DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Status of Claims
A request for continued examination under 37 CFR 1.114, including the fee set forth in 37 CFR
1.17(e), was filed in this application after final rejection. Since this application is eligible for continued
examination under 37 CFR 1.114, and the fee set forth in 37 CFR 1.17(e) has been timely paid, the
finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114. Applicant's submission filed on 06/18/2025 has been entered.
Claims 37, 40-42, 45-46, 48, 50, and 60 are amended. No additional claims have been cancelled, and no additional new claims have been added.
Claims 37–38, 40–42, and 44–61 are pending for examination.
Response to Arguments
In reference to 35 USC § 101
Applicant’s arguments, filed on 06/18/2025, with respect to the § 101 rejections have been fully considered and are persuasive.
Examiner notes that while the claims recite several limitations that are abstract ideas (mathematical concepts), the claims as a whole are not directed to an abstract idea. Applicant amended the claims, which collectively now recite a detailed system directed toward solving an optimization problem using a computing platform comprising at least one non-classical computer and at least one digital computer including “(c) implementing, at said at least one non-classical computer, said second Hamiltonian to obtain a first solution of said final Hamiltonian, wherein said implementing comprises an adiabatic evolution of said second Hamiltonian from said initial Hamiltonian to said final Hamiltonian, and wherein said adiabatic evolution comprises changing amplitudes of said initial Hamiltonian, said first Hamiltonian, and said final Hamiltonian to navigate said adiabatic evolution of said second Hamiltonian from said initial Hamiltonian to said final Hamiltonian” and “reconfiguring said second Hamiltonian using one or more second variational parameters to improve said implementing of said adiabatic evolution to a solution of said final Hamiltonian.” These additional limitations are not abstract ideas (see MPEP 2106.04(a)). Thus, these limitations must be considered additional elements to the abstract idea. Examiner notes that these additional elements integrate the abstract idea into a practical application because the entire claim amounts to a detailed system that requires implementing a specific combination of hardware with the methods of optimization (as opposed to a broad recitation at a high level of generality), and the specific combination of hardware and instructions recited in the additional element amounts to an improvement to the functioning of a computer/field, as set forth by MPEP 2106.05(a)), which states “the claim must include the components or steps of the invention that provide the improvement described in the specification.” Pursuant to this requirement set forth by the MPEP, examiner points out that the Specification states in at least [0037]: “The present disclosure provides systems and methods that advantageously use an intermediate Hamiltonian having variational parameters to generate solutions with value(s) that optimize a cost function in a rapid and accurate manner. This may advantageously enable users to efficiently identify an optimal state, e.g., the ground state, of a quantum system. In the present disclosure, finding such an optimal state can be achieved through a quantum annealing process that utilizes an intermediate Hamiltonian. The parameters of the intermediate Hamiltonian can be iteratively improved or optimized in order for the annealing process to converge to the ground state of the quantum system with a shorter annealing time.” Therefore, the additional elements reflect the improvement set forth and explains what the resulting improvement is.
Thus, the additional limitations do amount to significantly more, and the § 101 rejections are withdrawn.
In reference to 35 USC § 103
Applicant’s arguments filed on 06/18/2025, with respect to Peruzzo and QVE have been fully considered but are not persuasive. Applicant argues, beginning on Pg. 9 in the Remarks, that Peruzzo discloses "quantum expectation estimation (QEE)" a variation on the "quantum variational eigensolver (QVE)," which are not withing the same “framework.” Examiner notes the distinction between gate model and adiabatic quantum computing as put forth by applicant. However, examiner respectfully disagrees with the statement that the teachings of Peruzzo has “no notion of a Hamiltonians which evolve from an initial to a final Hamiltonian as evinced by the follow up paper, authored by a co-author of Peruzzo (Jarrod R. McClean) and cited below. McClean in at least [I. Introduction page 1, Right column] states “Moreover, the overhead of some asymptotically optimal algorithms is such that even the first quantum computers competitive with classical supercomputers may not be able to run them. To this end, in 2014 Peruzzo and McClean et al. developed the variational quantum eigensolver (VQE), a hybrid quantum-classical algorithm designed to utilize both quantum and classical resources to find variational solutions to eigenvalue and optimization problems not accessible to traditional classical computers [1] … The VQE has the notable property that it can run on any quantum device.” Emphasis added. See § 103 rejections below for a detailed analysis.
