DETAILED ACTION
Status of Claims
Claim(s) 1-17 and 21-23 are pending and are examined herein.
Claim(s) 1-17 have been Amended. Claim(s) 18-20 are Cancelled. Claim(s) 20-23 are New.
Claim(s) 1-17 and 21-23 are rejected under 35 U.S.C. §§ 101 and 103.
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 .
Response to Amendment
The amendment filed on February 18, 2026 has been entered. Claims 1-17 and 21-23 are pending in the application. Applicant’s amendments to the claims have overcome the rejection under 35 U.S.C. § 112 set forth in the Non-Final Office Action mailed on November 28, 2025. Applicant’s amendments to the claims have been fully considered and are addressed in the rejections below.
Response to Arguments
Applicant's arguments with respect to the rejection under 35 U.S.C. § 101, filed on 02/18/2026, have been fully considered but are not persuasive. (See Remarks pp. 10-17).
Applicant’s arguments:
Applicant argues that “proper to look at each element of a claim individually looking at words from the claim element taken out of their context from the overall technical solution for the technical problem identified in the specification when determining if the element is directed to a judicial exception." Applicant further cite USPTO subject matter eligibility guidance and PTAB cases related to artificial intelligence (Al) systems claims. (See pp. 10-13).
Applicant further argues that the specification describes a technical problem in quantum-assisted Markov Chain Monte Carlo sampling, specifically, “very long bum-in and mixing times in realistic, noisy hardware severely degrade the ability to sample accurately from Boltzmann distributions.” Applicant further asserts that the claimed invention provides a specific hybrid quantum-classical MCMC solution using a symmetric quantum channel and a classical acceptance rule that does not depend on explicit proposal probabilities, thus improving mixing behavior and providing robustness to realistic quantum hardware errors. (See pp. 14-15).
Applicant further argues that the Office Action characterizes the claim as reciting abstract ideas under Step 2A, Prong 1, that does not align with the actual language of amended claim 1 or with how the claim is situated in the technical field. Applicant asserts that the claims are directed to a specific hybrid quantum-classical system requiring concrete operations performed by physical devices (i.e., quantum and classical computers), and therefore are not abstract idea but a particular configuration to address a concrete hardware problem. (See pp. 15-16).
Applicant further argues that, even if the claims are considered to recite mathematical concepts, such concepts are integrated into a practical application that improves the operation of quantum-assisted sampling system making it robust against noise. Applicant further asserts that the claimed invention use of a symmetric quantum channel and an acceptance probability independent of proposal probabilities represents a non-conventional and non-generic of quantum and classical computers, thus providing improvement that integrate the claim into a practical application and amount to significantly more than the abstract idea. (See pp. 16-17).
Examiner's response:
The examiner respectfully disagrees and finds Applicant’s arguments unpersuasive. As set forth in the Office Action, the amended claim, as currently drafted, was evaluated under USPTO subject matter eligibility guidance, including MPEP § 2106, both individually and as a whole. With respect to Applicant’s citation of USPTO guidance and PTAB Appeal cases related to AI claims, Applicant does not clearly define how such guidance or case examples applies to the specific claim limitations of the present claims. The Examiner notes that the claims of the cited cases differ in scope and context from the present claims, and that the subject matter eligibility of the present claim has been properly evaluated in accordance with MPEP § 2106 patent subject matter eligibility framework.
With respect to Step 2A, Prong 1, it has been determined that the claim is directed to an abstract idea of mental process and/or mathematical concepts without significantly more. Specifically, the core of the claimed invention is directed to sampling from a Boltzmann distribution of an n-spin Ising model (i.e., mathematical model) through mathematical concepts and a probabilistic sampling algorithm. The recited steps including, selecting n-spin configuration, preparing and evolving a quantum state, generating proposal probabilities via a quantum channel (i.e., applying a unitary operator to generate proposal probabilities), measuring outcomes, and calculating an acceptance probability based on energy function (i.e., Hamiltonian). These steps collectively describe mathematical relationships, statistical modeling, and probabilistic decision-making processes. These concepts define well-known statistical Markov Chain Monte Carlo (MCMC) techniques (e.g., Metropolis-Hastings and Gibbs sampling), which fall within the category of abstract idea. See specification (e.g., paragraphs [0058]-[0073], [0079]-[0086], and [0090]-[0091]).
The additional elements recited in the claim, including the use of a classical computer and quantum computer, do not meaningfully limit the judicial exception. Rather, these elements merely invoked as tools to implement the abstract idea using generic computing components. Additionally, the recitation of quantum-specific elements (e.g., qubits, unitary operator, quantum channel) does not change the core of the claimed invention, which remains directed to the abstract idea of generating proposal probabilities through sampling and evaluating probabilistic state transition by computing an acceptance probability. Therefore, invoking a quantum computer to generate proposal probabilities and a classical computer to compute an acceptance probability amounts to using computing machinery as a tool to perform the abstract idea. Accordingly, the claim considered as a whole is directed to an abstract idea.
With respect to Applicant’s arguments regarding the identified technical problem and corresponding technical solution, the Examiner notes that while the specification describes issues such as long burn-in times, mixing time, and robustness against quantum noise, the claim does not recite specific technical implementation that meaningfully address these issues at a concrete technological implementation. In other words, the claim does not recite sufficient technical elements that would integrate the abstract idea into a patent-eligible subject matter. Instead, the claim broadly recites generating proposal probabilities via quantum channel using a generic quantum computing function (i.e., unitary operator) and performing an acceptance rule that depends on an energy function, which are steps of the well-known MCMC techniques. Furthermore, the recitation that the quantum channel is symmetric and that the acceptance probability does not depend on explicit proposal probabilities reflects a mathematical limitation on the underlying mathematical framework of the sampling algorithm. Such limitations define relationships within the probabilistic model itself, rather than reciting a technological implementation that would provide an improvement in how the quantum computer or classical computer operates. The alleged improvements are not reflected in the claim specific structural or operational limitations, but rather are asserted results of applying the described mathematical operations in the specification (i.e., MCMC).
With respect to Step 2A, Prong 2, even if the claim is considered to recite a judicial exception, the additional elements are not sufficient to integrate the judicial exception into a practical application. The additional elements, including the quantum computer and classical computer, whether considered individually or in combination, merely implement the abstract idea using generic computational components performing their ordinary functions. The recitation that the quantum channel is symmetric and that the acceptance probability does not depend on explicit proposal probabilities amounts to a mathematical limitation on the MCMC calculation, rather than an improvement to the functioning of the quantum or classical computer. Additionally, the claim does not recite specific implementation details that would demonstrate an improvement in quantum hardware operation or noise mitigation, but instead relies on the mathematical framework to achieve the alleged technical solution. Accordingly, the Examiner notes that the alleged improvement described by the applicant’s specification comes from the judicial exception itself, specifically, the mathematical framework using MCMC algorithm. As stated in the MPEP 2106.04(a), the judicial exception alone cannot provide the improvement. The improvement to computer functionality or another technology can be provided by additional elements that integrate the exception into a practical application. In this case, the additional elements are recited at a high level of generality and do not, individually or in combination, provide such an integration.
With respect to Step 2B, the additional elements, when considered individually and as an ordered combination, do not amount to significantly more than the abstract idea. The use of a quantum computer to perform unitary operation to generate proposal probabilities and measure outcomes and a classical computer to compute an acceptance probability represents the use of generic computational components to perform the abstract idea. As described in MPEP § 2106.05(f), additional elements that invoke computers or other machinery merely as a tool to perform an existing process will generally not amount to significantly more than a judicial exception. Additionally, the recited quantum elements defined in the claim such as preparing n-qubit state and unitary operator being part of a quantum channel defines generic and conventional elements in the field. Specifically, the recited generic functions have been recognized as traditional in the context of quantum computing, as evidence by Williams et. al., (US 20050167658 A1), which suggest that in the traditional model of quantum computation one prepares an n-qubit state, evolves it under the action of a unitary operator representing the desired computation, and performs measurement on the output state to obtain an answer (see Williams para. [0033]). Additionally, the claimed hybrid configuration of classical and quantum computers does not reflect a non-conventional or non-generic configuration that improves functionality of another technical field, but rather applies the abstract idea using generic computing tools. Accordingly, these generically recited elements amount to generic and conventional elements in the field and cannot amount to an inventive concept. See MPEP § 2106.05(d).
Accordingly, when viewed as whole, the claim does not qualify as patent-eligible subject matter and the rejection under 35 U.S.C. §101 is maintained.
Applicant's arguments with respect to the rejection under 35 U.S.C. § 103 filed on 02/18/2026 have been fully considered but they are not persuasive.
Applicant’s Arguments (Pp. 19-23 of the remarks):
Applicant argues that the cited references fails to teach or suggest the amended limitations of claim 1. Specifically, Applicant argues that Troyer uses “quantum walk constructions and Metropolis-Hastings discussion always assume an explicitly classical proposal kernel and an acceptance rule that depends on the ratio of those classical proposal probabilities, not on a quantum channel whose proposal probabilities are unknown to the classical side and symmetric in the sense required by the claim.” Applicant further argues that the amended claim requires a quantum channel that defines proposal probabilities, these proposal probabilities are symmetric (i.e.,
q
y
x
=
q
x
y
), and an acceptance probability that does not depend on any explicit numerical values of the proposal probabilities. Applicant contends that the cited references do not teach or suggest these claimed features.
Examiner's response: The examiner respectfully disagrees for the following reasons:
Under the broadest reasonable interpretation (BRI), the amended claim requires: a unitary operation being part of a quantum channel, proposal probabilities between configuration, symmetry of those proposal probabilities, and acceptance probability that depends on the Ising model but does not explicitly rely on numerical values of the proposal probabilities.
As described in Applicant’s specification (e.g., para. [0066], and [0078]-[0085]) and dependent claim 16, the claimed acceptance probability follows a Metropolis-Hastings framework, in which the acceptance probability formally depends on a ratio of proposal probabilities. However, when the proposal distribution is symmetric (i.e.,
q
y
x
=
q
x
y
), this ratio does not need to be computed, resulting in an acceptance probability that depends on the energy difference of the Ising model. Thus, the claimed negative limitation does not eliminate dependence on proposal probabilities altogether, but rather includes computing operation where such dependence is resolved through symmetry and therefore need not to be computed.
Troyer teaches this same concept for accelerating Markov chain Monte Carlo (MCMC) simulations on a quantum computer using quantum walks. Specifically, paragraph [0033] of Troyer discloses a two-step Markov Chain Monte Carlo process involving proposing a transition using a proposal probability and accepting or rejecting the transition based on acceptance probability.
Troyer explicitly teaches a unitary quantum walk procedure that produces transition probabilities between configurations (para. [0026]). The transformation evolves a quantum states into a superposition of states, and measurement of the quantum state yields new configuration with a probability corresponding to proposal probabilities. Paragraphs [0089] and [0101] of Troyer further teaches the quantum walk may be implemented using unary or binary encodings of move registers demonstrating that classical bootstrings configuration are represented and transformed via quantum operations.
Troyer further teaches that it is common practice to choose symmetric proposal probabilities Tyx=Txy, (para. [0034]). Under such symmetry, Troyer’s acceptance rule simplifies to an expression that does not include any explicit proposal probability terms and depends on the energy difference between configuration. Accordingly, Troyer teaches an acceptance probability that does not depend on explicit numerical values of proposal probabilities, as required by the claim. This concept is further discussed in paragraphs [0071]-[0072] of Troyer, both classical and quantum walks rely on evaluating energy differences between configurations in determining acceptance behavior. This confirms that acceptance determinations are based on the Ising model energy and not on the numerical values of transition probabilities.
Applicant’s argument that Troyer always uses explicit proposal probabilities is not supported. While proposal probabilities are part of the MCMC framework in both Troyer and the present application, both teach that when symmetry is used, the acceptance probability can be computed without using those values. Thus, the distinction drawn by the applicant’s arguments is not persuasive.
