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 .
Detailed Action
This action is in response to the claims filed 1/4/2024:
Claims 1 – 20 are pending.
Claims 1, 10, and 20 are independent.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 2, 5, 11, 13, 14, 15, 18, and 19 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Regarding claim 2, "selected from a group comprising" is an improper Markush group (See MPEP 2117(II)). In the interest of further examination the claim is interpreted as "selected from a group consisting of [...]".
Regarding claim 5, "selected from a group comprising" is an improper Markush group (See MPEP 2117(II)). In the interest of further examination the claim is interpreted as "selected from a group consisting of [...]".
Regarding claim 11, 13, and 14, "the quantum estimation" lacks antecedent basis. More importantly, the claim says the estimation "is a confidence interval," while the specification says the processor can provide a confidence interval for an estimated target variable. It is unclear whether the limitation concerns the estimation method, its output, or associated uncertainty. In the interest of further examination the claim limitation is interpreted as "a quantum estimation is a confidence interval".
Regarding claim 18, "modeled after a Monte Carlo simulation" is indefinite. The claim supplies no objective boundary for how closely the quantum walk must resemble Monte Carlo or how it was modeled after a Monte Carlo simulation. In the interest of further examination the claim is interpreted as "the quantum walk is a Monte Carlo walk" in view of the instant specification.
Regarding claim 19, "repeating one or more previous steps" is indefinite. "Previous" is a relative metric with no relative basis for comparison. In the interest of further examination the claim is interpreted as "repeating one or more steps".
Regarding claim 15, claim 15 is rejected with respect to its dependence on claim 14.
Claim Rejections - 35 USC § 101
101 Rejection
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.
Claims 1-20 are rejected under 35 USC § 101 because the claimed invention is directed to non-statutory subject matter.
Regarding Claim 1: Claim 1 is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 1 is directed to a system, which is directed to a product, one of the statutory categories.
Step 2A Prong One Analysis: Claim 1 under its broadest reasonable interpretation is a series of mental processes and mathematical calculations. For example, but for the generic computer components language, the above limitations in the context of this claim encompass machine learning processing, including the following:
initiating a quantum walk on the one or more variables and the one or more probability distributions, wherein the quantum walk comprises one or more predetermined steps, wherein each predetermined step is associated with a quantum arithmetic operation on the one or more variables and the one or more probability distributions (observation, evaluation, and judgement based on mathematical calculations and relationships),
determining, upon a last quantum arithmetic operation, a target variable by estimating a quantum state of the quantum system (observation, evaluation, and judgement based on mathematical calculations and relationships)
Therefore, claim 1 recites an abstract idea which is a judicial exception.
Step 2A Prong Two Analysis: Claim 1 recites additional elements “a quantum processor” and “a memory comprising instructions stored thereon, which, when executed by the quantum processor causes the system to perform operations comprising”. However, these additional features are computer components recited at a high-level of generality, such that they amount to no more than mere instructions to apply the judicial exception using a generic computer component. An additional element that merely recites the words “apply it” (or an equivalent) with the judicial exception, or merely includes instructions to implement an abstract idea on a computer, or merely uses a computer as a tool to perform an abstract idea, does not integrate the judicial exception into a practical application (See MPEP 2106.05(f)). Claim 1 also recites additional elements “loading one or more variables and one or more probability distributions to a quantum system” which amounts to gathering and outputting data which is insignificant extra-solution activity (See MPEP 2106.05(g)). Therefore, claim 1 is directed to a judicial exception.
Step 2B Analysis: Claim 1 does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to the lack of integration of the abstract idea into a practical application, the additional elements recited in claim 1 amount to no more than mere instructions to apply the judicial exception using a generic computer component and insignificant extra-solution activity. The gathering and outputting data is considered well-understood, routine, and conventional in the art (See MPEP 2106.05(d)(II)(i)).
For the reasons above, claim 1 is rejected as being directed to non-patentable subject matter under §101. This rejection applies equally to independent claims 10 and 20, which recite a method and non-transitory computer readable media, respectively, as well as to dependent claims 2-9 and 11-19.