Thus, with respect to Peruzzo, the § 103 rejections are maintained.
Applicant’s arguments filed on 06/18/2025, with respect to the newly amended claim limitations have been considered but are moot because the new ground of rejection does not rely on any reference applied in the prior rejection of record for any teaching or matter specifically challenged in the argument.
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.
Claims 37–38, 40–42, 44–49, 51–55, and 57–59 are rejected under 35 U.S.C. 103 as being unpatentable over Peruzzo et al. (“A variational eigenvalue solver on a photonic quantum processor.”, Nat Commun 5, 4213 (2014). https://doi.org/10.1038/ncomms5213), hereinafter “Peruzzo”, in view of McClean et al., ("The theory of variational hybrid quantum-classical algorithms," in New Journal of Physics, vol. 18, no. 2, pp. 023023, 2016, https://arxiv.org/abs/1509.04279), hereinafter “McClean”.
Regarding claim 37, Peruzzo teaches:
a computer-implemented method for solving an optimization problem using a computing platform comprising at least one non-classical computer and at least one digital computer, the method comprising (Peruzzo Pg. 1, Abstract: “The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer”):
(a) determining, by said at least one digital computer, one or more first parameters of a first Hamiltonian (Peruzzo Fig. 1, Pg. 3, Architecture of the quantum-variational eigensolver: “In QEE, quantum states that have been previously prepared are fed into the quantum modules, which compute ‹Hi›, where Hi is any given term in the sum defining H. The results are passed to the CPU, which computes ‹H›. In the quantum variational eigensolver, the classical minimization algorithm, run on the CPU, takes ‹H› and determines the new state parameters, which are then fed back to the QPU”—[wherein the CPU (i.e., digital computer) determines the new state parameters of H (i.e., the first Hamiltonian)]);
(b) configuring, at said at least one digital computer, a second Hamiltonian different than said first Hamiltonian using said one or more first variational parameters, wherein said second Hamiltonian comprises an initial Hamiltonian, said first Hamiltonian, and a final Hamiltonian (Peruzzo Pg. 3: “However, this state may be prepared efficiently on a quantum device. The reduced anti-hermitian cluster operator (T(k) - T(k)+) is the sum of a polynomial number of terms—namely, it contains a number of terms O(Nk(M-N)k), where M is the number of single-particle orbitals. By defining an effective Hermitian Hamiltonian H=i(T(k)-T(k)+) and performing the Jordan–Wigner transformation to reach a Hamiltonian that acts on the space of qubits, ~H, we are left with a Hamiltonian that is a sum of polynomially many products of Pauli operators. The problem then reduces to the quantum simulation of this effective Hamiltonian, ~H, which can be done in polynomial time using the procedure outlined by Ortiz et al … non-unitary coupled cluster ansatz is sometimes referred to as the ‘gold standard of quantum chemistry’ as it is the standard of accuracy to which other methods in quantum chemistry are often compared”; see also Peruzzo Pg. 4: “The ability to prepare an arbitrary two-qubit separable or entangled state enables us to investigate 4 × 4 Hamiltonians. For the experimental demonstration of our algorithm we choose a problem from quantum chemistry—namely, determining the bond dissociation curve of the molecule He–H+ in a minimal basis. The full configuration interaction Hamiltonian for this system has dimension 4, and can be written compactly as
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The coefficients and were determined using the PSI3 computational package32 and are tabulated in Supplementary Table 2”—[(emphasis added) wherein the algorithm procedurally performs transformations on the initial Hamiltonian (e.g., starting with the initial Hamiltonian and progressing to the final Hamiltonian; e.g., 1st, 2nd, final) and at each transformation, a new Hamiltonian is created until the final Hamiltonian is found which represents a sum of polynomially many products of Pauli operators (i.e., variational parameters) configured on a classical computer using the PSI3 computational package]).