Moreover, Applicant’s argument would be inconsistent with the specification of the present application, which acknowledges that the acceptance probability depends on proposal probability ratios but simplifies under conditions of symmetry. As also taught by Troyer ([0034]), when symmetric proposal probabilities are used, the acceptance probability depends only on the energy difference between configurations. Thus, the alleged distinction that the claimed acceptance probability is independent of proposal probabilities reflects a consequence of symmetric proposal distribution.
Accordingly, Troyer, in combination with McMahon, teaches the amended limitation of independent claims 1 and 21, including the use of symmetric transition probabilities, a quantum process defining transition probabilities, and acceptance rule dependent only on energy differences.
The same reasoning and rationale applies to corresponding dependent claims 2-17, 22 and 23 that depend from parent claims 1 and 21. For at least the above reasons set forth above, Applicant’s arguments are not persuasive, and the rejection under 35 U.S.C. § 103 is maintained.
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.
When considering subject matter eligibility under 35 U.S.C. 101, it must be determined whether the claim is directed to one of the four statutory categories of invention, i.e., process, machine, manufacture, or composition of matter (Step 1). If the claim does fall within one of the statutory categories, the second step in the analysis is to determine whether the claim is directed to a judicial exception (Step 2A). The Step 2A analysis is broken into two prongs. In the first prong (Step 2A, Prong 1), it is determined whether or not the claims recite a judicial exception (e.g., mathematical concepts, mental processes, certain methods of organizing human activity). If it is determined in Step 2A, Prong 1 that the claims recite a judicial exception, the analysis proceeds to the second prong (Step 2A, Prong 2), where it is determined whether or not the claims integrate the judicial exception into a practical application. If it is determined at step 2A, Prong 2 that the claims do not integrate the judicial exception into a practical application, the analysis proceeds to determining whether the claim is a patent-eligible application of the exception (Step 2B). If an abstract idea is present in the claim, any element or combination of elements in the claim must be sufficient to ensure that the claim integrates the judicial exception into a practical application, or else amounts to significantly more than the abstract idea itself. Applicant is advised to consult MPEP 2106 for more details of the analysis.
Under Step 1 analysis,
Claims 1-17 recite a method (representing a process); and
Claims 21-23 recite a system (representing a machine).
Therefore, each set of the claims falls into one of the four statutory categories (i.e., process, machine, article of manufacture, or composition of matter).
Claims
1-17 and 21-23 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more, and hence is not patent-eligible subject matter.
Regarding Currently Amended Claim 1,
Step 2A Prong 1: The claim recites an abstract idea enumerated in the 2019 PEG.
selecting, by a classical computer, a first n-spin configuration of n ordered spins associated with the n-spin Ising model; (The “selecting” step is an abstract idea of Mental Process. Examiner’s note:, the “selecting” step, as drafted, and under its broadest reasonable interpretation (BRI), covers concepts that can practically performed in the human mind. But for the recitation of generic computer components. That is, other than reciting “by a classical computer,” nothing in the claim precludes the selecting step from practically being performed in the human mind. The process of choosing spin configuration (arrangement e.g., see [0051) associated with Ising model (e.g., mathematical model) can be practically performed in the human mind with the aid of pen and paper. This step is a mental process. See MPEP § 2106.04(a)(2)(III).)
applying a unitary operator, by the quantum computer, a unitary operator to the first n-qubit state resulting in an evolved second n-qubit state, the unitary operator being part of a quantum channel
C
E
acting on computational-basis states and defining, for each pair of classical n-bit strings x and y, a proposal probability
q
y
x
, wherein
q
y
x
is defined as a probability that, when the quantum channel
C
E
is applied to the first n-qubit state
|
x
x
|
and a resulting second n-qubit state is measured in a quantum computational basis, a measurement result is the classical n-bit string y, and wherein the quantum channel
C
E
satisfies
q
y
x
=
q
x
y
for all classical n-bit strings x and y; (An abstract idea of “a Mental Step” and/or “Mathematical Concept.” The “applying” step, as drafted, and under its broadest reasonable interpretation, covers concepts that would fall under the mental process and mathematical concept. Examiner note: this step involves mathematical transformation using unitary evolution of the quantum state but for the recitation of generic computing component. That is, other than reciting “by the quantum computer,” nothing in the claim precludes the step from being directed to an abstract idea. See MPEP § 2106.04(a)(2)(I). The unitary evolution mathematically defined as matrices and linear transformation. (see spec [0071]-[0101]). The amended limitation defines a probabilistic relationship between states. In particular, this limitation describes how transition probabilities between configurations are generated and constrained (e.g., symmetry of
q
y
x
=
q
x
y
), which represents a mathematical relationships and formulas of a transition probability function within a Markov Chain Carlo algorithm. See specification [0059]-[0068] and [0076]-[0086].)
measuring, by the quantum computer, the evolved second n-qubit state to identify a corresponding second n-spin configuration represented by a classical n-bit string y; (An abstract idea of “a Mental Step” and/or “Mathematical Concept.” The “measuring” step, as drafted, and under its broadest reasonable interpretation, covers concepts that falls under the mental process and mathematical concepts. Examiner note: this step involves mathematical/statistical formulas and calculations (see spec [0099]-[0101]). See MPEP § 2106.04(a)(2)(I).)
calculating, by the classical computer, an acceptance probability
A
y
x
to determine whether to replace the selected first n-spin configuration represented by x with the second n-spin configuration represented by y corresponding to said evolved second n-qubit state or whether to keep the selected first n-spin configuration unmodified by the applying the unitary operator to obtain an output n-spin configuration, wherein the acceptance probability
A
y
x
depends on the n-spin Ising model and not on any explicit numerical value of the proposal probabilities
q
y
x
or
q
x
y
defined by the quantum channel
C
E
. (An abstract idea of a “Mental process” and “Mathematical Concept.” The “calculating” step involves mathematical/statistical calculation and decision making process. The step requires computing an acceptance probability based on defined mathematical relationships (e.g., proposal probabilities, energy function). See spec e.g., [0065]-[0069] and [0079]. Thus, the process of performing mathematical/statistical evaluation to decide whether to accept or reject a configuration can be practically performed in the human mind with the aid of pen and paper. See MPEP § 2106.04(a)(2)(III). The recitation of “wherein the acceptance probability
A
y
x
depends on the n-spin Ising model and not on any explicit numerical value of the proposal probabilities
q
y
x
or
q
x
y
defined by the quantum channel
C
E
” is part of the abstract mathematical framework. This merely defines the acceptance probability as being computed from a mathematical relationship involving an energy-based exponential function and a ratio of proposal probabilities, which simplifies when the proposal probabilities are symmetric. The claimed limitation represent a mathematical operation in the context of statistical modeling using MCMC techniques.)
Step 2A Prong 2: Under this prong, we evaluate whether the claim recites additional elements that integrate the abstract idea into a practical application by considering the claim as a whole. The judicial exception is not integrated into a practical application.
Additional Elements Analysis:
The recitation of “by a classical computer” to select spin-configuration and calculate an acceptance probability amounts to no more than mere instructions to apply an abstract idea on a computer. Merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea, see MPEP § 2106.05(f).
The recitation of “by the quantum computer” to perform unitary transformation and quantum phase estimation amounts to no more than invoking computer and/or other machinery in its ordinary capacity merely as a tool to perform the claimed step. The claimed “quantum computer” represents the tool that is used to perform mathematical operations (e.g., unitary operation). See MPEP § 2106.05(f).
The recitation of “n-qubit state and quantum channel
C
E
” merely define the elements represented in the mathematical relationships and being applied in the quantum computing environment. This does not change the core concept of the claimed invention, specifically, the MCMC statistical modeling algorithm.
The claim further recites the limitation “preparing a first n-qubit state, on a quantum computer, that is associated with said selected first n-spin configuration, wherein each n-qubit state is associated with a unique one n-spin configuration of said n ordered spins, and the first n-qubit state is a computational-basis state
|
x
encoding a classical n-bit string x;” and “applying, applying, by the quantum computer, a unitary operator” amount to no more than mere instructions to apply an abstract idea on a computer. Merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea, see MPEP § 2106.05(f). In other words, the claim invokes computers or other machinery in its ordinary capacity (i.e., quantum computer) merely as a tool to perform an existing process. The claimed “preparing n-qubit state” and “applying a unitary operator” represent generic quantum computing functions that are recited at a high level of generality. These generic computing functions do not meaningfully limit the claim.
Step 2B: Under this prong, the claim must include additional elements that amount to significantly more than the judicial exception. These elements must not be well-understood, routine, or conventional in the relevant field. When viewed individually and as an ordered combination, the claim does not include any such additional elements that are sufficient to amount to significantly more (i.e., inventive concept).
Additional Elements Analysis:
As explained above, the recitation of using classical computer and quantum computer to apply/implement an abstract idea of mental processes and/or mathematical concepts amounts to no more than invoking generic computer and/or other machinery in their ordinary capacity merely as a tool to perform the abstract idea. Mere instructions to apply an exception cannot provide an inventive concept. See MPEP § 2106.05(f).
The recitations of “preparing a first n-qubit state, on a quantum computer” merely applies a generic computer function on a generic computer and/or other machinery in their ordinary capacity to perform an existing process. The recited generic function has been recognized as traditional in the context of quantum computation, as evidence by Williams et. al., (US 20050167658 A1), which suggest that in the traditional model of quantum computation one prepares an n-qubit state, evolves it under the action of a unitary operator representing the desired computation, and performs measurement on the output state to obtain an answer (see Williams para. [0033]). Accordingly, these generically recited steps are well-known and conventional activities in the field and cannot amount to an inventive concept. See MPEP § 2106.05(d).
Accordingly, when viewed as a whole, the claim is primarily directed to the abstract idea of sampling from a probability distribution approximating a BoHzmann distribution of an n-spin Ising model, which is defined as a mathematical model and associated calculation for determining an acceptance probability to accept or reject a proposed configuration. The additional elements, such as the recited quantum and classical computers, whether considered individually or in combination with the judicial exception, are not sufficient to integrate the judicial exception into a practical application or amount to significantly more.
Therefore, claim 1 does not recite patent-eligible subject matter.
Regarding Currently Amended Claim 2,
Step 2A Prong 1: Claim 2, which incorporates the rejection of claim 1, recites further limitation such as:
repeating the preparing, the applying, the measuring, and the calculating until said output n-spin configuration is sufficiently close to the Boltzmann distribution of said n-spin Ising model according to a defined criterion. (The added limitation merely introduces an iterative repetition and evaluation condition (i.e., determining whether the configuration is “sufficiently close”). The evaluation of convergence or closeness based on the calculation of an acceptance probability constitutes an abstract idea of a mental process—an act of evaluation (including an observation, evaluation, judgment, or opinion) that can be performed in the human mind (see MPEP § 2106.04(a)(2)(III)).)
Step 2A Prong 2: The judicial exception is not integrated into a practical application.
The recitation of iterative operation (i.e., repeating previously recited steps until sufficiently close) is a generic computer function that represents insignificant extra-solution activity to the judicial exception, as discussed in MPEP § 2106.05(g). This repetition function is recited at a high level of generality and merely directs the computer to perform the abstract idea repeatedly until a condition is met, without imposing any meaningful limit on the claim scope.
Step 2B: the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As explained above in step 2A, prong Two, the added iterative process merely defines performing repeated calculations. The recited generic function of repeating steps until convergence remains insignificant extra-solution activity, even upon reconsideration. The generic function of performing repetitive calculations has been recognized by the courts as well‐understood, routine, and conventional function (see MPEP § 2106.05(d)). Accordingly, this limitation cannot provide an inventive concept.
Therefore, claim 2 is ineligible.
