreted as perturbation parameter perturbing the vector in the first direction; -μui,j is interpreted as perturbation parameter perturbing the vector in the opposite second direction; fi(x + μui,j) is interpreted as the first objective function; fi(x - μui,j) is interpreted as the second objective function).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Liu by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to evaluate the objective function with the current value of the at least one optimizable parameter perturbed the perturbation parameter in a second direction that opposes the first direction to obtain a second objective function value, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”);
determining a rate of change between the first and the second objective function values (see Liu at Pg. 54: “see Liu at Pg. 54: “Next, two variants of ZO-signSGD are shown, where the gradient will be estimated using the central difference of function values or the signs of ZO gradient estimates with majority vote. That is:
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“. Examiner interprets the quotient obtained when the result of subtracting the two objective functions is divided by (2μ):
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to be equivalent as the claimed “determining a rate of change between the first and the second objective function values”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Liu by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to determine the rate of change between the first and the second objective function values, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
Claims 12 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang) and in further view of Redmond et al. (US-20220147314-A1 - hereinafter Redmond) and in further view of Baumann et al. (NPL: “Estimation of the maximal Lyapunov exponent of nonsmooth systems using chaos synchronization” - hereinafter Baumann) and in further view of Brendel et al. (NPL: “Decision-based adversarial attacks: reliable attacks against black-box machine learning models” - hereinafter Brendel).
Referring to Claim 12, Wiebe – Wang teaches the method of claim 9.
However, Wiebe – Wang fails to teach:
generating an array of random directions using the set of samples generated by the quantum processor as an array of random binary variables;
Redmond teaches, in analogous system,
generating an array of random directions using the set of samples generated by the quantum processor as an array of random binary variables (see Redmond at Pg. 249-252: “Note that in one embodiment, the QDA creates a reservoir of random binary numbers 0 and 1. The 0s and 1s are transformed to −1 and 1 range to give zero mean and balance to the noise. The random number may also be optionally scaled to avoid saturating small values, or zeroing the activation. activation=activation*(1+unitary noise*scaler) (8). In the example of FIG. 28, quantum unitary noise (492) is scaled via scale factor 494 and applied to features or activations 490. Max pooling 497 or average pooling 498 are applied to the resultant values 496. Note that the double feature ‘20’ does not result in multiple maxima as described in connection supra with FIG. 26. This is due to the application of the quantum noise to the features or activations. Note that in one embodiment, the noise derived from the unitary quantum source is zero mean. Thus, the neural network can maintain balance from cycle to cycle within the striding pool. Since no bias is added, there is no need to resample to achieve a zero mean noise contribution. The standard deviation value functions as a scalar on the amount of unitary noise and can be adjusted during the training stage. This parameter can be decreased over the training time similarly to adjustment of a learning rate parameter”. Examiner interprets creating the reservoir of random binary numbers 0 and 1 to be equivalent as the claimed “generating an array of random directions”; the 0s and 1s being transformed to −1 and 1 is interpreted as generating the random directions; the noise derived from the unitary quantum source being zero mean is interpreted as “generated by the quantum processor”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Redmond by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to generating an array of random directions using the set of samples as an array of random binary variables, as taught by Redmond. The modification would have been obvious because one of ordinary skill in the art would be motivated to balance the noise (as suggested by Redmond at Pg. 249: “Note that in one embodiment, the QDA creates a reservoir of random binary numbers 0 and 1. The 0s and 1s are transformed to −1 and 1 range to give zero mean and balance to the noise. The random number may also be optionally scaled to avoid saturating small values, or zeroing the activation”).
However, Wiebe – Wang fails to teach:
determining a normalized perturbation strength;
Baumann teaches, in analogous system,
determining a normalized perturbation strength (see Baumann at Page 3: “The error
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z is of the order of the initial error z0, which itself is proportional to 𝜅. Analogously to the normalized perturbation 𝝃, we define the normalized synchronization error as
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𝜻
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(
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𝑡
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,
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𝒆
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,
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𝑡0
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)
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∶
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= lim𝜅→0
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𝒛/𝜅. Taking the limit
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𝜅
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→
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0 of (7), divided by 𝜅, and using
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𝒛
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∈𝒪
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(
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𝜅
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) yields d𝜻/d𝑡=𝑨(𝑡)𝜻−𝑘𝜻.(8). By comparing (3) and (8), we find that
𝜻=𝜱(𝑡,𝑡0)𝑒−𝑘(𝑡−𝑡0)𝒆=𝝃𝑒−𝑘(𝑡−𝑡0). (9)”. Examiner interprets equation (9) to be equivalent as the claimed “determining a normalized perturbation strength” where the normalized synchronization error 𝜻 is interpreted as “the normalized perturbation strength”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Baumann by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to determine the normalized perturbation strength, as taught by Baumann. The modification would have been obvious because one of ordinary skill in the art would be motivated to capture the average exponential growth or decay rate (as suggested by Baumann at Page 1: “The spectrum of Lyapunov exponents is an important characteristic of limit sets. It measures the exponential convergence or divergence of nearby trajectories, thereby capturing the sensitivity of solutions with respect to initial conditions. An infinitesimal sphere of perturbed initial conditions will deform into an ellipsoid under the flow of a smooth dynamical system. The Lyapunov exponents capture the average exponential growth or decay rate of the principal axes of the ellipsoid and the maximal Lyapunov exponent captures the long-term behavior of the dominating direction. For example, an attractive limit cycle has only negative Lyapunov exponents (except possibly one at zero corresponding to the freedom of phase [20]). A positive maximal Lyapunov exponent implies instability of the limit set (i.e., equilibrium, limit cycle, periodic or quasi-periodic solution) or it can be an indication for a chaotic attractor”).