Independent claim 20 recites additional instructions to apply the judicial exception using generic computer components “A non-transitory computer readable medium containing computer executable instructions that, when executed by a computer hardware arrangement, cause the computer hardware arrangement to perform procedures comprising:”.
The additional limitations of the dependent claims are addressed briefly below:
Dependent claim 2 recites additional observation, evaluation, and judgement based on mathematical calculations and relationships “the one or more probability distributions comprise at least one probability distribution selected from a group comprising a normal probability distribution, a log-normal probability distribution, a uniform probability distribution, or a constant probability distribution”
Dependent claim 3 recites additional insignificant extra-solution activity of gathering and outputting data (See MPEP 2106.05(g)) “the loading of the one or more variables and the one or more probability distributions comprises at least one or more sizes of the one or more probability distributions, one or more means of the one or more probability distributions, and one or more bounds of the one or more probability distributions” which is well-understood, routine, and conventional in the art (See MPEP 2106.05(d)(II)(i))
Dependent claim 4 recites additional observation, evaluation, and judgement based on mathematical calculations and relationships “defining a number of qubits for representing each of the one or more variables”
Dependent claim 5 recites additional observation, evaluation, and judgement based on mathematical calculations and relationships “the quantum arithmetic operations comprise at least one selected from a group comprising quantum addition, quantum multiplication, or quantum exponentiation”
Dependent claim 6 recites additional insignificant extra-solution activity of gathering and outputting data (See MPEP 2106.05(g)) “the one or more variables and the one or more probability distributions are loaded onto the quantum processor using one or more quantum gates and quantum registers” which is well-understood, routine, and conventional in the art (See MPEP 2106.05(d)(II)(i))
Dependent claim 7 recites additional observation, evaluation, and judgement “the quantum walk is performed with a variable number of predetermined steps.”
Dependent claim 8 recites additional insignificant extra-solution activity of gathering and outputting data (See MPEP 2106.05(g)) “transmitting the estimation of the target variable to a user device.” which is well-understood, routine, and conventional in the art (See MPEP 2106.05(d)(II)(i))
Dependent claim 9 recites additional observation, evaluation, and judgement “during the quantum walk[…] adjusts one or more quantum variables and probability distributions of the walk based on intermediate results of the quantum arithmetic” with instructions to apply the judicial exception using generic computer component “the quantum processor” (See MPEP 2106.05(f)).
Dependent claim 11 recites additional observation, evaluation, and judgement based on mathematical calculations and relationships “the quantum estimation is a confidence interval for the estimated target variable”
Dependent claim 12 recites additional insignificant extra-solution activity of gathering and outputting data (See MPEP 2106.05(g)) “storing, by the quantum processor, one or more results of the quantum arithmetic operations in a data storage unit” which is well-understood, routine, and conventional in the art (See MPEP 2106.05(d)(II)(i))
Dependent claim 13 recites additional observation, evaluation, and judgement “performing the quantum estimation of the target comprises evaluating an amplitude of the quantum state”
Dependent claim 14 recites additional observation, evaluation, and judgement based on mathematical calculations “amplifying the amplitude of the quantum state”
Dependent claim 15 recites additional observation, evaluation, and judgement “uses quantum amplitude estimation (QAE) to perform the quantum estimation” and instructions to apply the judicial exception using generic computer components “the quantum processor” (See MPEP 2106.05(f)).
Dependent claim 16 recites additional observation, evaluation, and judgement “the target variable is portfolio of investments”
Dependent claim 17 recites additional observation, evaluation, and judgement based on mathematical calculations “the quantum walk is simulated based on a function comprising one or more of the quantum state, a number of paths of a random stochastic walk, a number of steps spanning a time interval from 0 to T, or a state in a register representing a change in the quantum walk at time t”
Dependent claim 18 recites additional observation, evaluation, and judgement based on mathematical calculations “the quantum walk is modeled after a Monte Carlo simulation”
Dependent claim 19 recites additional observation, evaluation, and judgement “repeating one or more previous steps”
Therefore, when considering the elements separately and in combination, they do not add significantly more to the inventive concept. Accordingly, claims 1-20 are rejected under 35 U.S.C. § 101.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1-20 are rejected under U.S.C. §103 as being unpatentable over the combination of Mazzola (US12190201B2) and Troyer (US20200090072A1).