(c) implementing at least one non-classical computer said second Hamiltonian to obtain a first solution of said final Hamiltonian (Peruzzo Pg. 2, Right Column, First ¶: “A quantum device can efficiently evaluate the expectation value of a tensor product of an arbitrary number of simple Pauli operators23. Therefore, with an n-qubit state we can efficiently evaluate the expectation value of this 2n × 2n Hamiltonian”—[wherein the Hamiltonian (e.g., H2) is solved with a quantum device (i.e., implemented on a non-classical computer)]);
(d) determining a value of said optimization problem based at least in part on said first solution to said final Hamiltonian (Peruzzo Pg. 2, Right Column, Third ¶: “The expectation value of a tensor product of an arbitrary number of Pauli operators can be estimated by local measurement of each qubit. Such independent measurements can be performed in parallel, incurring a constant cost in time. Furthermore, since these operators are normalized and finite-dimensional, their spectra are bounded. As a result, each can be estimated to a precision p of an individual element with coefficient h, which is an arbitrary element from the set of constants
{
h
α
β
…
i
j
…
}
, at a cost of O(|hmax|2Mp−2) repetitions. Here M is the number of terms in the decomposition of the Hamiltonian and hmax is the coefficient with maximum norm in the decomposition of the Hamiltonian”—[(emphasis added) wherein the Hamiltonian is processed through decomposition and the value of the cost function is O(|hmax|2Mp−2) repetitions (i.e., optimization problem based on the first solution)]); and
Peruzzo does not appear to explicitly teach:
wherein said implementing comprises an adiabatic evolution of said second Hamiltonian from said initial Hamiltonian to said final Hamiltonian, and wherein said adiabatic evolution comprises changing amplitudes of said initial Hamiltonian, said first Hamiltonian, and said final Hamiltonian to navigate said adiabatic evolution of said second Hamiltonian from said initial Hamiltonian to said final Hamiltonian; and
(e) subsequent to (d), reconfiguring said second Hamiltonian using one or more second variational parameters to improve said implementing of said adiabatic evolution to a solution of said final Hamiltonian, wherein said one or more second variational parameters comprise an amplitude of said first Hamiltonian or a parameter in said first Hamiltonian of said adiabatic evolution, and wherein said solution is indicative of a solution of said optimization problem.
However, McClean teaches:
wherein said implementing comprises an adiabatic evolution from said initial Hamiltonian to said final Hamiltonian wherein said implementing comprises an adiabatic evolution of said second Hamiltonian from said initial Hamiltonian to said final Hamiltonian, and wherein said adiabatic evolution comprises changing amplitudes of said initial Hamiltonian, said first Hamiltonian, and said final Hamiltonian to navigate said adiabatic evolution of said second Hamiltonian from said initial Hamiltonian to said final Hamiltonian (McClean Pg. 1, Abstract: “To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the quantum variational eigensolver’ was developed [1] with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations” and McClean Eqs. 29, 33, Pg. 5–8, Adiabatically parameterized states: “One type of quantum state that can be explored as a parametric ansatz is that produced by adiabatic state state preparation with a variable path. In adiabatic quantum computation [54–56] and adiabatic state preparation [8, 27] one makes use of the adiabatic theorem [57], which states loosely that if one prepares the lowest eigenstate of an initial Hamiltonian Hi , by continuously changing the Hamiltonian from Hi to a final problem Hamiltonian Hp, one finishes in the lowest eigenstate of Hf if the evolution was slow enough. In adiabatic computation, slow enough is quantified relative to the minimum eigenvalue gap between the ground and first excited states along the evolution. While many developments have occurred in the area of adiabatic quantum computation and modifications to the Hamiltonian, perhaps the most commonly considered form of evolution is defined by
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where s ∈ [0, 1], A(0) = B(1) = 1, and A(1) = B(0) = 0. The evolution is controlled by continuously changing the parameter s as a function of time t”—[wherein the method explores quantum states, adiabatically, with variable paths as an extension to the quantum variational eigensolver (QVE), and wherein the parameter (s) (i.e., amplitude) is continuously changed throughout the adiabatic process for all associated Hamiltonians (e.g., equation (29))]);
(e) subsequent to (d), reconfiguring said second Hamiltonian using one or more second variational parameters to improve said implementing of said adiabatic evolution to a solution of said final Hamiltonian, wherein said one or more second variational parameters comprise an amplitude of said first Hamiltonian or a parameter in said first Hamiltonian of said adiabatic evolution, and wherein said solution is indicative of a solution of said optimization problem (McClean Eqs. 29, 33, Pg. 5–8, Adiabatically parameterized states: “In particular, we will consider this problem in a resource constrained context where the maximum evolution time τ is limited. In this problem, the Hamiltonian the initial and problem Hamiltonians are given by
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If we take the following form of the schedule Hamiltonian
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then the eigenvalues of this problem undergo an avoided crossing with a gap determined by the size of the perturbation ε. For this example we choose ε = 0.1 and the resulting spectrum is plotted in Fig.1 as a function of A(s). Suppose that we are attempting to prepare the ground state of our problem Hamiltonian in a situation where the total evolution time τ is limited. We will consider two types of paths, the first of which is a fixed standard linear path as a function of time. That is A(s) = s = t/τ with t ∈ [0, τ ]. The second type of path will be a parameterized path of two variables defined by the best cubic B-spline fit of the 4 points (0, 0),(.15τ, θ1),(.85τ, θ2),(τ, 1), where the the parameters θi are determined by a non-linear minimization the expectation value of the final state in the (possibly non- )adiabatic evolution with fixed maximum evolution time, H(1)(θ1, θ2)”—[wherein the method explores quantum states, adiabatically, by continuously changing at least one parameter (e.g., A(s)), and wherein the methods also include changing more than one parameter (e.g., the parameters θi) to arrive at the final solution]).