However, Wiebe – Wang fails to teach:
wherein the perturbation parameter is a product of the array of random directions and the normalized perturbation strength;
Brendel teaches, in analogous system,
wherein the perturbation parameter is a product of the array of random directions and the normalized perturbation strength (see Brendel at Page 4: “The efficiency of the algorithm crucially depends on the proposal distribution P, i.e. which random directions are explored in each step of the algorithm. The optimal proposal distribution will generally depend on the domain and / or model to be attacked, but for all vision-related problems tested here a very simple proposal distribution worked surprisingly well. The basic idea behind this proposal distribution is as follows: in the k-th step we want to draw perturbations ηk from a maximum entropy distribution subject to the following constraints:
The perturbed sample lies within the input domain,
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The perturbation has a relative size of δ,
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The perturbation reduces the distance of the perturbed image towards the original input by a relative amount ,
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“. Examiner interprets the equation (2) to be equivalent as the claimed “the perturbation parameter is a product of the array of random directions and the normalized perturbation strength”; where the perturbation vector ηk at step k is interpreted as “perturbation parameter”, the perturbation δ having a relative size is interpreted to be equivalent as the claimed “normalized perturbation strength”, d(o, o˜k−1) is interpreted as the array of random direction).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Brendel by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and the perturbation parameter being the product of the array of random directions and the normalized perturbation strength, as taught by Brendel. The modification would have been obvious because one of ordinary skill in the art would be motivated to reduce the distance of the perturbed image towards the original input (as suggested by Brendel at Page 4: “3. The perturbation reduces the distance of the perturbed image towards the original input by a relative amount
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𝜖,
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”).
Claims 15-16 are rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang) and in further view of Anschuetz et al. (US-11605015-B2- hereinafter Anschuetz)
Referring to Claim 15, Wiebe – Wang teaches the method of claim 9.
However, Wiebe – Wang fails to teach:
wherein: generating the training model comprises generating a model described by a transverse Ising Hamiltonian, and the at least one optimizable parameter comprises at least one Hamiltonian parameter;
Anschuetz teaches, in analogous system,
wherein: generating the training model comprises generating a model described by a transverse Ising Hamiltonian, and the at least one optimizable parameter comprises at least one Hamiltonian parameter (see Anschuetz at Cl. 4 Ln. 34-56: “A quantum Boltzmann machine (QBM) is a quantum generalization of a classical Boltzmann machine that is described by a quantum thermal probability distribution
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where HQBM is a semi-restricted transverse Ising Hamiltonian
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where {right arrow over (z)}v∈{−1,1}n v , {right arrow over (θ)}={{right arrow over (Γ)},{right arrow over (b)},{right arrow over (w)}}, and Πz v is a projector of the visible units of the QBM onto {right arrow over (z)}v. Here, the term “semi-restricted” means that the only connections between the hidden units are disallowed (see FIG. 4 )”. Examiner interprets HQBM being the semi-restricted transverse Ising Hamiltonian to be equivalent as the claimed “generating the training model comprises generating a model described by a transverse Ising Hamiltonian”; where
θ
→
is interpreted as Hamiltonian parameter).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Anschuetz by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to generate the model described by the transverse Ising Hamiltonian, and the optimizable parameter comprising the Hamiltonian parameter, as taught by Anschuetz. The modification would have been obvious because one of ordinary skill in the art would be motivated to model the given data set as a thermal state under the classical Ising energy function (as suggested by Anschuetz at Cl. 4 Ln. 1-8: “The goal of generative modeling is to train a model that generates data points that resemble a given set of data. In particular, a Boltzmann machine is an energy-based generative model that models the given data set as a thermal state under the classical Ising energy function”).
Referring to Claim 16, Wiebe – Wang teaches the method of claim 9.
However, Wiebe – Wang fails to teach:
minimizing the loss function describing a difference between data belonging to the training data set and the set of samples generated by the quantum processor;
estimating a gradient of the objective function comprises estimating a gradient of the loss function;
Anschuetz teaches, in analogous system,
minimizing the loss function describing a difference between data belonging to the training data set and the set of samples generated by the quantum processor (see Anschuetz at Cl. 5 Ln. 29-67: “For both classical and quantum Boltzmann machines, the parameters {right arrow over (θ)} may be trained to minimize the negative log-likelihood
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where pβ({right arrow over (z)}v;{right arrow over (θ)}) is the thermal distribution corresponding to either a classical Boltzmann machine or a QBM. For QBMs, gradients of
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are not efficiently sampleable. Thus, in practice, one trains on an upper bound of the loss function, which is given by
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where H v({right arrow over (θ)})=H QBM({right arrow over (θ)})−ln(Πv). (8). Training a QBM on
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not only prevents finding the optimal parameters for the true loss function
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, but also makes training {right arrow over (θ)}off-diag generally impossible. Using generalized measurements, it is possible to train the off-diagonal elements, though deriving such measurements requires prior knowledge of the data distribution, and thus is difficult in practice. Herein, only training on the upper bound
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is considered. For a generic QBM, derivatives of Eqn. 7 with respect to the diagonal parameters {{right arrow over (b)},{right arrow over (w)}} are of the form
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For an observable Oθ corresponding to the θ-component of the gradient, Eqns. 9 and 10 can be equivalently expressed as ∂θ
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({right arrow over (θ)})=β(
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z v ˜p data [
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QBM), (11)where the first expectation value is averaged with respect to the data distribution and the second with respect to the model distribution. Due to the form of Hv (see Eqn. 8), the first term of these derivatives—the positive phase—is efficiently computable classically. The second term—the negative phase—is not believed to be efficiently computable in general, and if done exactly would require sampling from a general quantum thermal distribution, which is NP-hard. Embodiments herein approximately sample the local observables of Eqn. 11 from this quantum thermal distribution, taking advantage of the low weight of the operators that must be sampled”. Examiner interprets the first expectation value being averaged with respect to the data distribution and the second with respect as well as the parameters {right arrow over (θ)} being trained to minimize the negative log-likelihood ℒ