Regarding Currently Amended Claim 3,
Step 2A Prong 1: Claim 3, which incorporates the rejection of claim 2, doesn’t recite an abstract idea.
Step 2A Prong 2: The judicial exception is not integrated into a practical application.
receiving, by the classical computer, coupling coefficients for spin-spin interactions between spins pairs of the n ordered spins, field coefficients local to each spin and a temperature for said n-spin Ising model, said n- spin Ising model having an energy associated with each configuration of n ordered spins. (The “receiving” step amount to adding insignificant extra-solution activity to the judicial exception, as discussed in MPEP § 2106.05(g). The claim recites a data gathering step to perform the abstract idea (i.e., mere data gathering in conjunction with an abstract idea). The claimed received data are defined as mathematical relationships and formulas. See Spec para. [0025].)
Step 2B: the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As explained above, the additional element of “receiving” the inputs representing an Ising model defines a generic computer function. This generic computer function amounts to insignificant extra-solution activity to the judicial exception (i.e., all uses of the recited judicial exception require such data gathering or data output). The courts have recognized generic computer functions such as “receiving or transmitting data over a network” and/or “storing and retrieving information in memory” as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner. See MPEP § 2106.05(d).
Therefore, claim 3 is ineligible.
Regarding Currently Amended Claim 4,
Step 2A Prong 1: Claim 4, which incorporates the rejection of claim 1, recites further limitation such as:
wherein the Boltzmann distribution of an n-spin Ising model is defined by a temperature T, a function
E
x
=
-
∑
k
>
j
=
1
n
J
j
k
x
j
x
k
-
∑
j
=
1
n
h
j
x
i
that assigns an energy value to every n-bit state x=(-1,...,±1) where
J
j
k
and
h
j
are coupling coefficients and field coefficients respectively, and where the Boltzmann distribution assigns a probability
μ
x
=
Z
-
1
e
-
E
x
T
to each n-bit state x where
Z
=
is a normalizing coefficient. (This limitation explicitly defines a mathematical formula for computing energy and probability values according to the Boltzmann distribution. The definition of the Boltzmann distribution and its associated energy function merely provides the mathematical framework for the sampling process recited in claim 1. The claimed limitation therefore recites a mathematical concepts, which is one of the enumerated categories of abstract idea identified in the 2019 PEG and MPEP § 2106.04(a)(2)(I). Specifically, the formula expresses relationships between variables using summation and exponential functions that describes a mathematical model. Accordingly, the newly added limitation is directed to a mathematical relationship and calculation that can be performed mentally or with the aid of pen and paper. See MPEP § 2106.04(a)(2)(III).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 4 is ineligible.
Regarding Currently Amended Claim 5,
Step 2A Prong 1: Claim 5, which incorporates the rejection of claim 4, recites further limitation such as:
wherein the quantum channel
C
E
defines the proposal probability
q
y
x
of proposing the evolved second n-qubit state in the quantum computational basis y starting with the first n-qubit state encoding the classical n-bit string x in the quantum computational basis that is equal to a proposal probability
q
x
y
of proposing the first n-qubit state in the quantum computational basis starting with the evolved second n-qubit state encoding the classical n-bit string y in the quantum computational basis, such that a ratio of the proposal probability
q
y
x
to the proposal probability
q
x
y
is equal to one. (The claim adds detail to the operations of “preparing the n-qubit state,” “measuring the evolved n-qubit state,” and “applying a unitary operator.” The n-qubit states corresponds to n-bit states (x,y) and measured in quantum computational basis and the unitary operator defines a quantum channel with a proposal probability symmetry (
q
y
x
=
q
x
y
). These limitations describe mathematical relationships between quantum state probabilities and transition state symmetries. Accordingly, these mathematical relationships used to approximate the Boltzmann distribution. This is part of the mathematical concept (see MPEP § 2106.04(a)(2)(I)).)
Step 2A Prong 2: The judicial exception is not integrated into a practical application.
The recitation of implementing the claimed mathematical relationships and operations on a quantum computer (state preparation, measurement, and unitary evolution) amounts to using a generic quantum computer to implement the generic quantum computational basis operation as a tool to carry out the mathematical relationships. In other words, the claim invokes computer or other machinery in their ordinary capacity merely as a tool to perform an existing process. Accordingly, the claim merely apply the identified abstract mathematical relationships on a quantum computing without integrating them into a particular technological solution. See MPEP § 2106.05(f).
Step 2B: the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As explained above in step 2A, prong Two, the claim merely applies generic quantum computer functions. In other words, the claim invokes computer or other machinery in their ordinary capacity merely as a tool to perform an existing process. The recited “preparing,” “quantum computational basis,” and “unitary operation” are generic functions in the context of quantum computing, and as evidence by Williams et. al., (US 20050167658 A1), which suggest that in the traditional model of quantum computation one prepares an n-qubit state, evolves it under the action of a unitary operator representing the desired computation, and performs measurement on the output state to obtain an answer (see Williams para. [0033]). Accordingly, this generically recited steps is well-known and conventional activity in the field and cannot amount to an inventive concept. See MPEP § 2106.05(d).
Therefore, claim 5 is ineligible.
Regarding Currently Amended Claim 6,
Step 2A Prong 1: Claim 6, which incorporates the rejection of claim 5, recites further limitation such as:
wherein the acceptance probability
A
y
x
depends on the ratio of the proposal probability
q
y
x
to the proposal probability
q
x
y
. (This limitation is part of the abstract idea recited claim 1. The claim further recites the mathematical relationship—ratio of probabilities defining a function used for determining acceptance or rejection of a new state in a probabilistic sampling algorithm. The claim is directed to the abstract idea of mathematical concepts (i.e., mathematical relationship and calculation) and mental process (i.e., decision making). See MPEP § 2106.04(a)(2)(I) & (III).)
Step 2A Prong 2: The judicial exception is not integrated into a practical application.
The recitation of “the classical computer” amounts to no more than invoking a generic computer component as a tool to perform the abstract idea (i.e., calculating the acceptance probability to determine whether to replace the input n-bit state with the output n-bit state or whether to keep the input n-bit state unmodified). See MPEP § 2106.05(f).
Step 2B: the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As explained above in step 2A, prong Two, the claim merely uses a generic computer component to perform the abstract idea. The use of generic computer to perform an abstract idea cannot provide an inventive concept.
Therefore, claim 6 is ineligible.
Regarding Currently Amended Claim 7,
Step 2A Prong 1: Claim 7, which incorporates the rejection of claim 6, recites further limitation such as:
implementing, by the quantum computer, the quantum channel
C
E
using Hamiltonian dynamics through an analog or a digital quantum simulation, which defines the proposal probability
q
y
x
and the proposal
q
x
y
.(The claim merely defines a mathematical simulation of Hamiltonian dynamics through mathematical relationships and formulas. The claim recites an abstract idea of a mathematical concepts. See MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The judicial exception is not integrated into a practical application.
The recitation of “using the quantum computer” amounts to no more than invoking computer or other machinery in their ordinary capacity as a tool to carry out the mathematical representation and formulas. See MPEP § 2106.05(f).
Step 2B: the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
As explained above in step 2A, prong Two, the claim merely uses a generic quantum computer as a tool to carry out the abstract idea (mathematical concepts).
Therefore, claim 7 is ineligible.
Regarding Currently Amended Claim 8,
Step 2A Prong 1: Claim 8, which incorporates the rejection of claim 7, recites further limitation such as:
wherein using the Hamiltonian dynamics comprises evolving a quantum state by a Hamiltonian
H
θ
=
1
-
θ
α
H
E
+
θ
H
m
i
x
, for
θ
selected within an interval from zero to one and an arbitrary scaling parameter
α
, wherein:
H
E
=
∑
x
E
x
|
x
x
|
=
-
∑
k
>
j
=
1
n
J
j
k
Z
j
Z
k
-
∑
j
=
1
n
h
j
Z
j
,
which depends on specified parameters {
J
j
k
}, {
h
j
},wherein {
J
j
k
}, {
h
j
} are, respectively, the coupling coefficients and field coefficients, wherein
Z
j
and
Z
k
are respectively Pauli
σ
z
(sigma-z) matrices on qubits j and k, and
H
m
i
x
=
∑
p
c
p
P
, where
c
p
are arbitrary real numbers and each p is a matrix from the set formed by arbitrary products of one or more of
X
j
or
Y
j
Y
k
, where
X
j
is Pauli
σ
x
(sigma-x) matrix on qubit j, and where
Y
j
and
Y
k
are Pauli
σ
y
(sigma-y) matrices on qubits j and k respectively, so that
y
H
m
i
x
|
x
∈
R
for all n-bit states x and y. (The claim explicitly defines the use of Hamiltonian dynamics through mathematical relationships and formulas. The claimed limitations therefore recite a mathematical concepts, which is one of the enumerated categories of abstract idea identified in the 2019 PEG and MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 8 is ineligible.
Regarding Currently Amended Claim 9,
Step 2A Prong 1: Claim 9, which incorporates the rejection of claim 8, recites further limitation such as:
wherein using the Hamiltonian dynamics further comprises applying an evolution by the Hamiltonian
H
(
θ
)
with time
t
for fixed values of
θ
. (This limitation is part of the abstract idea recited claim 8. The claim merely defines the variables that are used as part of the mathematical representation and calculation. See MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 9 is ineligible.
Regarding Currently Amended Claim 10,
Step 2A Prong 1: Claim 10, which incorporates the rejection of claim 9, recites further limitation such as:
wherein calculating the acceptance probability
A
y
x
comprises calculating the acceptance probability
A
y
x
using a same value
θ
and different times
t
. (This limitation is part of the abstract idea of calculating the acceptance probability using the defined values. The claim merely recites the abstract idea of mathematical concepts (i.e., mathematical calculation). See MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 10 is ineligible.
Regarding Currently Amended Claim 11,
Step 2A Prong 1: Claim 11, which incorporates the rejection of claim 6, recites further limitation such as:
wherein calculating the acceptance probability
A
y
x
comprises calculating the acceptance probability
A
y
x
using different values
θ
and different times
t
selected at random for each jump between spin configurations from pre-determined distributions. (The claim introduces the randomly selecting samples from the distribution used for calculating the acceptance probability. This limitation is part of the abstract idea of mathematical concept and mental process that can be performed in the human mind. See MPEP § 2106.04(a)(2)(I) & (III).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 11 is ineligible.
Regarding Currently Amended Claim 12,
Step 2A Prong 1: Claim 12, which incorporates the rejection of claim 8, recites further limitation such as:
wherein using the Hamiltonian dynamics comprises performing a quantum measurement in an eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
. (This limitation is part of the abstract idea of performing quantum estimation using the mathematical relationships and formulas for fixed values. The claim merely recites the abstract idea of mathematical concepts (i.e., mathematical calculation). See MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 12 is ineligible.
Regarding Currently Amended Claim 13,
Step 2A Prong 1: Claim 13, which incorporates the rejection of claim 12, recites further limitation such as:
wherein performing the quantum measurement in the eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
comprises performing a quantum phase estimation algorithm on the quantum computer using controlled exp[-iH(
θ
)
τ
]-like gates through the analog or the digital quantum simulation, wherein
τ
represents time. (The claim explicitly defines the quantum estimation using mathematical relationships and formulas. The claimed limitations therefore recite a mathematical concepts (e.g., mathematical calculation), which is one of the enumerated categories of abstract idea. See MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 13 is ineligible.
Regarding Currently Amended Claim 14,
Step 2A Prong 1: Claim 14, which incorporates the rejection of claim 8, recites further limitation such as:
wherein using the Hamiltonian dynamics comprises applying a nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
for fixed values of
θ
. (This limitation is part of the abstract idea of performing quantum estimation using the mathematical relationships and formulas for different values. The claim merely recites the abstract idea of mathematical concepts (i.e., mathematical calculation). See MPEP § 2106.04(a)(2)(I).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 14 is ineligible.