The methods of Peruzzo, the teachings of McClean, and the instant application are analogous art because they pertain to solving optimization problems using Hamiltonians.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Peruzzo with the teachings of McClean to provide Adiabatic Quantum Computation to evolve the Hamiltonian from the initial state to the ground state to find the solution of the system by changing the amplitude of the Hamiltonians throughout the adiabatic process. One would be motivated to do so to detect the final state which encodes a solution to the problem by optimizing the quantum problem including reducing evolution time (McClean Pg. 7: “That is, at the cost of some classical minimization, we have reduced the quantum evolution time requirement by a factor of 10 by slightly deforming the schedule in a black-box manner relying only on measurements of the final state of the evolution and no prior knowledge of the problem. Moreover, even at this reduced evolution time, we achieve the desirable property that the success of the computation is a monotonically increasing function of s, which is not true of the linear schedule in this case”).
Regarding claim 38, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo teaches:
wherein said first Hamiltonian is an intermediate Hamiltonian (Peruzzo Pg. 3, Right Col., Definition 1: “As already noted in (Aharonov et al., 2007), it is useful to allow for more general “paths” between H0 and H1, e.g., by introducing an intermediate “catalyst” Hamiltonian that vanishes at s = 0, 1 (see, e.g., Sec. VII.E)”—[emphasis added]).
Regarding claim 40, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein said second Hamiltonian comprises a sum of said initial Hamiltonian, said final Hamiltonian, and said first Hamiltonian weighted by said amplitudes (McClean Pg. 12, IV Operator Averaging: “Once a trial state |Ψ(~θ)i has been prepared, the next crucial step in the VQE is the evaluation of the objective function corresponding to the problem operator H, Hi(θ) = hΨ(~θ)| H |Ψ(~θ)I … As a result, all that is required is the weighted sum of the results from simple Pauli measurements”).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 40.
Regarding claim 41, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein said amplitudes of said second Hamiltonian are time-dependent (McClean Pg. 7: “We will consider two types of paths, the first of which is a fixed standard linear path as a function of time. That is A(s) = s = t/τ with t ∈ [0, τ ]. The second type of path will be a parameterized path of two variables defined by the best cubic B-spline fit of the 4 points (0, 0),(.15τ, θ1),(.85τ, θ2),(τ, 1), where the the parameters θi are determined by a non-linear minimization the expectation value of the final state in the (possibly non- )adiabatic evolution with fixed maximum evolution time, H(1)(θ1, θ2)”—[wherein the system considers two types of path, the first one a fixed standard linear path as a function of time (i.e., time-dependent)]).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 41.
Regarding claim 42, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein said amplitudes of said second Hamiltonian are time-independent (McClean Pg. 7: “We will consider two types of paths, the first of which is a fixed standard linear path as a function of time. That is A(s) = s = t/τ with t ∈ [0, τ ]. The second type of path will be a parameterized path of two variables defined by the best cubic B-spline fit of the 4 points (0, 0),(.15τ, θ1),(.85τ, θ2),(τ, 1), where the the parameters θi are determined by a non-linear minimization the expectation value of the final state in the (possibly non- )adiabatic evolution with fixed maximum evolution time, H(1)(θ1, θ2)”—[wherein the system considers two types of path, the first one is time-dependent while the second is determined where the parameters θi are determined by a non-linear minimization the expectation value of the final state (i.e., time-independent)]).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 42.