(
θ
→
)
to be equivalent as the claimed “minimizing the loss function describing a difference between data belonging to the training data set and the set of samples generated by the quantum processor”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Anschuetz by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to minimize the loss function describing the difference between data belonging to the training data set and the set of samples, as taught by Anschuetz. The modification would have been obvious because one of ordinary skill in the art would be motivated to model the given data set as a thermal state under the classical Ising energy function (as suggested by Anschuetz at Cl. 4 Ln. 1-8: “The goal of generative modeling is to train a model that generates data points that resemble a given set of data. In particular, a Boltzmann machine is an energy-based generative model that models the given data set as a thermal state under the classical Ising energy function”);
estimating a gradient of the objective function comprises estimating a gradient of the loss function (see Anschuetz at Cl. 25 Ln. 30-33: “(H) In any of the hybrid quantum-classical computers denoted as (A)-(G), the classical computing component uses the first and second sets of expectation values to estimate a gradient of a loss function”. Examiner interprets the classical computing component using the first and second sets of expectation values to estimate a gradient of a loss function to be equivalent as the claimed “estimating a gradient of the objective function comprises estimating a gradient of the loss function”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Anschuetz by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to estimate the gradient of the loss function, as taught by Anschuetz. The modification would have been obvious because one of ordinary skill in the art would be motivated to determine a parameter step that is added to previous parameters to obtain updated parameters (as suggested by Anschuetz at Cl. 12 Ln. 152-58: “Parameter updater 632 updates parameters 626 based on the first set of expectation values 620 and the value 624 of the temperature parameter. For example, parameter updater 632 may estimate a gradient of a loss function (e.g., see Eqns. 9 and 10) to determine a parameter step that is added to previous parameters to obtain updated parameters 626”).
Claims 18 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang) and in further view of Horii et al. (US-20210383267-A1 - hereinafter Horii).
Referring to Claim 18, Wiebe – Wang teaches the method of claim 9, Wiebe further teaches:
the quantum processor comprises a plurality of qubits (see Wiebe at Cl. 16 Ln. 16-23: “Referring to FIG. 4, a method 400 of establishing and sampling a model average includes receiving a Boltzmann machine specification at 402 and computing a mean field approximation to a Gibbs state at 404. At 406, the mean-field values are used to prepare a mean-field state on qubits in a quantum computer and at 408, a qubit string is prepared that stores energy of each configuration (v,h)”. Examiner interprets preparing a mean-field state on qubits in a quantum computer to be equivalent as the claimed “the quantum processor comprises a plurality of qubits”);
instructing the quantum processor to generate the set of samples from the probability distribution comprises: programming the quantum processor to have the probability distribution over the plurality of qubits (see Wiebe at Cl. 6 Ln. 46-54: “Disclosed below are methods by which an initial quantum distribution is refined into a quantum coherent Gibbs state (often called a coherent thermal state or CTS). Mean-field approaches or generalizations thereof can be used to provide suitable initial states for the quantum computer to refine into the CTS. All units are assumed to be binary-valued in the following examples, but other units (such as Gaussian units) can be approximated within this framework by forming a single unit out of a string of several qubits”. Examiner interprets providing suitable initial states for the quantum computer to refine into the CTS to be equivalent as the claimed “programming the quantum processor”; initial quantum distribution being refined into a quantum coherent Gibbs state is interpreted to be equivalent as the claimed “to have the probability distribution”; forming a single unit out of a string of several qubits is interpreted to be equivalent as the claimed “over the plurality of qubits”).
However, Wiebe – Wang fails to teach:
instructing the quantum processor to generate the set of samples from the probability distribution comprises: instructing the quantum processor to perform quantum evolution using the plurality of qubits;
receiving, by the at least one digital processor, the set of samples having the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution;
Horii teaches, in analogous system,
instructing the quantum processor to generate the set of samples from the probability distribution comprises: instructing the quantum processor to perform quantum evolution using the plurality of qubits (see Horii at Pg. 54: “System 300 depicted in FIG. 3 can comprise an illustration of an example quantum system (e.g., a superconducting system) that can comprise a quantum circuit 302 (denoted as Circuit in FIG. 3). Quantum circuit 302 can comprise an algorithm (e.g., a quantum-based algorithm) that can comprise one or more operators 304 a, 304 b, and/or 304 c (denoted as Kraus 1, Kraus2, and Kraus3, respectively, in FIG. 3). Although operators 304 a, 304 b, 304 c are depicted in FIG. 3 as Kraus operators, it should be appreciated that such operators 304 a, 304 b, 304 c can comprise one or more other operators such as, for instance, conditional operators. When executed, operators 304 a, 304 b, 304 c can respectively yield a probability distribution and/or a quantum state associated with quantum circuit 302 and/or with one or more quantum bits (qubits) of quantum circuit 302. In the example embodiment illustrated in FIG. 3, execution of quantum circuit 302 and/or operators 304 a, 304 b, 304 c is depicted as one or more shots 306 a, 306 b, 306 c, 306 d, 306 e, and/or 306 n (denoted as shot1, shot2, shot3, shot4, shot5, and shotn, respectively, in FIG. 3, where n represents a total quantity of shots). As referenced herein, a shot can denote a single algorithm execution instance that can yield a probability range (also referred to herein as a probability distribution or a probability amplitude) associated with a result”. Examiner interprets executing operators respectively yield the probability distribution and/or the quantum state associated with quantum circuit and/or with one or more quantum bits (qubits) of quantum circuit; to be equivalent as the claimed “instructing the quantum processor to perform quantum evolution using the plurality of qubits”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Horii by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to instruct the quantum processor to perform quantum evolution using the plurality of qubits, as taught by Horii. The modification would have been obvious because one of ordinary skill in the art would be motivated to facilitate sampling of an operator in a quantum system (as suggested by Horii at Pg. 53: “FIGS. 3-9 illustrate block diagrams of example, non-limiting systems 300, 400, 500, 600, 700, 800, and 900, respectively, that can facilitate sampling of an operator in a quantum system in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity”).