Regarding claim 1, Mazzola teaches A system comprising: a quantum processor; and([Col. 2 l. 60-67] "FIGS. 1, 2, and 3 illustrate block diagrams of example, non-limiting systems 100, 200, and 300, respectively, that can each facilitate estimation of quantum resources to calculate an expectation value of a stochastic process using a re-parameterization method in accordance with one or more embodiments described herein. System 100, 200, and 300 can each comprise a quantum resource estimation system 102" [Col. 3 l. 33-40] "when executed by processor 106 (e.g., a classical processor, a quantum processor, and/or another type of processor),")
a memory comprising instructions stored thereon, which, when executed by the quantum processor causes the system to perform operations comprising:([Col. 3 l. 33-40] "Memory 104 can store one or more computer and/or machine readable, writable, and/or executable components and/or instructions that, when executed by processor 106 (e.g., a classical processor, a quantum processor, and/or another type of processor), can facilitate performance of operations defined by the executable component(s) and/or instruction(s)")
loading one or more variables and one or more probability distributions to a quantum system;([Col. 12 l. 33-40] "Algorithm 2.1 defined below can proceed in four phases. First, a probability distribution is loaded in the form of a superposition over all possible paths" [Col. 16 l. 38] "2. Load the initial prices {right arrow over (S)}0 into the zero-th nd-qubit register." The variables are asset prices/log-returns/path variables. The probability distributions are transition/path distributions. They are explicitly loaded into quantum registers)
initiating a quantum walk on the one or more variables and the one or more probability distributions, ([Col. 7 l. 5-15] "to prepare the quantum state as a superposition over possible paths of a discrete time multivariate stochastic process" [Col. 16 l. 9-41] "The Riemann summation method gives an approach to construct the path loading operator in Algorithm 2.1. Let N=2ndT be the size of the Hilbert space that contains all possible paths. Let {tilde over (P)}max be the maximum value of the d-asset multivariate transition probabilities from Equation (2). Then {tilde over (P)}({right arrow over (S)}t|{right arrow over (S)}t−1)=P({right arrow over (S)}t|{right arrow over (S)}t−1)/{tilde over (P)}max∈[0,1] is the normalized transition probabilities over all choices [...] Apply each of the T transition operators Wt to construct" Mazzola discloses a quantum path evolution in Hilbert space, namely a superposition over all stochastic paths in an ndT qubit register with T transition operators. This is interpreted as a quantum walk.)
wherein the quantum walk comprises one or more predetermined steps, ([Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers. Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla via")
wherein each predetermined step is associated with a quantum arithmetic operation on the one or more variables and the one or more probability distributions; and ([Col. 29 l. 25-30] "Quantum arithmetic can be involved in path loading using the Riemann summation method (Section 3.1)" [Col. 16 l. 28-31] "3.1 Riemann Summation […] Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla" [Col. 29 l. 30-40] "For the Riemann sum method, all the arithmetic operations involved in Equation (12) can be performed, as well as computation of the arcsine and square root of a quantum register for the payoff calculation in Equation (15)" Each W_t applies transition probabilities for step t. Section 8 ties Riemann path loading and payoff calculation to quantum arithmetic.)
determining, upon a last quantum arithmetic operation, a target variable by estimating a quantum state of the quantum system.([Col. 12 l. 40-55] "2. Calculate δ(ω)=arcsin √{square root over ({tilde over (f)}(ω))} into a quantum register […] 4. Use amplitude estimation to extract the probability of the […] expected payoff" After payoff/arithmetic calculation and ancilla encoding, Mazzola estimates amplitude (quantum state) to obtain expected payoff (target value)).
However, Mazzola does not explicitly use the phrase quantum walk.
Troyer, in the same field of endeavor, teaches that the stochastic path Hilbert-space process in Mazzola is a quantum walk ([¶0026] "Szegedy's quantum walk is formulated in an oracle setting. For a classical walk W, it assumes a unitary transformation W acting on a Hilbert space").