Regarding Currently Amended Claim 15,
Step 2A Prong 1: Claim 15, which incorporates the rejection of claim 14, recites further limitation such as:
wherein applying the nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
with time varying
θ
comprises applying the nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
using a reverse quantum annealing procedure, wherein θ initially equals 0 and is slowly increased to some value of at most 1, then slowly decreased back to 0 in a symmetric manner. (The claim describes a mathematical process in which the quantum state is evolved according to continuous schedule of the parameter
θ
. The “adiabatic evolution” refers to gradually changing the Hamiltonian to maintain the system in its ground state, and “reverse quantum annealing” specific a particular schedule of increasing and decreasing
θ
. Both steps define mathematical rules or algorithm that determine how to move from an initial quantum state to a target state. This process is represented mathematical using mathematical/statistical algorithm (see spec para. [0104].) This process can be performed in the human mind with the aid of pen and paper. Accordingly, the claim is directed to the abstract idea of mathematical concepts and mental processes. See MPEP § 2106.04(a)(2)(I) & (III).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 15 is ineligible.
Regarding Currently Amended Claim 16,
Step 2A Prong 1: Claim 16, which incorporates the rejection of claim 6, recites further limitation such as:
wherein calculating the acceptance probability
A
y
x
comprises calculating coefficients
a
y
x
, wherein
a
y
x
=
e
[
E
x
-
E
y
]
T
q
x
y
q
y
x
=
e
[
E
x
-
E
y
]
T
, wherein the acceptance probability satisfies
1
≥
A
y
x
=
a
y
x
A
x
y
>
0
to guarantee detailed balance, for instance
A
y
x
=
m
i
n
(
1
,
a
y
x
)
which gives a Metropolis-Hastings algorithm, or
A
y
x
=
1
+
1
a
y
x
-
1
which gives a Glauber dynamics/Gibbs sampler algorithm, wherein E(x) corresponds to an energy value in the n-spin Ising model of the first n-qubit state x and E(y) corresponds to an energy value in the n-spin Ising model of the evolved second n-qubit state y, and T corresponds to the temperature. (The claim explicitly defines the mathematical formulas and statistical calculation used to compute the acceptance probability in the context of Metropolis-Hastings and/or Glauber dynamics/Gibbs sampler algorithm. This step involves using the mathematical relationships and formulas to perform arithmetic calculation and evaluation to determine the acceptance probability. The claimed limitations therefore recite a mathematical concepts (e.g., mathematical calculation) and/or mental process (i.e., decision making), which is one of the enumerated categories of abstract idea. See MPEP § 2106.04(a)(2)(I) & (III).)
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 16 is ineligible.
Regarding Currently Amended Claim 17,
Step 2A Prong 1: Claim 17, which incorporates the rejection of claim 2, recites further limitation such as:
The claim recites similar limitations as corresponding claim 1 and merely specify that the process is repeated for another n-qubit state. Therefore, the same analysis (subject matter eligibility analysis) that was utilized for claim 1, as described above, is equally applicable to claim 17.
Step 2A Prong 2: The claim does not recite additional element that integrates the judicial exception into a practical application.
Step 2B: The claim does not recite additional elements that amount to significantly more than the judicial exception.
Therefore, claim 17 is ineligible.
Regarding New Claim 21,
The claim recites similar limitations as corresponding claim 1. Therefore, the same analysis (subject matter eligibility analysis) that was utilized for claim 1, as described above, is equally applicable to claim 21. The only difference is that claim 1 is drawn to a method, and claim 21 is drawn to a system.
Therefore, claim 21 is ineligible.
Regarding New Claim 22,
The claim recites similar limitations as corresponding claim 2. Therefore, the same subject matter eligibility analysis (including the abstract idea) that was utilized for claim 2, as described above, is equally applicable to claim 22.
Therefore, claim 22 is ineligible.
Regarding New Claim 23,
The claim recites similar limitations as corresponding claim 3. Therefore, the same subject matter eligibility analysis (including the abstract idea) that was utilized for claim 3, as described above, is equally applicable to claim 23.
Therefore, claim 23 is ineligible.
Claim Rejections - 35 USC § 103
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.
Claim(s) 1-7, 11, 16-17 and 21-23 are rejected under 35 U.S.C. 103 as being unpatentable over McMahon et al., (Pub. No.: US 20220391741 A1) in view of Troyer et al., (Pub. No.: US 20200090072 A1).
Regarding Currently Amended Claim 1,
McMahon discloses the following:
A method of sampling from a probability distribution approximating a Boltzmann distribution of an n-spin Ising model, comprising: (McMahon, [0024] FIG. 1 : A flow chart illustrated a method to simulate a classical spin model on a quantum computer using a hybrid method that uses a quantum processor (QPU) 201 and a classical processor 200, according to an embodiment. [0031] “a method to embed a classical spin model with exponentially many spins in a quantum computer. Related aspects of the disclosure are methods for initializing and manipulating spin configurations in a quantum computer; hybrid quantum-classical algorithms for evolving the spin configuration in time in a way that mimics the spin system being coupled with a thermal bath at a particular temperature T; methods for reading properties of the spin configuration (such as energy, magnetization, and correlation functions) out from the quantum computer; and methods to use the disclosed quantum embedding of a classical spin model to implement neural networks that have exponentially many neurons as a function of the number of qubits in the quantum computer.”)
selecting, by a classical computer, a first n-spin configuration of n ordered spins associated with the n-spin Ising model; (McMahon, [0077] FIG. 1 is a flow chart illustrating a method for simulating a classical spin model using a combination of a QPU (quantum processor unit) 201 and a Classical Processor 200. The Classical Processor 200 and the QPU 201 are communicatively coupled together. [0078] A spin model is input 100 to the classical processor. This model is typically specified by a Hamiltonian. [0079] The Classical Processor 200 determines an initial spin-configuration-preparation circuit to be executed on the QPU 201. [0096] “The Classical Processor 200 determines initial spin-configuration-preparation circuit to be executed on the QPU 201.”)
preparing, by a quantum computer, a first n-qubit state that is associated with said selected first n-spin configuration, wherein each n-qubit state is associated with a unique one n-spin configuration of said n ordered spins... (McMahon, [0028] FIG. 4 is an example spin-configuration-preparation circuit that prepares an Ising-model spin configuration using the sign encoding for spins. [0080] The QPU 201 executes 220 the circuit to prepare the spin configuration. [0105] “Some embodiments relate to a method for embedding a spin configuration of a classical spin model with N:=2n spins in n qubits of a quantum computer. The method comprises representing the spin configuration in a superposition state of n qubits, ..., where each amplitude αi represents the value of a classical spin.” Further see [0049].)
applying, by a quantum computer, a unitary operator to the first n-qubit state resulting in an evolved second n-qubit state,.. (McMahon, [0089] The QPU 201 performs 222 a measurement of the energy of the spin configuration 222. [0091] The Classical Processor 200 updates 213 the circuit by proposing a (e.g., random) modification (either to the circuit structure or to one of the parameters of the gates in the circuit) and the updated circuit may again be passed to the QPU 201. [0103] “FIG. 4 is an example spin-configuration-preparation circuit that prepares an Ising-model spin configuration using the sign encoding for spins. This circuit comprises Hadamard gates H followed only by Z and Controlled-Z gates. Any sequence of Z and Controlled-Z gates may produce a state that corresponds to an Ising spin configuration with sign encoding.” [0112] “A gate represents a unitary operation performed on one or more qubits. Quantum gates may be described using unitary matrices.” Further see [0051] and [0054]..) [Examiner’s Note: the evolved state is interpreted as the transformed by the controlled-U gates (i.e., unitary operation).]
measuring, by the quantum computer, the evolved second n-qubit state to identify a corresponding second n-spin configuration represented by a classical n-bit string y; (McMahon, [0081] The QPU 201 performs 221 a measurement of a macroscopic property of the spin configuration 221. The choice of macroscopic property is to be determined by the user based on their application. [0089] The QPU 201 performs 222 a measurement of the energy of the spin configuration 222. [0098] The QPU 201 performs 220 a measurement of the energy of the spin configuration. [0101] “a measurement of the spins corresponding to the variables in the original constrained problem may be performed 223.” [Examiner’s Note: measurement reveals energy and spin values of the configuration reads on the identifying spin configuration.]) and
calculating, by the classical computer, an acceptance probability
A
y
x
to determine whether to replace the selected first n-spin configuration represented by x with the second n-spin configuration represented by y corresponding to said evolved second n-qubit state or whether to keep the selected first n--spin configuration unmodified by the applying the unitary operator to obtain an output n-spin configuration, ... (McMahon, [0090] “The QPU 201 sends to the measurement result to the Classical Processor 200. The Classical Processor 200 determines 212 how to update the spin-configuration-preparation circuit based on the energy. For example, if the new energy is lower than the energy of the previous configuration, then the new spin-configuration-preparation circuit is accepted—meaning that the Classical Processor 200 updates a memory containing the spin-configuration-preparation circuit to store the new circuit. If the new energy is not lower, then the new-spin-configuration-preparation circuit is only accepted with some probability p that is typically be chosen to be <1. This procedure may be analogous to simulated annealing or related Markov Chain Monte Carlo methods used in simulations of spin systems on classical computers, where the choice of probability p can govern the effective temperature that the system is simulated at.” [0107] “The classical computer may use a Markov Chain Monte Carlo (Simulated Annealing) procedure for choosing updated variational parameters. For example, a previous update of the parameters is accepted with probability 1 if the new spin configuration's energy is lower than an artificial temperature T, and the update of parameters is accepted with probability <1 based the difference in energy and the artificial temperature T, if the new spin configuration's energy is higher.” Further see [0025] & [0090].) [Examiner’s Note: the acceptance probability is used to determine whether to accept the new spin configuration or maintain previous configuration. If accepted [Wingdings font/0xE0] memory updates new configuration and if rejected [Wingdings font/0xE0] memory is not updated and the next iteration would use the previous configuration (i.e., if the new energy is lower than the energy of the previous configuration). MCMC method, by definition, keep the current state when rejecting proposal. Thus, if rejected, logically the “previous configuration” become the “current configuration.”]
As explained above, McMahon discloses a method/system for iteratively initializing, preparing, applying, measuring, and outputting spin configuration, and described the hybrid quantum-classical algorithms for evolving the spin configuration in time to find the optimal spin configuration. Additionally, McMahon describes performing Markov-Chain-Monte-Carlo (MCMC) iterations. However, McMahon does not appear to explicitly define the repetition based on a Boltzmann distribution. McMahon does not appear to explicitly teach:
sampling from a probability distribution approximating a Boltzmann distribution of an n-spin Ising model
the first n-qubit state is a computational-basis state Ix) encoding a classical n-bit string x;
the unitary operator being part of a quantum channel
C
E
acting on computational-basis states and defining, for each pair of classical n-bit strings x and y, a proposal probability
q
y
x
, wherein
q
y
x
is defined as a probability that, when the quantum channel
C
E
is applied to the first n-qubit state
|
x
x
|
and a resulting second n-qubit state is measured in a quantum computational basis, a measurement result is the classical n-bit string y, and wherein the quantum channel
C
E
satisfies
q
y
x
=
q
x
y
for all classical n-bit strings x and y;
wherein the acceptance probability
A
y
x
depends on the n-spin Ising model and not on any explicit numerical value of the proposal probabilities
q
y
x
or
q
x
y
defined by the quantum channel
C
E
.