receiving, by the at least one digital processor, the set of samples having the probability distribution generated by the quantum processor comprises: receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution (see Horii at Pg. 54: “System 300 depicted in FIG. 3 can comprise an illustration of an example quantum system (e.g., a superconducting system) that can comprise a quantum circuit 302 (denoted as Circuit in FIG. 3). Quantum circuit 302 can comprise an algorithm (e.g., a quantum-based algorithm) that can comprise one or more operators 304 a, 304 b, and/or 304 c (denoted as Kraus 1, Kraus2, and Kraus3, respectively, in FIG. 3). Although operators 304 a, 304 b, 304 c are depicted in FIG. 3 as Kraus operators, it should be appreciated that such operators 304 a, 304 b, 304 c can comprise one or more other operators such as, for instance, conditional operators. When executed, operators 304 a, 304 b, 304 c can respectively yield a probability distribution and/or a quantum state associated with quantum circuit 302 and/or with one or more quantum bits (qubits) of quantum circuit 302. In the example embodiment illustrated in FIG. 3, execution of quantum circuit 302 and/or operators 304 a, 304 b, 304 c is depicted as one or more shots 306 a, 306 b, 306 c, 306 d, 306 e, and/or 306 n (denoted as shot1, shot2, shot3, shot4, shot5, and shotn, respectively, in FIG. 3, where n represents a total quantity of shots). As referenced herein, a shot can denote a single algorithm execution instance that can yield a probability range (also referred to herein as a probability distribution or a probability amplitude) associated with a result”. Examiner interprets the combination of the following passages: quantum system executing quantum circuit which comprises operators (executing quantum circuit and operators is interpreted as quantum evolution); executing operators respectively yield the probability distribution and/or the quantum state associated with quantum circuit and/or with one or more quantum bits (qubits) of quantum circuit; execution of quantum circuit and/or operators is depicted as one or more shots (interpreted as samples); to be equivalent as the claimed “receiving a set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Horii by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to receive the set of states of the plurality of qubits observable after quantum evolution that correspond to samples from the probability distribution, as taught by Horii. The modification would have been obvious because one of ordinary skill in the art would be motivated to facilitate sampling of an operator in a quantum system (as suggested by Horii at Pg. 53: “FIGS. 3-9 illustrate block diagrams of example, non-limiting systems 300, 400, 500, 600, 700, 800, and 900, respectively, that can facilitate sampling of an operator in a quantum system in accordance with one or more embodiments described herein. Repetitive description of like elements and/or processes employed in respective embodiments is omitted for sake of brevity”).
Claims 20 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Wang (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang) and in further view of Arute et al. (NPL: “Quantum supremacy using a programmable superconducting processor” - hereinafter Arute).
Referring to Claim 20, Wiebe – Wang teaches the method of claim 9.
However, Wiebe – Wang fails to teach:
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving samples obtained in a coherent regime when the quantum processor exhibits non-equilibrium dynamics;
Arute teaches, in analogous system,
wherein receiving, from the quantum processor, a set of samples from a probability distribution generated by the quantum processor comprises: receiving samples obtained in a coherent regime when the quantum processor exhibits non-equilibrium dynamics (see Arute at Page 2-3: “The processor is fabricated using aluminium for metallization and Josephson junctions, and indium for bump-bonds between two silicon wafers. The chip is wire-bonded to a superconducting circuit board and cooled to below 20 mK in a dilution refrigerator to reduce ambient thermal energy to well below the qubit energy. The processor is connected through filters and attenuators to room-temperature electronics, which synthesize the control signals. The state of all qubits can be read simultaneously by using a frequency-multiplexing technique33,34. We use two stages of cryogenic amplifiers to boost the signal, which is digitized (8 bits at 1 GHz) and demultiplexed digitally at room temperature. In total, we orchestrate 277 digital-to-analog converters (14 bits at 1 GHz) for complete control of the quantum processor. We execute single-qubit gates by driving 25-ns microwave pulses resonant with the qubit frequency while the qubit–qubit coupling is turned off. The pulses are shaped to minimize transitions to higher transmon states35. Gate performance varies strongly with frequency owing to two-level-system defects36,37, stray microwave modes, coupling to control lines and the readout resonator, residual stray coupling between qubits, flux noise and pulse distortions. We therefore optimize the single-qubit operation frequencies to mitigate these error mechanisms. We benchmark single-qubit gate performance by using the cross entropy benchmarking protocol described above, reduced to the single qubit level (n = 1), to measure the probability of an error occurring during a single-qubit gate. On each qubit, we apply a variable number m of randomly selected gates and measure FXEB averaged over many sequences; as m increases, errors accumulate and average FXEB decays. We model this decay by [1 − e1 /(1 − 1/D2)]m where