Mazzola as well as Troyer are directed towards performing Monte Carlo simulation on quantum processors. Therefore, Mazzola as well as Troyer are analogous art in the same field of endeavor. It would have been obvious before the effective filing date of the claimed invention to combine the teachings of Mazzola with the teachings of Troyer by calling the stochastic path Hilbert-space process a quantum walk. Troyer provides as additional motivation for combination ([¶0026] "Szegedy's quantum walk is formulated in an oracle setting. For a classical walk W, it assumes a unitary transformation W acting on a Hilbert space"). This motivation for combination also applies to the remaining claims which depend on this combination.
Regarding claim 2, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the one or more probability distributions comprise at least one probability distribution selected from a group comprising a normal probability distribution, a log-normal probability distribution, a uniform probability distribution, or a constant probability distribution.(Mazzola [Col. 6 l. 47-56] "the probability distribution can comprise a standard normal probability distribution and the target probability distribution can comprise a normal probability distribution").
Regarding claim 3, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the loading of the one or more variables and the one or more probability distributions comprises at least one or more sizes of the one or more probability distributions, (Mazzola [Col. 15 l. 10-15] "let there be n qubits used to represent each underlying asset, the domain is divided into 2ndT cells" [Col. 12 l. 40-45] "Obtain an operator P for loading a probabilistically weighted superposition of paths onto a register of ndT-qubits" Mazzola defines the discretized distribution size through n, d, T, the ndT-qubit register, and the 2^(ndT) grid cells)
one or more means of the one or more probability distributions, (Mazzola [Col. 6 l. 20-30] "the quantum state corresponding to the target probability distribution with a defined mean of the target probability distribution")
and one or more bounds of the one or more probability distributions.(Mazzola [Col. 20 l. 1-5] "Consider the case of preparing a standard normal distribution g(xi) defined a discretized mesh of points xi=−w+iΔx, with i=0, . . . 2n−1, and Δx=2w/2n. In the following example the domain is fixed to w=5 so that the full range of value considered is 2w=10" [Col. 14 l. 34-44] ""the prices and/or log-returns are restricted to a range [Bl, Bu]. This restriction of the domain leaves out a probability mass of α. Given an upper bound of Pmax on the density functions at each step and an upper bound fδ on the payoff"").
Regarding claim 4, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the operations further comprise: defining a number of qubits for representing each of the one or more variables.(Mazzola [Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers" [Col. 15 l. 10-15] "let there be n qubits used to represent each underlying asset").
Regarding claim 5, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the quantum arithmetic operations comprise at least one selected from a group comprising quantum addition, quantum multiplication, or quantum exponentiation.(Mazzola [Col. 30 l. 8-Col. 33 l. 45] "Perform addition of two n-qubit registers […] For multiplication, use a controlled addition circuit […] computing the exponential of a register").
Regarding claim 6, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the one or more variables and the one or more probability distributions are loaded onto the quantum processor using one or more quantum gates and quantum registers.(Mazzola [Col. 16 l. 36-40] "1. Apply Hadamards to ndT qubits to prepare an equal superposition of all paths. 2. Load the initial prices {right arrow over (S)}0 into the zero-th nd-qubit register." [Col. 20 l. 20-21] "The variational ansatz of choice is represented by a so-called Ry-Controlled NOT (Ry-CNOT) ansatz,").
Regarding claim 7, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the quantum walk is performed with a variable number of predetermined steps.(Mazzola [Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers" [Col. 16 l. 40-45] "Apply each of the T transition operators Wt " [Col. 18 l. 30-55] "T=20, d=3, […] d=1, T=26" Mazzola uses T as the number of time/path steps and examples use different/variable T values).