However, McMahon in view of Troyer teaches the following:
sampling from a probability distribution approximating a Boltzmann distribution of an n-spin Ising model (Troyer, [0016] “More generally, MCMC simulations are used in sampling from arbitrary distributions, Gibbs sampling, optimization, simulated annealing, and related methods. Quantum computers accelerate MCMC simulations by implementing them as quantum walks. In order to accomplish this acceleration, a Markov transition matrix is desirably implemented in embodiments of the disclosed technology as a walk oracle.” [0101] “the quantum walk procedure is performed using a Boltzmann coin having a coin register that is rotated using the Metropolis-Hastings rotation. In some implementations, the quantum walk procedure is performed using a Boltzmann coin having a coin register that is rotated using the Glauber dynamics rotation.”) [Examiner’s Note: Troyer teaches sampling from Boltzmann distributions defined over Ising models.]
the first n-qubit state is a computational-basis state Ix) encoding a classical n-bit string x; (Troyer, [0026] “For a classical walk W , it assumes a unitary transformation W acting on a Hilbert space
C
d
⨂
C
d
with the following action
W
|
x
⨂
|
0
=
|
w
x
⨂
|
x
=
:
|
ϕ
x
, ... . Define
∏
, the projector onto the subspace en spanned by states ...” [0036] “it will be assumed that a (k, d) local Ising model , where X = { + 1 , -1 } " [0092] “preparing a move register in a uniform superposition of all bit locations ... copying the state of the left register onto the right register, resulting in
|
ϕ
M
⨂
|
x
L
⨂
|
x
R
... conditioned on the state of the move register , flipping the j - th bit , of the left register ...”) [Note: Troyer use the initial state x as the computational basis state encoding an n-bit spin configuration through its quantum walk formulation.]
the unitary operator being part of a quantum channel
C
E
acting on computational-basis states and defining, for each pair of classical n-bit strings x and y, a proposal probability
q
y
x
, wherein
q
y
x
is defined as a probability that, when the quantum channel
C
E
is applied to the first n-qubit state
|
x
x
|
and a resulting second n-qubit state is measured in a quantum computational basis, a measurement result is the classical n-bit string y, and wherein the quantum channel
C
E
satisfies
q
y
x
=
q
x
y
for all classical n-bit strings x and y; (Troyer, [0033]-[0034] “The Metropolis-Hastings algorithm is a special class of Markov chains which obey detailed balance Eq. (1) by construction. The basic idea is to break the transition probability x→y into two steps. In a first step, a transition from x to y≠x is proposed with probability Tyx. This transition is accepted with probability Ayx, and if the transition is rejected the state remains x. ... The Metropolis-Hastings algorithm is widely used to generate a Boltzmann distribution as used in statistical physics and machine learning. Given a real energy function E(x) on the configuration space X, the Boltzmann distribution at inverse temperature β is defined as
π
x
β
=
1
Z
(
β
)
e
-
β
E
(
x
)
where the partition function Z(β) ensures normalization. In this setting, it is common practice to choose a symmetrical proposed transition Tyx=Txy, so the acceptance probability depends on the energy difference A yx=min(1,e β[|E(x)-E(y)]). (21)” [0037] “As is the case for Ising models, it will be assumed that the proposed transition of the Metropolis-Hastings walk is obtained by choosing a random set of spins and inverting their signs. In other words. Tyx=ƒ(x·y) where the product is taken bit, by bit and where ƒ(z) is a probability distribution on X−{1n} (it does not contain a trivial move), so Tyx is symmetrical.” [0101] “quantum walk procedure is performed using binary encodings of the move registers. In certain implementations, the quantum walk procedure is performed using unary encodings of the move registers. In certain implementations, the quantum walk procedure is performed using a Boltzmann coin having a coin register that is rotated using the Metropolis-Hastings rotation” Further see [0041]-[0042] and [0091]-[0101].) [Note: quantum walk is composed into components of Move preparation V, Spin Flip F, Boltzmann Coin B, and Reflection R. It prepares a superposition over all spin-flip moves, and conditionally flips the system register based on each move, producing the evolved state in the system register. Measuring this evolved state in the computational state yields the result of y, where the proposed probability Tyx defines as the proposal probability for transition x→y. The quantum implementation is further defined in para. [0092].]
wherein the acceptance probability
A
y
x
depends on the n-spin Ising model and not on any explicit numerical value of the proposal probabilities
q
y
x
or
q
x
y
defined by the quantum channel
C
E
. (Troyer, [0034] “The Metropolis-Hastings algorithm is widely used to generate a Boltzmann distribution as used in statistical physics and machine learning. Given a real energy function E(x) on the configuration space X, the Boltzmann distribution at inverse temperature β is defined as
π
x
β
=
1
Z
(
β
)
e
-
β
E
(
x
)
where the partition function Z(β) ensures normalization. In this setting, it is common practice to choose a symmetrical proposed transition Tyx=Txy, so the acceptance probability depends on the energy difference A yx=min(1,e β[|E(x)-E(y)]). (21)” [0072] “This operation is required by both classical and quantum walks, so their cost should be relatively equal. Note that one does not need the energy of a configuration E(x) directly, but more accurately, one only needs to compute the energy difference of two configurations E(x)−E(x·z).”) [Note: Troyer describes MCMC algorithm where the proposal probability is symmetric, and the proposal probability terms cancel from the acceptance ratio, where the acceptance Ayx depends only on the energy difference computed from the Ising model.]
Accordingly, at the effective filing date, it would have been prima facie obvious to one ordinarily skilled in the art to modify the method/system of McMahon to incorporate the method of operating a quantum computing device to implement a Markov Chain Monte Carlo method as taught by Troyer. One would have been motivated to make such a combination in order to efficiently implement a quantum walk oracle of an MCMC algorithm to accelerate the random walk as a quantum walk (Troyer [0016]).
Regarding Currently Amended Claim 2, McMahon in view of Troyer teaches the elements of claim 1 as outlined above, and further teaches:
McMahon in view of Troyer further teaches: further comprising repeating the preparing, the applying, the measuring, and the calculating until said output n-spin configuration is sufficiently close to the Boltzmann distribution of said n-spin Ising model according to a defined criterion. (McMahon, [0082]-[0084] “The QPU 201 sends to the measurement result to the Classical Processor 200. The Classical Processor 200 determines 210 how to update the spin-configuration-preparation circuit based on the measurement result. The Classical Processor 200 updates 211 the circuit and the updated circuit may again be passed to the QPU 201. This cycle repeats until it stops (e.g., due to a stopping condition being met). The stopping condition may, for example, be that a threshold number of iterations has been performed, or that the record of measurement results satisfies some condition (such as that the macroscopic property has not changed substantially over a certain number of iterations, e.g., it has converged). The output of the method is a record 101 of the measured macroscopic property for each iteration of the method.”) [Examiner’s Note: the claimed “sufficiently close to the Boltzmann distribution” broadly interpreted as a threshold convergence.]
Regarding Currently Amended Claim 3, McMahon in view of Troyer teaches the elements of claim 2 as outlined above, and further teaches:
further comprising receiving, by the classical computer, coupling coefficients for spin-spin interactions between spins pairs of the n ordered spins, field coefficients local to each spin and a temperature for said n-spin Ising model, said n- spin Ising model having an energy associated with each configuration of n ordered spins. (McMahon, [0027] “In FIGS. 1-3 , steps 100, 101, and 102 describe inputs and outputs of the classical processor 200. These inputs/outputs may be transmitted/received by another classical processor. Steps 104 and 105 may be performed on a classical processor, such as classical processor 200 or another classical processor.” [0062]-[0064] “this method of performing readout of energy of the spin configuration can be used for arbitrary Ising or XY-model Hamiltonians. For both the Ising and the XY models, there is a matrix J that defines the energies due to spin-spin interactions. Since both the spin state |ψ
PNG
media_image1.png
42
17
media_image1.png
Greyscale
and the state |ϕ
PNG
media_image1.png
42
17
media_image1.png
Greyscale
that the Hadamard or Swap Test are used to compute the dot product between have dimension N, the test can compute an energy for at most N spin-spin-interaction terms. However, the J matrix in general encodes N2 spin-spin interactions, so to perform energy readout for a general J matrix may require the execution of N different Hadamard or Swap Tests, using N different states |ϕ
PNG
media_image1.png
42
17
media_image1.png
Greyscale
The readout of energy from an Ising or XY model is very related to the problem of reading out correlation functions. The methods described above for reading out energies can be readily adapted to read out either individual spin-spin correlations (such as si=1sj for any choice of spin index j) or sums of spin-spin correlations ...”)
Regarding Currently Amended Claim 4, McMahon in view of Troyer teaches the elements of claim 1 as outlined above, and further teaches:
McMahon in view of Troyer further teaches: wherein the Boltzmann distribution of the n-spin Ising model is defined by a temperature T, a function
E
x
=
-
∑
k
>
j
=
1
n
J
j
k
x
j
x
k
-
∑
j
=
1
n
h
j
x
i
that assigns an energy value to every n-bit state x=(-1,...,±1) where
J
j
k
and
h
j
are coupling coefficients and field coefficients respectively, and where the Boltzmann distribution assigns a probability
μ
x
=
Z
-
1
e
-
E
x
T
to each n-bit state x where
Z
=
is a normalizing coefficient. (Troyer, [0034]-[0036] “The Metropolis-Hastings algorithm is widely used to generate a Boltzmann distribution as used in statistical physics and machine learning. Given a real energy function E(x) on the configuration space X, the Boltzmann distribution at inverse temperature β is defined as as
π
x
β
=
1
Z
(
β
)
e
-
β
E
(
x
)
where the partition function Z(β) ensures normalization. In this setting, it is common practice to choose a symmetrical proposed transition Tyx=Txy, so the acceptance probability depends on the energy difference A yx=min(1,e β[|E(x)-E(y)]). (21) Quantum algorithms built from quantitation of classical walks usually assume an oracle formulation of the walk operator, where the ability to implement the transformation W of Eq. (2) is taken for granted. As is discussed below, this transformation requires costly arithmetic operations. One of the many innovations in this disclosure is to provide a detailed and simplified implementation of a walk operator along with a detailed cost analysis for Metropolis-Hastings walks. Some example embodiments of the disclosed technology circumvent the use of W altogether. For concreteness, it will be assumed that a (k,d)-local Ising model, where X={+1, −1}n, and the energy function takes a simple form … where Ωl are subsets of at most k Ising spins and the Jl are real coupling constants, and each spin interacts with at most d other spins.”)
Regarding Currently Amended Claim 5,
McMahon in view of Troyer teaches the elements of claim 4 as outlined above, and further teaches:
wherein the quantum channel
C
E
defines the proposal probability
q
y
x
of proposing the evolved second n-qubit state in the quantum computational basis y starting with the first n-qubit state encoding the classical n-bit string x in the quantum computational basis that is equal to a proposal probability
q
x
y
of proposing the first n-qubit state in the quantum computational basis starting with the evolved second n-qubit state encoding the classical n-bit string y in the quantum computational basis, such that a ratio of the proposal probability
q
y
x
to the proposal probability
q
x
y
is equal to one. (Troyer, [0025] “A classical walk is defined on a d-dimensional state space X={x} by a d×d transition matrix
PNG
media_image2.png
38
42
media_image2.png
Greyscale
where the transition probability x→y is given by matrix element
W
y
x
. Thus, the walk maps the distribution py to the distribution
p
'
y
=
Σ
x
W
y
x
,
or in matrix form
p
'
=
W
p
. A walk is ergodic or irreducible if every state in X is accessible from every other state in X, which implies the existence of a unique equilibrium distribution π=Wπ. Finally, a walk is reversible if it obeys the detailed balance condition
W
y
x
π
x
=
W
x
y
π
y
.
One can now explain how to quantize an reversible classical walk W. [0033]-[0034] “The Metropolis-Hastings algorithm is a special class of Markov chains which obey detailed balance Eq. (1) by construction. The basic idea is to break the transition probability x→y into two steps. In a first step, a transition from x to y≠x is proposed with probability
T
y
x
. This transition is accepted with probability
A
y
x
, and if the transition is rejected the state remains x. .... In this setting, it is common practice to choose a symmetrical proposed transition
T
y
x
=
T
x
y
, so the acceptance probability depends on the energy difference ... [0037] “... it will be assumed that the proposed transition of the Metropolis-Hastings walk is obtained by choosing a random set of spins and inverting their signs. In other words.