e1 is the Pauli error prob ability. The state (Hilbert) space dimension term, D = 2n, which equals 2 for this case, corrects for the depolarizing model where states with errors partially overlap with the ideal state. This procedure is similar to the more typical technique of randomized benchmarking27,38,39, but supports non-Clifford-gate sets40 and can separate out decoherence error from coherent control error. We then repeat the experiment with all qubits executing single-qubit gates simultaneously (Fig. 2), which shows only a small increase in the error probabilities, demonstrating that our device has low microwave crosstalk”. Examiner interprets the combination of the following passages: reading out the state of all qubits simultaneously and digitizing the amplified signal (interpreted as sampling); and supporting non-clifford-gate sets and separating out decoherence error from coherent control error (interpreted as coherent regime); as well as executing single-qubit gates by driving 25-ns microwave pulses resonant with the qubit frequency while the qubit-qubit coupling is turned off (interpreted as non-equilibrium dynamics); to be equivalent as the claimed “receiving samples obtained in a coherent regime when the quantum processor exhibits non-equilibrium dynamics”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Wang with the above teachings of Arute by generating the training model associated with the machine learning model, the training model having an objective function and initializing the training model parameters as well as estimating the gradient of the objective function, as taught by Wiebe and Wang, and to receive samples obtained in a coherent regime when the quantum processor exhibits non-equilibrium dynamics., as taught by Arute. The modification would have been obvious because one of ordinary skill in the art would be motivated to obtain small increase in the error probabilities (as suggested by Arute at Page 3: “We then repeat the experiment with all qubits executing single-qubit gates simultaneously (Fig. 2), which shows only a small increase in the error probabilities, demonstrating that our device has low microwave crosstalk”).
Claims 21-23, 31 are rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang).
Referring to independent Claim 21, this claim is rejected on the same basis as independent claim 1 since they are analogous claims.
Referring to Claim 22, Wiebe – Huang teaches the system 21, Wiebe further teaches:
wherein the quantum processor comprises a plurality of qubits (see Wiebe at Cl. 16 Ln. 16-23: “Referring to FIG. 4, a method 400 of establishing and sampling a model average includes receiving a Boltzmann machine specification at 402 and computing a mean field approximation to a Gibbs state at 404. At 406, the mean-field values are used to prepare a mean-field state on qubits in a quantum computer and at 408, a qubit string is prepared that stores energy of each configuration (v,h)”. Examiner interprets preparing a mean-field state on qubits in a quantum computer to be equivalent as the claimed “the quantum processor comprises a plurality of qubits”).
Referring to Claim 23, Wiebe – Huang teaches the system 22, Wiebe further teaches:
wherein each sample of the set of samples is a set of states of the plurality of qubits of the quantum processor (see Wiebe at Cl. 6 Ln. 46-49: “Disclosed below are methods by which an initial quantum distribution is refined into a quantum coherent Gibbs state (often called a coherent thermal state or CTS). Mean-field approaches or generalizations thereof can be used to provide suitable initial states for the quantum computer to refine into the CTS. All units are assumed to be binary-valued in the following examples, but other units (such as Gaussian units) can be approximated within this framework by forming a single unit out of a string of several qubits”. Examiner interprets initial quantum distribution being refined into the quantum coherent Gibbs state to be equivalent as the claimed “set of samples is a set of states”; the string of several qubits is interpreted as plurality of qubits of the quantum processor).
Referring to Claim 31, Wiebe – Huang teaches the system 21, Wiebe further teaches:
wherein prior to receipt of the set of samples from the quantum processor, the at least one digital processor is to instruct the quantum processor to generate the set of samples from the probability distribution (see Wiebe at Cl. 3 Ln. 40-53: “The methods and apparatus described herein generally use a classical computer coupled to a quantum computer to train a deep Boltzmann machine. In order for the classical computer to update a model for the deep Boltzmann machine given training data, certain expectation values are computed. A quantum computer is arranged to accelerate this process. In typical examples, a classically tractable approximation to the state provided by a mean field approximation, or a related approximation, is used to prepare a quantum state that is close to the distribution that yields the desired expectation values. The quantum computer is then used to efficiently refine this approximation into precisely the desired distribution. The required expectation values are then learned by sampling from this quantum distribution”. Examiner interprets the required expectation values being learned by sampling from this quantum distribution; to be equivalent as the claimed “instructing the quantum processor to generate the set of samples from the probability distribution”).
Claims 24 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Anschuetz et al. (US-11605015-B2 - hereinafter Anschuetz).
Referring to Claim 24, Wiebe – Huang teaches the system 21.