Regarding claim 44, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo teaches:
prior to (a), receiving, by said at least one digital computer, a cost function of said optimization problem (Peruzzo Fig. 1, Pg. 2, Introduction: “The QPU has been experimentally implemented using integrated photonics technology with a spontaneous parametric down conversion single-photon source and combined with an optimization algorithm run on a classical processing unit (CPU), which variationally computes the eigenvalues and eigenvectors of . By using a variational algorithm, this approach reduces the requirement for coherent evolution of the quantum state, making more efficient use of quantum resources, and may offer an alternative route to practical quantum-enhanced computation”; see also Peruzzo Pg. 6, Mapping from the state parameters to the chop phases: “The set of phases {θi}, which uniquely identifies the state |ψ›, is not equivalent to the phases that are written to the photonic circuit {φi}, since the chip phases are also used to implement the desired measurement operators σα⊗σβ. Therefore, knowing the desired state parameters and measurement operator we compute the appropriate values of the chip phases on the CPU at each iteration of the optimization algorithm”—[where the BRI of cost function is problem or mathematical equation related to any type of optimization problem (see present disclosure ¶¶0039–0041)]), and wherein the CPU runs the optimization algorithm (i.e., cost function of said optimization problem) received from the Quantum modules (e.g., Fig. 1)).
Regarding claim 45, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
prior to (a), initializing, by said at least one digital computer, a list of parameters and solutions (McClean Pg. 5, III. State Parameterization and Preparation: “The set of states a quantum computer can easily manipulate that a classical computer cannot is not yet fully understood [48–50]. Given the set of parameters ~θ, it’s clear that in order for a quantum computer to have an advantage, one would like the state |Ψ(~θ)i to be good at describing the solution of interest, while also difficult to prepare and/or sample from classically using currently known methods. Here we will first discuss topics relevant to state preparation for all classes of states in the variational quantum eigensolver, independent of any notion of how difficult they are to prepare classically. We will then discuss some details concerning two classes of states currently believed to be both good at describing systems of interest and difficult to prepare and/or sample from classically, namely adiabatically parameterized states and (multi-reference) unitary coupled cluster states”—[where in the system prepares (i.e., initializes) the set of parameters and solutions independent of how they are prepared classically (i.e., prepared classically on a digital computer)]).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 45.
Regarding claim 46, Peruzzo in view of McClean teaches all the limitations of claim 45.
McClean teaches:
wherein (a) comprises (i) setting said list of parameters and solutions to zero for an initial iteration (McClean Pg. 5, B. Adiabatically parameterized states: “Consider the set of all paths of A(s) and B(s) from 0 to 1 as a function of time t ∈ [0, τ ], and denote it 6 F(τ ), where τ is some finite time”—[wherein the system considers the set of all paths from 0 (i.e., initial iteration) to 1 (i.e., final iteration)]);
Peruzzo teaches:
(ii) updating, by said at least one digital computer, said list of parameters and solutions with said one or more second variational parameters, and a solution for an iteration subsequent to said initial iteration (Peruzzo Fig. 1, Pg. 3, Architecture of the quantum-variational eigensolver: “In QEE, quantum states that have been previously prepared are fed into the quantum modules, which compute ‹Hi›, where Hi is any given term in the sum defining H. The results are passed to the CPU, which computes ‹H›. In the quantum variational eigensolver, the classical minimization algorithm, run on the CPU, takes ‹H› and determines the new state parameters, which are then fed back to the QPU—[wherein the various parameters and Hamiltonians (i.e., solutions) are initialized to ground state (i.e., initialize to zero) and wherein the parameters are fed back into the system iteratively by the CPU to update the solutions]).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 46.
Regarding claim 47, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo teaches:
prior to (a), providing an indication of said first Hamiltonian (Peruzzo Fig. 1, Pg. 3, Architecture of the quantum-variational eigensolver: “In QEE, quantum states that have been previously prepared are fed into the quantum modules, which compute ‹Hi›, where Hi is any given term in the sum defining H. The results are passed to the CPU, which computes ‹H›. In the quantum variational eigensolver, the classical minimization algorithm, run on the CPU, takes ‹H› and determines the new state parameters, which are then fed back to the QPU—[(emphasis added) wherein the CPU computes ‹H› (i.e., an indication of said first Hamiltonian)]).