T
y
x
=ƒ(x·y) where the product is taken bit, by bit and where ƒ(z) is a probability distribution on X−{1n} (it does not contain a trivial move), so
T
y
x
is symmetrical.”) [Examiner’s Note: Troyer teaches a quantum unitary/channel that encodes the proposal probabilities
T
y
x
of moving from state x to state y. Troyer suggest that it is common to choose a symmetrical
T
y
x
=
T
x
y
(i.e., the ratio of the proposal probability qyx to the proposal probability qxy is equal to one). The sequence of quantum walk transition with symmetric proposal probability reads on the “quantum Channel
C
E
.”]
Regarding Currently Amended Claim 6,
McMahon in view of Troyer teaches the elements of claim 5 as outlined above, and further teaches:
McMahon in view of Troyer Further teaches: wherein the acceptance probability
A
y
x
depends on the ratio of the proposal probability
q
y
x
to the proposal probability
q
x
y
. (Troyer, [0033]–[0034] “The Metropolis-Hastings algorithm is a special class of Markov chains which obey detailed balance Eq. (1) by construction. The basic idea is to break the transition probability x→y into two steps. In a first step, a transition from x to y≠x is proposed with probability
T
y
x
. This transition is accepted with probability
A
y
x
, and if the transition is rejected the state remains x. .... it is common practice to choose a symmetrical proposed transition
T
y
x
=
T
x
y
, so the acceptance probability depends on the energy difference ...”)
Regarding Currently Amended Claim 7,
McMahon in view of Troyer teaches the elements of claim 6 as outlined above.
McMahon in view of Troyer further teaches: further comprising implementing, by the quantum computer, the quantum channel
C
E
using Hamiltonian dynamics through an analog or a digital quantum simulation, (McMahon, [0052] “If a given spin model has constraints on the values that the spins can take (e.g., as may arise when considering a binary-variable optimization problem that has constraints on the binary variables, and where the objective function of the optimization problem is given as an Ising Hamiltonian), it is possible to design the quantum circuit that creates the quantum state representing a spin configuration in such a way that any created spin configuration is guaranteed to satisfy the constraints associated with the Hamiltonian.” [0073] “By being able to prepare spin configurations efficiently using variational ansatzes with moderate numbers of parameters, and by being able to read out the energy of a prepared spin configuration, one has the ingredients to perform a hybrid algorithm that operates partially on a quantum computer and partially on a classical computer (also referred to as a non-quantum computer or a classical processor) to either optimize (e.g., minimize) the energy of a given spin Hamiltonian, or to compute thermal properties of the Hamiltonian at a particular temperature T. For the thermal-property-calculation use case, a Markov-Chain-Monte-Carlo-style algorithm (such as Simulated Annealing) may be applied in which an artificial temperature T is introduced and is used to control the probability of accepting a change to the variational ansatz's parameters, which in turn change the spin configuration (e.g., see FIG. 2 ).”) which defines the proposal probability
q
y
x
and the proposal probability
q
x
y
. (Specifically, Troyer teaches the symmetry of proposed transition probabilities (
T
y
x
=
T
x
y
) for states x and y of the Hamiltonian Ising model using quantum computing device.)
Regarding Currently Amended Claim 11, McMahon in view of Troyer teaches the elements of claim 6 as outlined above, and further teaches:
wherein calculating the acceptance probability
A
y
x
comprises calculating the acceptance probability
A
y
x
using different values
θ
and different times
t
selected at random for each jump between spin configurations from pre-determined distributions. (Troyer, [0037]-[0038] “it will be assumed that the proposed transition of the Metropolis-Hastings walk is obtained by choosing a random set of spins and inverting their signs. In other words. Tyx=ƒ(x·y) where the product is taken bit, by bit and where ƒ(z) is a probability distribution on X−{1n} (it does not contain a trivial move), so Tyx is symmetrical. The distribution ƒ(z) is sparse, in the sense that it has only N<<2n non-zero entries. ... It will be supposed that ƒ is uniform over some set M of moves, ... One example comprises single-spin moves, where a single spin is chosen uniformly at random to be flipped.” [0047]-[0049] “ In more detail, the Boltzmann coin is a component that desirably uses rotations of arbitrary angles. For example, conditioned on move qubit j being 1 and the system register being in state r, the coin register undergoes a rotation by an angle θx,j=arcsin(√{square root over (min{e −βΔ j (x),1})} (30) for Metropolis-Hastings or … for Glauber dynamics, where Δk=E(x·zj)−E(x). Given the sparsity constraints of the function E and of the moves zj∈
M
, the quantity Δj can be evaluated from a subset of qubits of the system register, namely
N
=
{
k
:
k
∈
Ω
l
&
z
j
∩
Ω
l
≠
Ø
,
∀
l
}
. For single-spin flips on a (k,d)-local Hamiltonian.” [0063] “a protocol was proposed where each unitary was applied a random number of times. The motivation for these randomized transformations was to phase randomize in the eigenbasis of the instantaneous unitary operator. When the spectral gap of a unitary operator is 6 and that unitary is applied a random number of times in the interval ...” [0071] “Indeed, when implementing a single step of the classical walk operator W, a spin transition x→x·z is chosen with probability ƒ(z), the acceptance probability is computed, and the move is either accepted or rejected. Each transition x→x·z typically involve only a few spins (one in the setting that is being currently considering), so implementing such a transition in the classical walk does not require al extensive number of gates. The complexity in that case is actually dominated by the generation of a pseudo-random number selecting the location of the spin to be flipped.”) [Examiner’s Note: Each jump (transition) from x[Wingdings font/0xE0]y involves a randomly chosen move (i.e., random set of spins) drawn from a pre-determined distribution f(z). The acceptance probability depends on rotation angle (see Eq. (30)) that vary per transition depending on local energy differences and parameters such as β. Thus, these angles serve as randomly varying with each jump (transition).]
Regarding Currently Amended Claim 16, McMahon in view of Troyer teaches the elements of claim 6 as outlined above, and further teaches:
wherein calculating the acceptance probability
A
y
x
comprises calculating coefficients
a
y
x
, wherein
a
y
x
=
e
[
E
x
-
E
y
]
T
q
x
y
q
y
x
=
e
[
E
x
-
E
y
]
T
, wherein the acceptance probability satisfies
1
≥
A
y
x
=
a
y
x
A
x
y
>
0
to guarantee detailed balance, for instance
A
y
x
=
m
i
n
(
1
,
a
y
x
)
which gives a Metropolis--Hastings algorithm, or
A
y
x
=
1
+
1
a
y
x
-
1
which gives a Glauber dynamics/Gibbs sampler algorithm, wherein E(x) corresponds to an energy value in the Ising model of the first n-bit state x and E(y) corresponds to an energy value in the n-spin Ising model of the evolved second n-qubit state y, and T corresponds to the temperature. (Troyer, [0033]-[0034] “The Metropolis-Hastings algorithm is a special class of Markov chains which obey detailed balance Eq. (1) by construction. The basic idea is to break the transition probability x→y into two steps. In a first step, a transition from x to y≠x is proposed with probability Tyx. This transition is accepted with probability Ayx, and if the transition is rejected the state remains x. The overall transition probability is thus (see Eq.(17)) The detailed balance condition Eq. (1) becomes Rxy:=AyxAxy= (See Eq. (18)) which in the Metropolis-Hastings algorithm is solved with the choice A yx=min(1,R xy). (19) One can note that the quantum algorithm can also be applied to the Glauber. or heat-bath, choice
A
y
x
=
1
1
+
R
y
x
. (20) … In this setting , it is common practice to choose a symmetrical proposed transition Tyx = Txy , so the acceptance probability depends on the energy difference
A
y
x
=
m
i
n
(
1
,
e
β
[
|
E
x
-
E
y
]
)
.” [0037] “As is the case for Ising models, it will be assumed that the proposed transition of the Metropolis-Hastings walk is obtained by choosing a random set of spins and inverting their signs. In other words. Tyx=ƒ(x·y) where the product is taken bit, by bit and where ƒ(z) is a probability distribution on X−{1n} (it does not contain a trivial move), so Tyx is symmetrical. The distribution ƒ(z) is sparse, in the sense that it has only N<<2n non-zero entries.” Further see [0047].)
Regarding Currently Amended Claim 17, McMahon in view of Troyer teaches the elements of claim 2 as outlined above, and further teaches:
Claim 17 recites steps substantially similar to those of claim 1, with the addition that another n-qubit state is defined and processed as part of an iterative Markov-chain or Monte Carlo sampling procedure. McMahon in view of Troyer of another n-qubit state as part of the iterative process of the hybrid quantum-classical algorithms using a Markov Chain Monte Carlo procedure. (McMahon [0091] “ This cycle repeats until it stops (e.g., due to a stopping condition being met). The stopping condition may, for example, be that a threshold number of iterations has been performed, or that the record of measured energies satisfies some condition (such as that the energy has not changed substantially over a certain number of iterations, e.g., it has converged).”)
Regarding New Claim 21,
The claim recites substantially similar limitations as corresponding claim 1 and is rejected for similar reasons as claim 1 using similar teachings and rationale. Claim 1 is directed to a method, and claim 21 is directed to a system.
McMahon also discloses a computing system. (McMahon, [0105] “The method may be performed by a computing system (e.g., including a quantum processor (e.g., QPU 201) and a classical processor (e.g., 200)) that executes instructions stored on a non-transitory computer-readable storage medium.”)
Regarding New Claim 22,
The claim recites substantially similar limitations as corresponding claim 2 and is rejected for similar reasons as claim 2 using similar teachings and rationale.
Regarding New Claim 23,
The claim recites substantially similar limitations as corresponding claim 3 and is rejected for similar reasons as claim 3 using similar teachings and rationale.
Claim(s) 8-10 and 14 are rejected under 35 U.S.C. 103 as being unpatentable over McMahon in view of Troyer as described above, and further in view of Amin et al., (Pub. No.: US 20180196780 A1).
Regarding Currently Amended Claim 8,
McMahon in view of Troyer teaches the elements of claim 7 as outlined above.