However, Wiebe – Huang fails to teach:
wherein the quantum processor is a quantum annealer or an adiabatic quantum processor;
Anschuetz teaches, in analogous system,
wherein the quantum processor is a quantum annealer or an adiabatic quantum processor (see Anschuetz at Cl. 13 Ln. 3-12: “In some embodiments, the first and second plurality of qubits 610, 612 are quenched under the Hamiltonian (e.g., see Eqn. 17). This quenching of the first and second plurality of qubits 610, 612 may include simulating time evolution of the first and second plurality of qubits 610, 612 by a quantum circuit in quantum computer 604. Alternatively, the simulating of time evolution may be performed by an analog quantum simulator in the quantum computer 604. Alternatively, the simulating of time evolution may be performed by a quantum annealer in the quantum computer 604”. Examiner interprets the simulating of time evolution being performed by the quantum annealer in the quantum computer to be equivalent as the claimed “the quantum processor is a quantum annealer or an adiabatic quantum processor”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Anschuetz by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and the quantum processor being a quantum annealer or an adiabatic quantum processor, as taught by Anschuetz. The modification would have been obvious because one of ordinary skill in the art would be motivated to simulate time evolution (as suggested by Anschuetz at Cl. 13 Ln. 3-12: “In some embodiments, the first and second plurality of qubits 610, 612 are quenched under the Hamiltonian (e.g., see Eqn. 17). This quenching of the first and second plurality of qubits 610, 612 may include simulating time evolution of the first and second plurality of qubits 610, 612 by a quantum circuit in quantum computer 604. Alternatively, the simulating of time evolution may be performed by an analog quantum simulator in the quantum computer 604. Alternatively, the simulating of time evolution may be performed by a quantum annealer in the quantum computer 604”).
Claims 25-26 are rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) and in further view of Liu et al. (US-20200279155-A1 - hereinafter Liu).
Referring to Claim 25, Wiebe – Huang teaches the system 21.
However, Wiebe – Huang fails to teach:
wherein, the gradient is based on the current value of the at least one optimizable parameter and an array of random directions, wherein the array of random directions is based on the set of samples generated by the quantum processor;
Liu teaches, in analogous system,
wherein, the gradient is based on the current value of the at least one optimizable parameter and an array of random directions, wherein the array of random directions is based on the set of samples generated by the quantum processor (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3), where x=xk in Algorithm 1,
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is a mini-batch of size |
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|=bi{ui,j}j=1 q are independent and identically distributed (i.i.d.) random directions drawn from a uniform distribution over a unit sphere, and {circumflex over (∇)}ƒi(xiui,j) gives a conventional two-point based random gradient estimate with direction ui,j and smoothing parameter μ>0”. Examiner interprets the gradient estimate being constructed through the forward difference of two function values; and the algorithm having only access to function values of {ƒi(x)} given a query point x (x interpreted as on the current value of the optimizable parameter); as well as q directional vectors ui,j being independently and identically drawn from a uniform distribution over a unit sphere; to be equivalent as the claimed “the gradient is based on the current value of the at least one optimizable parameter and an array of random directions, wherein the array of random directions is based on the set of samples generated by the quantum processor”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and the gradient being based on the current value of the optimizable parameter and an array of random directions, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
Referring to Claim 26, Wiebe – Huang teaches the system 21.
However, Wiebe – Huang fails to teach:
the gradient is based on a rate of change between a first objective function value and a second objective function value;
the first objective function value is an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction;
the second objective function value is an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction;
Liu teaches, in analogous system,
the gradient is based on a rate of change between a first objective function value and a second objective function value (see Liu at Pg. 54: “see Liu at Pg. 54: “Next, two variants of ZO-signSGD are shown, where the gradient will be estimated using the central difference of function values or the signs of ZO gradient estimates with majority vote. That is:
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“. Examiner interprets the quotient obtained when the result of subtracting the two objective functions is divided by (2μ):
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to be equivalent as the claimed “rate of change between a first objective function value and a second objective function value”; the formula:
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is interpreted to be equivalent as the claimed “the gradient is based on a rate of change between a first objective function value and a second objective function value”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and the gradient being based on a rate of change between a first objective function value and a second objective function value, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”);
the first objective function value is an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by a perturbation parameter in a first direction (see Liu at Pg. 33-34: “In the ZO setting where the first-order information is unavailable, the gradient estimator at Step 3 of Algorithm 1 in FIG. 3 has only access to function values of {ƒi(x)} given a query point x. Based on that, a ZO gradient estimate is constructed through a forward difference of two function values. In Algorithm 1, GradEstimate (x) is then specified as equation (3):
∇
^
f
i
x
;
u
=
d
μ
f
i
x
+
μ
u
-
f
i
x
⋅
u
“. Examiner interprets fi(x;u) to be equivalent as the claimed “evaluating the objective function”; the given query point x is interpreted to be equivalent as the claimed “the current value of the at least one optimizable parameter”; μ is interpreted to be equivalent as the claimed “perturbation parameter”; u is interpreted as the first direction vector; fi(x + μu) is interpreted as the first objective function value).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and the first objective function value being an evaluation of the objective function at the current value of the optimizable parameter perturbed by a perturbation parameter in a first direction, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”);
the second objective function value is an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction (see Liu at Pg. 54: “Next, two variants of ZO-signSGD are shown, where the gradient will be estimated using the central difference of function values or the signs of ZO gradient estimates with majority vote. That is:
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“. Examiner interprets the central difference of function values as perturbing the parameter in two opposing directions; x is interpreted to be equivalent as the claimed “the current value of the at least one optimizable parameter”; +μui,j is interpreted as perturbation parameter perturbing the vector in the first direction; -μui,j is interpreted as perturbation parameter perturbing the vector in the opposite second direction; fi(x + μui,j) is interpreted as the first objective function; fi(x - μui,j) is interpreted as the second objective function).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Liu by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and the second objective function value being an evaluation of the objective function at the current value of the at least one optimizable parameter perturbed by the perturbation parameter in a second direction that opposes the first direction, as taught by Liu. The modification would have been obvious because one of ordinary skill in the art would be motivated to solve ML problems where explicit expressions of the gradients are difficult or infeasible to obtain (as suggested by Liu at Pg. 32: “Now, with reference to the inventive ZO-signSGD technique for black box optimization, one limitation of signSGD is the need of first-order information (i.e., stochastic gradients). However, as highlighted above, there exists a large practical demand for solving ML problems where explicit expressions of the gradients are difficult or infeasible to obtain. This motivates the inventive ZO-signSGD method”).