Regarding claim 8, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein the operations further comprise: transmitting the estimation of the target variable to a user device.(Troyer [¶0082] "the computing device 520 is configured to transmit input, data to the computing device 530, and the computing device 534) is configured to implement an MCMC technique according to any of the disclosed embodiments and/or a circuit generation or compilation/synthesis methods for generating quantum circuits based on or in conjunction with any of the MCMC techniques disclosed herein. The computing device 530 can output results to the computing device 5320. Any of the data received from the computing device 530 can be stored or displayed on the computing device 520 (e.g., displayed as data on a graphical user interface or web page at, the computing devices 520)").
Regarding claim 9, the combination of Mazzola, and Troyer teaches The system of claim 1, wherein, during the quantum walk, the quantum processor adjusts one or more quantum variables and probability distributions of the walk based on intermediate results of the quantum arithmetic.(Troyer [¶0105] "At 1014, a rewinding procedure of one or more but not all steps of the quantum walk procedure is performed if the intermediate measurement produces an incorrect outcome.").
Regarding claim 10, Mazzola teaches A method for estimating a target outcome, the method comprising: loading, by a quantum processor, one or more variables and one or more probability distributions into a quantum system;([Col. 12 l. 33-40] "Algorithm 2.1 defined below can proceed in four phases. First, a probability distribution is loaded in the form of a superposition over all possible paths" [Col. 16 l. 38] "2. Load the initial prices {right arrow over (S)}0 into the zero-th nd-qubit register." The variables are asset prices/log-returns/path variables. The probability distributions are transition/path distributions. They are explicitly loaded into quantum registers)
initiating, by the quantum processor, a quantum walk on the one or more variables and probability distributions, ([Col. 7 l. 5-15] "to prepare the quantum state as a superposition over possible paths of a discrete time multivariate stochastic process" [Col. 16 l. 9-41] "The Riemann summation method gives an approach to construct the path loading operator in Algorithm 2.1. Let N=2ndT be the size of the Hilbert space that contains all possible paths. Let {tilde over (P)}max be the maximum value of the d-asset multivariate transition probabilities from Equation (2). Then {tilde over (P)}({right arrow over (S)}t|{right arrow over (S)}t−1)=P({right arrow over (S)}t|{right arrow over (S)}t−1)/{tilde over (P)}max∈[0,1] is the normalized transition probabilities over all choices [...] Apply each of the T transition operators Wt to construct" Mazzola discloses a quantum path evolution in Hilbert space, namely a superposition over all stochastic paths in an ndT qubit register with T transition operators. This is interpreted as a quantum walk.)
wherein the quantum walk comprises one or more predetermined steps, ([Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers. Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla via")
wherein each predetermined step is associated with a quantum arithmetic operation on the one or more variables and the one or more probability distributions; and([Col. 29 l. 25-30] "Quantum arithmetic can be involved in path loading using the Riemann summation method (Section 3.1)" [Col. 16 l. 28-31] "3.1 Riemann Summation […] Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla" [Col. 29 l. 30-40] "For the Riemann sum method, all the arithmetic operations involved in Equation (12) can be performed, as well as computation of the arcsine and square root of a quantum register for the payoff calculation in Equation (15)" Each W_t applies transition probabilities for step t. Section 8 ties Riemann path loading and payoff calculation to quantum arithmetic.)
determining, upon a last quantum arithmetic operation, a target variable by estimating a quantum state of the quantum system.([Col. 12 l. 40-55] "2. Calculate δ(ω)=arcsin √{square root over ({tilde over (f)}(ω))} into a quantum register […] 4. Use amplitude estimation to extract the probability of the […] expected payoff" After payoff/arithmetic calculation and ancilla encoding, Mazzola estimates amplitude (quantum state) to obtain expected payoff (target value)).
However, Mazzola does not explicitly use the phrase quantum walk.
Troyer, in the same field of endeavor, teaches that the stochastic path Hilbert-space process in Mazzola is a quantum walk ([¶0026] "Szegedy's quantum walk is formulated in an oracle setting. For a classical walk W, it assumes a unitary transformation W acting on a Hilbert space").