McMahon further teaches:
Wherein:
H
E
=
∑
x
E
x
|
x
x
|
=
-
∑
k
>
j
=
1
n
J
j
k
Z
j
Z
k
-
∑
j
=
1
n
h
j
Z
j
,
which depends on specified parameters {
J
j
k
}, {
h
j
},wherein {
J
j
k
}, {
h
j
} are, respectively, the coupling coefficients and field coefficients, wherein
Z
j
and
Z
k
are respectively Pauli
σ
z
(sigma-z) matrices on qubits j and k, (McMahon, [0032] “The Ising model is defined by a set of N spins, {si}, and a Hamiltonian (energy function) H=−Σ1≤i<j≤NJijsisj−Σ1≤i≤Nhisi, where si represents the value of the ith spin and takes a value of either −1 or +1, Jij represents the coupling between the ith and jth spins, and hi represents the external field applied to the ith spin. The XY model is defined by a set of N spins,
{
s
i
⃑
}
, and a Hamiltonian H=−Σ1≤i<j≤NJij
s
i
⃑
h
i
⃑
−Σ1≤i≤N
h
i
⃑
s
i
⃑
, represents the value of the ith spin and is a two-dimensional vector with unit length.” [0062] “ For both the Ising and the XY models, there is a matrix J that defines the energies due to spin-spin interactions.” [0051] “start with all qubits in the state 0 in the computational basis, apply the Hadamard gate to each qubit, and then apply only Z (single-qubit) gates and, Controlled-Z (two-qubit) gates (e.g., see FIG. 4 ).”) and
H
m
i
x
=
∑
p
c
p
P
, where
c
p
are arbitrary real numbers and each p is a matrix from the set formed by arbitrary products of one or more of
X
j
or
Y
j
Y
k
, where
X
j
is Pauli
σ
x
(sigma-x) matrix on qubit j, and where
Y
j
and
Y
k
are Pauli
σ
y
(sigma-y) matrices on qubits j and k respectively, so that
y
H
m
i
x
|
x
∈
R
for all n-bit states x and y. (McMahon, [0037]-[0042] “However, by allowing αi to take arbitrary real values, more complex spin dynamics can be implemented (which in the case of optimization can support a mean-field-annealing implementation). 2.) a magnitude encoding, where αi can be a real or a complex number, and we use the magnitude of αi to encode the spin value. For example, a threshold value t can be chosen that is a real number between 0 and 1, and if |αi|<t then the ith spin has value si=−1, and if |αi|>t then the ith spin has value si=+1. For Ising spin models, the preferred encoding may be the sign encoding. 1.) a phase encoding, where αi is set to be a complex number and angle (αi) determines the spin value. For example, we can set θi=angle (αi). 2.) a magnitude encoding, where αi is set to be a real or a complex number, and we use the magnitude of αi to encode the spin value. For example, we can set θi=2π|αi|/|αmax|, where |αmax| is the maximum value that |αi| can take.” [0065] “As a concrete example of energy readout for an XY model, if the phase encoding is used, then the dot product
ϕ
ψ
between
|
ψ
and
|
ϕ
=C Σi=0 N−1 Jiαi+1|
i
is a complex number whose real part is Re[
ϕ
ω
]∝Σi=0 N−1 Ji cos(θi+1−θi). This quantity, Re[
ϕ
ψ
], can be read out using a Hadamard Test. This is precisely the energy of the nearest-neighbor interactions in the XY model. As has been explained for the Ising model, by appropriate choice and construction of
|
ϕ
, different sums of energy terms from the XY model can be read out.”) [Examiner’s Note: the inner dot product for the matrix for the x and y spin-spin-interaction reads on the claimed mixing Hamiltonian.]
While McMahon defines the Hamiltonian as energy function and X/Y spin interactions. McMahon in view of Troyer does not appear to explicitly teach:
wherein using the Hamiltonian dynamics comprises evolving a quantum state by a Hamiltonian
H
θ
=
1
-
θ
α
H
E
+
θ
H
m
i
x
, for
θ
selected within an interval from zero to one and an arbitrary scaling parameter
α
,
However, Amin, in combination with McMahon in view of Troyer, teaches the limitations:
wherein using the Hamiltonian dynamics comprises evolving a quantum state by a Hamiltonian
H
θ
=
1
-
θ
α
H
E
+
θ
H
m
i
x
, for
θ
selected within an interval from zero to one and an arbitrary scaling parameter
α
, wherein:
H
E
=
∑
x
E
x
|
x
x
|
=
-
∑
k
>
j
=
1
n
J
j
k
Z
j
Z
k
-
∑
j
=
1
n
h
j
Z
j
,
which depends on specified parameters {
J
j
k
}, {
h
j
},wherein {
J
j
k
}, {
h
j
} are, respectively, the coupling coefficients and field coefficients, wherein
Z
j
and
Z
k
are respectively Pauli
σ
z
(sigma-z) matrices on qubits j and k, and
H
m
i
x
=
∑
p
c
p
P
, where
c
p
are arbitrary real numbers and each p is a matrix from the set formed by arbitrary products of one or more of
X
j
or
Y
j
Y
k
, where
X
j
is Pauli
σ
x
(sigma-x) matrix on qubit j, and where
Y
j
and
Y
k
are Pauli
σ
y
(sigma-y) matrices on qubits j and k respectively, so that
y
H
m
i
x
|
x
∈
R
for all n-bit states x and y. (Amin, [0019]-[0020] “A Hamiltonian is an operator whose eigenvalues are the allowed energies of the system. Adiabatic quantum computation can include evolving a system from an initial Hamiltonian to a final Hamiltonian by a gradual change. One example of adiabatic evolution is a linear interpolation between the initial Hamiltonian Hi and the final Hamiltonian Hf, as follows: H e=(1−s)H i +sH f (4) where He is the evolution, or instantaneous, Hamiltonian, and s is an evolution coefficient that can control the rate of evolution. As the system evolves, the evolution coefficient s changes value from 0 to 1. At the start, the evolution Hamiltonian He is equal to the initial Hamiltonian Hi, and, at the end, the evolution Hamiltonian He is equal to the final Hamiltonian Hf.” [0026] “An objective function, such as an optimization problem, can be encoded in a problem Hamiltonian HP, and the method can introduce quantum effects by adding a disordering Hamiltonian HD that does not commute with the problem Hamiltonian HP. An example case is as follows: H E =A(t)H D B(t)H P (6) where A(t) and B(t) are time-dependent envelope functions. For example, A(t) can be a function that changes from a large initial value to substantially zero during the evolution.” [0095]-[0099] In quantum Monte Carlo (QMC) simulation, the quantum statistics are reproduced by Monte Carlo sampling from trajectories (paths) x(τ) along the imaginary time dimension τϵ[0,β]. Monte Carlo updates change the trajectory x→x′, which can be represented by a transition matrix Pθ[x(τ)|x′(τ)] that satisfied the stationary condition P θ [x(τ)]=∫D[x′(τ)]P θ [x(τ)|x′(τ)]P θ [x′(τ)] (14). ... Quantum annealing can be implemented in a physical quantum annealer such as an adiabatic quantum computer . In some implementations , the physical quantum annealer implements the following Hamiltonian :
H
(
s
)
=
-
A
s
∑
i
σ
i
x
+
B
s
[
∑
i
h
i
σ
i
z
+
∑
i
h
i
,
j
σ
i
z
σ
j
z
]
(15) where hi and Jij are tunable or programmable parameters , and A ( s ) and B ( s ) are monotonic functions of an annealing parameter s, where 0≤s≤1, A(0)>>B(0)≈0 and B(1)>>A(1)≈0.)
Therefore, it would have been prima facie obvious to one of ordinary skill in the art, before the effective date of the claimed invention, having the combination of McMahon, Troyer, and Amin to incorporate the re-Equilibrated Quantum Sampling techniques as taught by Amin. One would have been motivated to make such a combination in order to provide a broad-scale update operator in an MCMC method sampling from classical and/or quantum Boltzmann distribution. Doing so would improve the performance of the MCMC method (Amin [0072]).
Regarding Currently Amended Claim 9, the combination of McMahon, Troyer, and Amin teaches the elements of claim 8 as outlined above, and further teaches:
wherein using the Hamiltonian dynamics further comprises applying an evolution by the Hamiltonian
H
(
θ
)
with time
t
for fixed values of
θ
. (Amin, [0020] “As the system evolves, the evolution coefficient s changes value from 0 to 1. At the start, the evolution Hamiltonian He is equal to the initial Hamiltonian Hi, and, at the end, the evolution Hamiltonian He is equal to the final Hamiltonian Hf.” [0116]-[0117] “From 212 to 222, method 200 iterates over linear increments of counter i.At 212, the at least one digital processor programs the at least one analog processor so that the at least analog processor evolves from a value s=1 to a value si* of the annealing parameter s within a time tramp, where si* and tramp where determined at 206 and 208, respectively.” [0187] “denoting the evolution from s=1 to s=s* over time tramp as U1→s* PQA(tramp):Z→Ψ and denoting the evolution from s=s* to s=1 over time tramp as Us*→1 PQA(tramp):Ψ→Z, where Z is the space of classical states. [0197] At 606, classical state z is reverse annealed (e.g. via a ramp operation over time tramp) from s=1 to s=s* in the evolution to yield quantum state ψ. This reverse annealing may be executed by a physical quantum annealer.”)
Regarding Currently Amended Claim 10, the combination of McMahon, Troyer, and Amin teaches the elements of claim 9 as outlined above, and further teaches:
wherein calculating the acceptance probability
A
y
x
comprises calculating the acceptance probability
A
y
x
using a same value
θ
and different times
t
. (Amin, [0013] “The Markov chain can be obtained by proposing a new point according to a Markovian proposal process (generally referred to as an “update operation”). The new point is either accepted or rejected. If the new point is rejected, then a new proposal is made, and so on. New points that are accepted are ones that make for a probabilistic convergence to the target distribution. Convergence is guaranteed if the proposal and acceptance criteria satisfy detailed balance conditions and the proposal satisfies the ergodicity requirement. Further, the acceptance of a proposal can be done such that the Markov chain is reversible, i.e., the product of transition rates over a closed loop of states in the chain is the same in either direction. A reversible Markov chain is also referred to as having detailed balance. Typically, in many cases, the new point is local to the previous point.” [0190] “Accelerating the annealing rate may involve, for example, relaxing one or more proposal acceptance criteria.” [0199]-[0201] “At 610, re-equilibrated quantum state ψ′ is forward-annealed (e.g. via a ramp operation over time tramp, which may be the same as or different than the time period of reverse-annealing act 606) s=s* to s=1. ... At 612, re-equilibrated classical state z′ is reverse-annealed from s=1 to s=s* to yield re-equilibrated intermediate state x′. This reverse-annealing may be performed, for example, by a classical computer implementing the same or a similar method to the MCMC method of act 604 (subject to any changes involved in reversing the annealing and, optionally, using a different annealing rate). ... At 614, re-equilibrated classical state x′ is used as a basis for an update proposal for the MCMC method which generated intermediate state x. For instance, the MCMC method may use re-equilibrated intermediate state x′ as an update proposal with or without further post-processing and/or other modification. The resulting update proposal may be accepted or rejected according to the criteria of MCMC method.”)
Regarding Currently Amended Claim 14, McMahon in view of Troyer teaches the elements of claim 8 as outlined above.
While McMahon in view of Troyer disclose the use of Adiabatic State Preparation, McMahon in view of Troyer does not appear to explicitly teach:
wherein using the Hamiltonian dynamics comprises applying a nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
with time varying
θ
.
However, Amin, in combination with McMahon and Troyer, teaches the limitation:
wherein using the Hamiltonian dynamics comprises applying a nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
with time varying
θ
. (Amin, Adiabatic Quantum Computation [0019] A Hamiltonian is an operator whose eigenvalues are the allowed energies of the system. Adiabatic quantum computation can include evolving a system from an initial Hamiltonian to a final Hamiltonian by a gradual change. One example of adiabatic evolution is a linear interpolation between the initial Hamiltonian Hi and the final Hamiltonian Hf ...” [0027] “In this respect, quantum annealing can be similar to adiabatic quantum computation in that the system starts with an initial Hamiltonian, and evolves through an evolution Hamiltonian to a final problem Hamiltonian HP whose ground state encodes a solution to the problem.” [0100] “In some implementations, the annealing parameters is varied linearly with time t: s(t)=t/ta, where ta is the annealing time. Alternatively, or in addition, the annealing parameter s may be varied non-linearly with time.”)
The same motivation that was utilized for combining McMahon, Troyer, and Amin, as set forth in claim 8, is equally applicable to claim 14.
Claim(s) 12 is rejected under 35 U.S.C. 103 as being unpatentable over the combination of McMahon, Troyer, and Amin as outlined above, further in view of Babbush et al., (Pub. No.: US 20210174236 A1).
Regarding Currently Amended Claim 12, the combination of McMahon, Troyer, and Amin teaches the elements of claim 8 as outlined above.
McMahon in view of Troyer does not appear to explicitly teach:
wherein using the Hamiltonian dynamics comprises performing a quantum measurement in an eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
.