Claims 27 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) in further view of Liu et al. (US-20200279155-A1 - hereinafter Liu) and in further view of Brendel et al. (NPL: “Decision-based adversarial attacks: reliable attacks against black-box machine learning models” - hereinafter Brendel).
Referring to Claim 27, Wiebe – Huang - Liu teaches the system 26.
However, Wiebe – Huang - Liu fails to teach:
wherein, the gradient is based on the current value of the at least one optimizable parameter and an array of random directions, wherein the array of random directions is based on the set of samples generated by the quantum processor;
Brendel teaches, in analogous system,
wherein the perturbation parameter is based on a normalized perturbation strength and the set of samples generated by the quantum processor (see Brendel at Page 4: “The efficiency of the algorithm crucially depends on the proposal distribution P, i.e. which random directions are explored in each step of the algorithm. The optimal proposal distribution will generally depend on the domain and / or model to be attacked, but for all vision-related problems tested here a very simple proposal distribution worked surprisingly well. The basic idea behind this proposal distribution is as follows: in the k-th step we want to draw perturbations ηk from a maximum entropy distribution subject to the following constraints:
1. The perturbed sample lies within the input domain,
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2. The perturbation has a relative size of δ,
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3. The perturbation reduces the distance of the perturbed image towards the original input by a relative amount
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𝜖,
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“. Examiner interprets the perturbation vector ηk at step k to be equivalent as the claimed “perturbation parameter”, the perturbation δ having a relative size is interpreted to be equivalent as the claimed “normalized perturbation strength”, drawing perturbations ηk from a maximum entropy distribution is interpreted as the set of samples).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe, Huang and Liu with the above teachings of Brendel by estimating, updating and evaluating the gradient of the objective function and determining the rate of change between the first and the second objective function values, as taught by Wiebe, Huang and Liu, and the perturbation parameter being based on a normalized perturbation strength and the set of samples, as taught by Brendel. The modification would have been obvious because one of ordinary skill in the art would be motivated to reduce the distance of the perturbed image towards the original input (as suggested by Brendel at Page 4: “3. The perturbation reduces the distance of the perturbed image towards the original input by a relative amount
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𝜖,
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”).
Claims 28 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) in further view of Liu et al. (US-20200279155-A1 - hereinafter Liu) and in further view of Brendel et al. (NPL: “Decision-based adversarial attacks: reliable attacks against black-box machine learning models” - hereinafter Brendel) and in further view of Baumann et al. (NPL: “Estimation of the maximal Lyapunov exponent of nonsmooth systems using chaos synchronization” - hereinafter Baumann).
Referring to Claim 28, Wiebe – Huang - Liu – Brendel teaches the system 27.
However, Wiebe – Huang – Liu - Brendel fails to teach:
wherein the normalized perturbation strength is based on a perturbation strength and a current perturbation strength decay;
Baumann teaches, in analogous system,
wherein the normalized perturbation strength is based on a perturbation strength and a current perturbation strength decay (see Baumann at Page 3: “The error
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z is of the order of the initial error z0, which itself is proportional to 𝜅. Analogously to the normalized perturbation 𝝃, we define the normalized synchronization error as
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𝜻
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(
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∶
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= lim𝜅→0
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𝒛/𝜅. Taking the limit
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𝜅
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→
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0 of (7), divided by 𝜅, and using
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∈𝒪
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(
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𝜅
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) yields d𝜻/d𝑡=𝑨(𝑡)𝜻−𝑘𝜻.(8). By comparing (3) and (8), we find that 𝜻=𝜱(𝑡,𝑡0)𝑒−𝑘(𝑡−𝑡0)𝒆=𝝃𝑒−𝑘(𝑡−𝑡0). (9)”. Examiner interprets the normalized synchronization error 𝜻 to be equivalent as the claimed “the normalized perturbation strength”, the term 𝒆 is interpreted to be equivalent as the claimed “perturbation strength”, 𝝃 = 𝜱(𝑡,𝑡0)𝒆 is interpreted to be equivalent as the claimed “current perturbation strength”, the term 𝑒−𝑘(𝑡−𝑡0) is interpreted as the decaying factor).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe, Huang, Liu and Brendel with the above teachings of Baumann by estimating, updating and evaluating the gradient of the objective function and determining the rate of change as well as determining the perturbation parameter based on the normalized perturbation strength and the set of samples from the probability distribution, as taught by Wiebe, Huang, Liu and Brendel, and the normalized perturbation strength being based on a perturbation strength and a current perturbation strength decay, as taught by Baumann. The modification would have been obvious because one of ordinary skill in the art would be motivated to capture the average exponential growth or decay rate (as suggested by Baumann at Page 1: “The spectrum of Lyapunov exponents is an important characteristic of limit sets. It measures the exponential convergence or divergence of nearby trajectories, thereby capturing the sensitivity of solutions with respect to initial conditions. An infinitesimal sphere of perturbed initial conditions will deform into an ellipsoid under the flow of a smooth dynamical system. The Lyapunov exponents capture the average exponential growth or decay rate of the principal axes of the ellipsoid and the maximal Lyapunov exponent captures the long-term behavior of the dominating direction. For example, an attractive limit cycle has only negative Lyapunov exponents (except possibly one at zero corresponding to the freedom of phase [20]). A positive maximal Lyapunov exponent implies instability of the limit set (i.e., equilibrium, limit cycle, periodic or quasi-periodic solution) or it can be an indication for a chaotic attractor”).