Mazzola as well as Troyer are directed towards performing Monte Carlo simulation on quantum processors. Therefore, Mazzola as well as Troyer are analogous art in the same field of endeavor. It would have been obvious before the effective filing date of the claimed invention to combine the teachings of Mazzola with the teachings of Troyer by calling the stochastic path Hilbert-space process a quantum walk. Troyer provides as additional motivation for combination ([¶0026] "Szegedy's quantum walk is formulated in an oracle setting. For a classical walk W, it assumes a unitary transformation W acting on a Hilbert space"). This motivation for combination also applies to the remaining claims which depend on this combination. Regarding claim 11, the combination of Mazzola, and Troyer teaches The method of claim 10, wherein the quantum estimation is a confidence interval for the estimated target variable.(Mazzola [Col. 18 l. 49-55] "If a target ϵamp is chosen for the amplitude estimation of 10−3 and a target confidence level of α=10−2 then Noracle wc≤8 k can be obtained. This means that the total T-depth is about 1.9×108").
Regarding claim 12, the combination of Mazzola, and Troyer teaches The method of claim 10 further comprising storing, by the quantum processor, one or more results of the quantum arithmetic operations in a data storage unit.(Mazzola [Col. 13 l. 4-10] "estimation system 102 can normalize the payoff in order to store it in the amplitude of a state").
Regarding claim 13, the combination of Mazzola, and Troyer teaches The method of claim 10, wherein performing the quantum estimation of the target comprises evaluating an amplitude of the quantum state.(Mazzola [Col. 13 l. 4-10] "estimation system 102 can normalize the payoff in order to store it in the amplitude of a state").
Regarding claim 14, the combination of Mazzola, and Troyer teaches The method of claim 13 further comprising amplifying the amplitude of the quantum state.(Mazzola [Col. 13 l. 4-35] "estimation system 102 can normalize the payoff in order to store it in the amplitude of a state […] Amplitude estimation determines a by repeated applications of the operator (often referred to as the Grover operator)" Amplitude estimation using repeated applications of a Grover operator is interpreted as amplitude amplification of the quantum state).
Regarding claim 15, the combination of Mazzola, and Troyer teaches The method of claim 14, wherein the quantum processor uses quantum amplitude estimation (QAE) to perform the quantum estimation.(Mazzola [Col. 13 l. 25-30] "using quantum amplitude estimation for Monte Carlo").
Regarding claim 16, the combination of Mazzola, and Troyer teaches The method of claim 10, wherein the target variable is portfolio of investments.(Mazzola [Col. 2 l. 45-50] "a “derivative” and/or a “derivative asset” is a contract between an issuer and a holder" [Col. 10 l. 40-45] "a basket of auto-callable (auto) options with 5 auto-call dates and a knock-in put option, and a TARF with one underlying and 26 simulation dates" A basket of derivative assets (options) interpreted as synonymous with a portfolio of investments).
Regarding claim 17, the combination of Mazzola, and Troyer teaches The method of claim 16, wherein the quantum walk is simulated based on a function comprising one or more of the quantum state, a number of paths of a random stochastic walk, a number of steps spanning a time interval from 0 to T, or a state in a register representing a change in the quantum walk at time t.(Mazzola [Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers. Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla via").
Regarding claim 18, the combination of Mazzola, and Troyer teaches The method of claim 10, wherein the quantum walk is modeled after a Monte Carlo simulation.(Mazzola [Col. 13 l. 25-30] "using quantum amplitude estimation for Monte Carlo").
Regarding claim 19, the combination of Mazzola, and Troyer teaches The method of claim 10 further comprising repeating one or more previous steps.(Mazzola [Col. 13 l. 4-35] "estimation system 102 can normalize the payoff in order to store it in the amplitude of a state […] Amplitude estimation determines a by repeated applications of the operator (often referred to as the Grover operator)" [Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers. Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla").