However, Babbush, in combination with McMahon, Troyer, and Amin, teaches the limitations:
wherein implementing Hamiltonian dynamics comprises performing a quantum measurement in the eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
. (Babbush, [0006]-[0007] “In some implementations variationally adjusting the intermediate state to determine a wavefunction that approximates the target quantum state of the quantum system comprises: defining a variational ansatz wavefunction dependent on one or more variational parameters as being equal to the action of a parameterized quantum circuit applied to the intermediate state; performing a variational algorithm using the defined variational ansatz wavefunction to determine fixed values of the one or more variational parameters; and using the fixed values of the one or more variational parameters to define the wavefunction that approximates the target quantum state of the quantum system. In some implementations the fixed values of the one or more variational parameters minimize an energy expectation of the target Hamiltonian.” [0051]- [0052] “The system performs a variational algorithm to determine an optimized set of variational parameters θ optimal (step 210). The system repeatedly applies the parameterized quantum circuit U({right arrow over (θ)}) to the intermediate quantum state |ψn Figure ... and measures the quantum system using the target Hamiltonian as an observable to determine an energy expectation value. The system then performs a classical optimization with respect to the variational parameters to determine a minimizing set of parameters θ optimal that minimizes the energy expectation of the target Hamiltonian. ... Determining properties about the quantum system or an approximate solution to the optimization task may include measuring the approximation to the target quantum state, e.g., to determine an energy eigenvalue.”)
Accordingly, it would have been obvious to a person having ordinary skill in the art, before the effective filing date of the claimed invention, having the combination of McMahon, Troyer, Amin, and Babbush before them, to incorporate the variational quantum state preparation method as taught by Babbush. One would have been motivated to make such a combination in order to determine an approximate solution to the optimization task. Thus, preparing quantum states of respective quantum systems may be computationally more efficient compared to other systems and methods for preparing quantum states of respective quantum systems (Babbush [0019]).
Claim(s) 13 is rejected under 35 U.S.C. 103 as being unpatentable over the combination of McMahon, Troyer, Amin, and Babbush as outlined above, and further in view of Temme et al., (NPL: “Quantum Metropolis Sampling.” (2010)).
Regarding Currently Amended Claim 13,
the combination of McMahon, Troyer, and Babbush teaches the elements of claim 12 as outlined above, and further teaches:
Babbush further teaches: wherein performing the quantum measurement in the eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
comprises performing a quantum phase estimation algorithm on the quantum computer ... through the analog or the digital quantum simulation, wherein
τ
represents time. (Babbush, [0028] “One example technique for preparing or solving for a target quantum state of a given quantum system includes adiabatic quantum state preparation. Adiabatic quantum state preparation is a method for determining a target ground state of a quantum system using the adiabatic theorem. The time evolution of a quantum system is governed by a Hamiltonian that interpolates between an initial Hamiltonian, whose ground state is known and easy to construct or determine, and a final Hamiltonian, whose ground state is the target ground state. To ensure that the quantum system evolves to the target ground state, the quantum system must evolve for a period of time that depends on a minimum energy difference between the two lowest eigenstates of the interpolating Hamiltonian.” [0041] “The quantum hardware 102 can evolve an eigenstate, e.g., the ground state, of the initial Hamiltonian according to the truncated time evolution operator for a predetermined number of time steps to generate an intermediate quantum state of the quantum system.” [0046]-[0047] “The system approximates the time evolution of the total Hamiltonian using a truncated Taylor series to generate a truncated time evolution operator (step 206). The system evolves an eigenstate, e.g., the ground state, of the initial Hamiltonian according to the truncated time evolution operator for a predetermined number of time steps n to generate an intermediate quantum state |ψn (step 208). More specifically, the system evolves an eigenstate of the initial Hamiltonian corresponding to the target quantum state of the target Hamiltonian, e.g., if the target quantum state is a ground state of the target Hamiltonian the system evolves a ground state of the initial Hamiltonian. Evolving the eigenstate of the initial Hamiltonian according to the truncated time evolution operator for a predetermined number of time steps can include performing a quantum simulation or quantum computation that realizes the action of the truncated time evolution operator for the predetermined number of steps.”)
While Babbush discloses the quantum measurement in eigenbasis of the target Hamiltonian including performing a quantum simulation (using linear combinations of unitaries simulations of time evolution). The combination of McMahon, Troyer, and Babbush does not appear to explicitly teach:
wherein performing the quantum measurement in the eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
comprises performing a quantum phase estimation algorithm on the quantum computer using controlled exp[-iH(
θ
)
τ
]-like gates through analog or digital quantum simulation, wherein
τ
represents time.
However, Temme, in combination with McMahon, Troyer, and Babbush, teaches the limitations:
wherein performing the quantum measurement in the eigenbasis of the Hamiltonian
H
(
θ
)
for fixed values of
θ
comprises performing a quantum phase estimation algorithm on the quantum computer using controlled exp[-iH(
θ
)
τ
]-like gates through the analog or the digital quantum simulation, wherein
τ
represents time. (Temme, [P. 9, Section: 4] “We therefore need to investigate the fixed point of the actual completely positive map that is generated by the circuit. We will see that the quantum Metropolis algorithm yields the exact Gibbs state as its fixed point, if the quantum phase estimation algorithm resolves the energies of all eigenstates exactly. ... Simulation errors. The quantum phase estimation algorithm requires implementing the dynamics U = e −iHt generated by the system’s Hamiltonian for various times t. This can only be done within a finite accuracy. Phase estimation fluctuations. As seen in Eq. (71), given an energy eigenstate of the system, the quantum phase estimation procedure outputs a random r-bit estimate of the corresponding energy. The output distribution is highly peaked around the true energy, but fluctuations are important and cannot be ignored.” [P. 20 Section: 5] “In this section we describe how to efficiently implement the quantum gates required by our algorithm on a quantum computer. ... The first nontrivial operation required by our procedure is a means to simulate the unitary dynamics e −itH generated by a k-particle Hamiltonian H. We assume that H can be written as the sum of s terms, each of which is easy to simulate on a quantum computer. The best way to do this follows the method described by Berry et. al. [19] and by Childs [31]: this procedure provides a simulation of the dynamics e −itH using a quantum circuit of length TH, ... Thus we can simulate e −itH for a length of time t ∼ p(N) and to precision ǫH ∼ 1/q(N) with an effort scaling polynomially with N, where p and q are polynomials. The next operation required by our algorithm is a method to measure the observable H. This can be done by making use of the quantum phase estimation [17, 18], which is a discretization of von Neumann’s prescription to measure a Hermitian observable. ... Supposing that |ψi is an eigenstate |ψj i of H we find that the system evolves to (see Eq. (0065)) A measurement of the position of the pointer with sufficiently high accuracy will provide an approximation to Ej . To carry out the above operation efficiently on a quantum computer we discretize the pointer using r qubits, replacing the continuous quantum variable with a 2 r -dimensional space, where the computational basis states |zi of the pointer represent the basis of momentum eigenstates of the original continuous quantum variable.”)
Accordingly, it would have been obvious to a person having ordinary skill in the art, before the effective filing date of the claimed invention, having the combination of McMahon, Troyer, Amin, Babbush, and Temme to incorporate the quantum Metropolis sampling method as taught by Temme. One would have been motivated to implement a quantum version of the Metropolis algorithm on a quantum computer (Temme [Abstract]).
Claim(s) 15 is rejected under 35 U.S.C. 103 as being unpatentable over the combination of McMahon, Troyer, and Amin as outlined above, and further in view of Reinhardt et al., (Pub. No.: US 20180218281 A1).
Regarding Currently Amended Claim 15, the combination of McMahon, Troyer, and Amin teaches the elements of claim 14 as outlined above, and further teaches:
wherein applying the nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
with time varying
θ
comprises applying the nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
using a reverse quantum annealing procedure, (Amin, [0109] “FIG. 2 is a flow chart illustrating a method 200 for operating a hybrid computing system including at least one digital processor and at least one analog processor with a fast ramp operation and a reverse annealing operation for generating equilibrium statistics. The analog processor may be a quantum annealing processor.” [0190] “Preferably, the annealing rate is selected to be sufficiently fast to limit changes introduced over the course of an operation z=Us*→1 MCMCx to local changes. Similarly, the operator U1→s* MCMC may comprise reverse annealing quickly back to point s*, although in some embodiments the annealing rate of U1→s* MCMC is slower than the annealing rate of Us*→1 MCMC to provide a greater opportunity for U1→s* MCMC to invert changes introduced by Us*→1 MCMC. The annealing rate and other characteristics of operation Us*→1 MCMC and U1→s* MCMC may be pre-selected, provided by a user, and/or otherwise obtained. Accelerating the annealing rate may involve, for example, relaxing one or more proposal acceptance criteria.” [0197] “At 606, classical state z is reverse annealed (e.g. via a ramp operation over time tramp) from s=1 to s=s* in the evolution to yield quantum state ψ. This reverse annealing may be executed by a physical quantum annealer. For instance, classical state z may be read out from a classical processor, transmitted to a physical quantum annealer (e.g. a physical quantum annealer in a hybrid computer which also comprises the classical processor), and reverse-annealed by the physical quantum annealer.”)
the combination of McMahon, Troyer, and Amin does not appear to explicitly suggest:
wherein θ initially equals 0 and is slowly increased to some value of at most 1, then slowly decreased back to 0 in a symmetric manner.
However, Reinhardt, in combination with McMahon, Troyer, and Amin, teaches the limitation:
applying the nearly-adiabatic evolution by the Hamiltonian
H
(
θ
)
using a reverse quantum annealing procedure, wherein θ initially equals 0 and is slowly increased to some value of at most 1, then slowly decreased back to 0 in a symmetric manner. (Reinhardt, [0076]-[0077] “The normalized evolution coefficient s changes monotonically over time, increasing from 0 to a maximum value of 1. A person skilled in the art will understand that the rate of change of the normalized evolution coefficient s over time is shown in FIG. 3A for illustration purposes only and in other implementations the normalized evolution coefficient can increase at a slower or faster rate. Techniques described herein are used to operate a hybrid processor comprising an analog processor and a digital processor where the normalized evolution coefficient s may increase and/or decrease over the course of the operation of the hybrid processor.” [0083]-[0087] “After time interval 310, the evolution of the analog processor resumes in a direction opposite the direction before time interval 310, i.e., backwards. During this phase the normalized evolution coefficient s decreases from 1 to a value s* until time t3. The digital processor may determine the value of e before the start of example evolution 300 b or during time interval 310. … After time interval 320, the evolution of the analog processor resumes in the same direction as the evolution from 0 to time t1, i.e., the normalized evolution coefficient s increases from value s*to 1 until the analog processor reaches a classical spin state at time t5.”)
Accordingly, it would have been obvious to a person having ordinary skill in the art, before the effective filing date of the claimed invention, having the combination of McMahon, Troyer, Amin, and Reinhardt before them, to incorporate the quantum annealing method as taught by Reinhardt. One would have been motivated to make such a combination in order enable facilitating quantum annealing to use quantum effects as a source of delocalization to reach a global energy minimum more accurately and/or more quickly than classical annealing while classical annealing uses classical thermal fluctuations to guide a system to a low-energy state and ideally global energy minimum (Reinhardt [0008]).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure:
(Pub. No.: US 20180157775 A1) – “Pooya RONAGH” relates to “Method for estimating the thermodynamic properties of a quantum ising model with transverse field.”
(Pub. No.: US 20220114470 A1) – “Daisuke Kushibe” relates to “an optimization method that extends time in terms of a quantum-mechanical time propagation operator to a complex number for the purpose of introducing the effect of heat dissipation to finding the ground state of an Ising model and implements heat dissipation based on an imaginary time propagation (ITP) method.”
(Pub. No.: US 20220207402 A1) – “Wolfgang Lechner” relates to “Method and apparatus for performing a quantum computation.”
THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to SADIK ALSHAHARI whose telephone number is (703)756-4749. The examiner can normally be reached Monday Friday, 9 A.M - 6 P.M. ET..
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Li Zhen can be reached on (571) 272-3768. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/S.A.A./Examiner, Art Unit 2121
/Li B. Zhen/Supervisory Patent Examiner, Art Unit 2121