Claims 29 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) in further view of Wang et al. (NPL: “An overview of SPSA: recent development and applications” - hereinafter Wang).
Referring to Claim 29, Wiebe – Huang teaches the system 27.
However, Wiebe – Huang fails to teach:
wherein the set of samples generated by the quantum processor are samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound;
Wang teaches, in analogous system,
wherein the set of samples generated by the quantum processor are samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound (see Wang at Page 2: “A good choice for ∆ni is the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5. Other choices are possible too, but note that the uniform and normal distributions cannot be used because they do not satisfy the finite inverse moment conditions”. Examiner interprets choosing ∆ni as the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5 and ∆ni satisfying the finite inverse moment conditions; to be equivalent as the claimed “samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Wang by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and samples from a symmetric, zero mean probability distribution that satisfies an inverse moment bound, as taught by Wang. The modification would have been obvious because one of ordinary skill in the art would be motivated to satisfy the finite inverse moment conditions (as suggested by Wang at Pg. 2: “A good choice for ∆ni is the Rademacher distribution, i.e. Bernoulli +-1 with probability 0.5. Other choices are possible too, but note that the uniform and normal distributions cannot be used because they do not satisfy the finite inverse moment conditions”).
Claims 30 is rejected under 35 U.S.C. 103 as being unpatentable over Wiebe et al. (US-11295207-B2 - hereinafter Wiebe) in view of Huang et al. (CN-111932017-A - hereinafter Huang) in further view of Arute et al. (NPL: “Quantum supremacy using a programmable superconducting processor” - hereinafter Arute).
Referring to Claim 30, Wiebe – Huang teaches the system 27.
However, Wiebe – Huang fails to teach:
wherein the set of samples generated by the quantum processor are samples obtained when the quantum processor exhibits non-equilibrium dynamics in a coherent regime;
Arute teaches, in analogous system,
wherein the set of samples generated by the quantum processor are samples obtained when the quantum processor exhibits non-equilibrium dynamics in a coherent regime (see Arute at Page 2-3: “The processor is fabricated using aluminium for metallization and Josephson junctions, and indium for bump-bonds between two silicon wafers. The chip is wire-bonded to a superconducting circuit board and cooled to below 20 mK in a dilution refrigerator to reduce ambient thermal energy to well below the qubit energy. The processor is connected through filters and attenuators to room-temperature electronics, which synthesize the control signals. The state of all qubits can be read simultaneously by using a frequency-multiplexing technique33,34. We use two stages of cryogenic amplifiers to boost the signal, which is digitized (8 bits at 1 GHz) and demultiplexed digitally at room temperature. In total, we orchestrate 277 digital-to-analog converters (14 bits at 1 GHz) for complete control of the quantum processor. We execute single-qubit gates by driving 25-ns microwave pulses resonant with the qubit frequency while the qubit–qubit coupling is turned off. The pulses are shaped to minimize transitions to higher transmon states35. Gate performance varies strongly with frequency owing to two-level-system defects36,37, stray microwave modes, coupling to control lines and the readout resonator, residual stray coupling between qubits, flux noise and pulse distortions. We therefore optimize the single-qubit operation frequencies to mitigate these error mechanisms. We benchmark single-qubit gate performance by using the cross entropy benchmarking protocol described above, reduced to the single qubit level (n = 1), to measure the probability of an error occurring during a single-qubit gate. On each qubit, we apply a variable number m of randomly selected gates and measure FXEB averaged over many sequences; as m increases, errors accumulate and average FXEB decays. We model this decay by [1 − e1 /(1 − 1/D2)]m where e1 is the Pauli error prob ability. The state (Hilbert) space dimension term, D = 2n, which equals 2 for this case, corrects for the depolarizing model where states with errors partially overlap with the ideal state. This procedure is similar to the more typical technique of randomized benchmarking27,38,39, but supports non-Clifford-gate sets40 and can separate out decoherence error from coherent control error. We then repeat the experiment with all qubits executing single-qubit gates simultaneously (Fig. 2), which shows only a small increase in the error probabilities, demonstrating that our device has low microwave crosstalk”. Examiner interprets the combination of the following passages: reading out the state of all qubits simultaneously and digitizing the amplified signal (interpreted as sampling); and supporting non-clifford-gate sets and separating out decoherence error from coherent control error (interpreted as coherent regime); as well as executing single-qubit gates by driving 25-ns microwave pulses resonant with the qubit frequency while the qubit-qubit coupling is turned off (interpreted as non-equilibrium dynamics); to be equivalent as the claimed “samples obtained when the quantum processor exhibits non-equilibrium dynamics in a coherent regime”).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the teachings of Wiebe and Huang with the above teachings of Arute by estimating, updating and evaluating the gradient of the objective function based on a current value of the optimizable parameter and the set of samples from the probability distribution, as taught by Wiebe and Huang, and samples obtained when the quantum processor exhibits non-equilibrium dynamics in a coherent regime, as taught by Arute. The modification would have been obvious because one of ordinary skill in the art would be motivated to obtain small increase in the error probabilities (as suggested by Arute at Page 3: “We then repeat the experiment with all qubits executing single-qubit gates simultaneously (Fig. 2), which shows only a small increase in the error probabilities, demonstrating that our device has low microwave crosstalk”).
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to AWADAGBE G HOUNTON whose telephone number is (571)270-0670. The examiner can normally be reached Monday-Friday 8am-5pm.
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/AWADAGBE G HOUNTON/Examiner, Art Unit 2126
/DAVID YI/Supervisory Patent Examiner, Art Unit 2126