Regarding claim 20, Mazzola teaches A non-transitory computer readable medium containing computer executable instructions that, when executed by a computer hardware arrangement, cause the computer hardware arrangement to perform procedures comprising:([Col. 3 l. 33-40] "Memory 104 can store one or more computer and/or machine readable, writable, and/or executable components and/or instructions that, when executed by processor 106 (e.g., a classical processor, a quantum processor, and/or another type of processor), can facilitate performance of operations defined by the executable component(s) and/or instruction(s)")
loading, by a quantum processor, one or more variables and one or more probability distributions into a quantum system;([Col. 12 l. 33-40] "Algorithm 2.1 defined below can proceed in four phases. First, a probability distribution is loaded in the form of a superposition over all possible paths" [Col. 16 l. 38] "2. Load the initial prices {right arrow over (S)}0 into the zero-th nd-qubit register." The variables are asset prices/log-returns/path variables. The probability distributions are transition/path distributions. They are explicitly loaded into quantum registers)
initiating, by the quantum processor, a quantum walk on the one or more variables and distributions, ([Col. 7 l. 5-15] "to prepare the quantum state as a superposition over possible paths of a discrete time multivariate stochastic process" [Col. 16 l. 9-41] "The Riemann summation method gives an approach to construct the path loading operator in Algorithm 2.1. Let N=2ndT be the size of the Hilbert space that contains all possible paths. Let {tilde over (P)}max be the maximum value of the d-asset multivariate transition probabilities from Equation (2). Then {tilde over (P)}({right arrow over (S)}t|{right arrow over (S)}t−1)=P({right arrow over (S)}t|{right arrow over (S)}t−1)/{tilde over (P)}max∈[0,1] is the normalized transition probabilities over all choices [...] Apply each of the T transition operators Wt to construct" Mazzola discloses a quantum path evolution in Hilbert space, namely a superposition over all stochastic paths in an ndT qubit register with T transition operators. This is interpreted as a quantum walk.)
wherein the quantum walk comprises one or more predetermined steps, ([Col. 16 l. 28-31] "Use parameters n, d, and T that are all positive integers. Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla via")
wherein each predetermined step is associated with a quantum arithmetic operation on the one or more variables and probability distributions; and([Col. 29 l. 25-30] "Quantum arithmetic can be involved in path loading using the Riemann summation method (Section 3.1)" [Col. 16 l. 28-31] "3.1 Riemann Summation […] Obtain access to operators Wt, t=1, . . . , T that apply the transition probabilities of the stochastic process into an ancilla" [Col. 29 l. 30-40] "For the Riemann sum method, all the arithmetic operations involved in Equation (12) can be performed, as well as computation of the arcsine and square root of a quantum register for the payoff calculation in Equation (15)" Each W_t applies transition probabilities for step t. Section 8 ties Riemann path loading and payoff calculation to quantum arithmetic.)
determining, upon a last quantum arithmetic operation, a target variable by estimating a quantum state of the quantum system.([Col. 12 l. 40-55] "2. Calculate δ(ω)=arcsin √{square root over ({tilde over (f)}(ω))} into a quantum register […] 4. Use amplitude estimation to extract the probability of the […] expected payoff" After payoff/arithmetic calculation and ancilla encoding, Mazzola estimates amplitude (quantum state) to obtain expected payoff (target value)).
However, Mazzola does not explicitly use the phrase quantum walk.
Troyer, in the same field of endeavor, teaches that the stochastic path Hilbert-space process in Mazzola is a quantum walk ([¶0026] "Szegedy's quantum walk is formulated in an oracle setting. For a classical walk W, it assumes a unitary transformation W acting on a Hilbert space").
Mazzola as well as Troyer are directed towards performing Monte Carlo simulation on quantum processors. Therefore, Mazzola as well as Troyer are analogous art in the same field of endeavor. It would have been obvious before the effective filing date of the claimed invention to combine the teachings of Mazzola with the teachings of Troyer by calling the stochastic path Hilbert-space process a quantum walk. Troyer provides as additional motivation for combination ([¶0026] "Szegedy's quantum walk is formulated in an oracle setting. For a classical walk W, it assumes a unitary transformation W acting on a Hilbert space"). This motivation for combination also applies to the remaining claims which depend on this combination.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure. Atanassov (“Efficient quasi-Monte Carlo sampling for quantum random walks”, 2020) is directed towards Monte Carlo sampling for quantum random walks.
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/SIDNEY VINCENT BOSTWICK/Examiner, Art Unit 2124
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