Regarding claim 48, Peruzzo in view of McClean teaches all the limitations of claim 47.
McClean teaches:
wherein said first Hamiltonian is based at least in part on use of one or more members selected from the group consisting of said optimization problem, a cost function of said optimization problem, and said final Hamiltonian (McClean Pg., 13, A. Bayesian Perspective: “An alternative perspective that addresses such concerns from the outset is a Bayesian perspective, which has been investigated in the context of quantum phase estimation [79], and we now explore in the context of Hamiltonian averaging”).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 48.
Regarding claim 49, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein determining said one or more first variational parameters in (a) or said one or more second variational parameters in (e) comprises using one or more optimizers selected from the group consisting of a Bayesian optimization method, black-box optimization, gradient-free optimization, gradient-based optimization, a first-order or second- order method, a gradient descent method, a stochastic gradient decent method, an adaptive gradient descent method, a Nelder-Mead method, a Powell method, constrained optimization by linear approximation (COBYLA), and a Broyden-Fletcher-Goldfarb-Shanno (BFGS) method (McClean Pg., 13, A. Bayesian Perspective: “In a Bayesian perspective, we start from an uninformative prior for the distribution Hγi. In the case of two measurement outcomes, the likelihood function is the binomial likelihood, and the posterior distributions after measurement can be worked out analytically when used with a conjugate Beta prior. These distributions are well defined even for small numbers of measurements or when ρ is close to an eigenstate of Hγ, resulting in potentially unobserved events in a sequence of measurements” and McClean Pg. 7, 1. Variational Adiabatic Path Example: “That is, at the cost of some classical minimization, we have reduced the quantum evolution time requirement by a factor of 10 by slightly deforming the schedule in a black-box manner relying only on measurements of the final state of the evolution and no prior knowledge of the problem”—[(emphasis added)]).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 49.
Regarding claim 51, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein (b) comprises determining a schedule for changing said one or more first variational parameters of said first Hamiltonian (McClean Pg. 8, Fig. 3: “It can be seen here that the performance of the variational schedule offers similar performance to a linear schedule roughly 10 times as long, indicating an order of magnitude reduction in the quantum evolution time required for the variationally optimal schedule” and McClean Pg. 7, 1. Variational Adiabatic Path Example: “That is, at the cost of some classical minimization, we have reduced the quantum evolution time requirement by a factor of 10 by slightly deforming the schedule in a black-box manner relying only on measurements of the final state of the evolution and no prior knowledge of the problem”—[emphasis added]).
The same motivation that was utilized for combining Peruzzo with McClean, as set forth in claim 37, is equally applicable to claim 51.
Regarding claim 52, Peruzzo in view of McClean teaches all the limitations of claim 51.
McClean teaches:
wherein (c) is performed based at least in part on said schedule (McClean Pg. 7, 1. Variational Adiabatic Path Example: “If we take the following form of the schedule Hamiltonian H(s) = A(s)Hi + [1 − A(s)] Hp (36) then the eigenvalues of this problem undergo an avoided crossing with a gap determined by the size of the perturbation ε. For this example we choose ε = 0.1 and the resulting spectrum is plotted in Fig.1 as a function of A(s)”—[wherein the method uses the schedule Hamiltonian]).
The same motivation that was utilized for combining Peruzzo and McClean, as set forth in claim 37, is equally applicable to claim 52.
Regarding claim 53, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo teaches:
wherein (c) comprises determining an encoding scheme variationally and obtaining information of said encoding scheme (Peruzzo Pg. 3–4, Prototype demonstration: “We have implemented the QPU using integrated quantum photonics technology30. Our device, shown schematically in Fig. 2, is a reconfigurable waveguide chip that can prepare and measure arbitrary two-bit pure states using several single-qubit rotations and one two-qubit entangling gate. The state is path-encoded using photon pairs generated via a spontaneous parametric downconversion process. State preparation and measurement in the Pauli basis is achieved by setting 8 voltage-driven phase shifters and counting photon detection events with silicon single-photon detectors31”—[wherein the state preparation includes using the path encoding (i.e., determined encoding scheme) and the information is obtained by counting photon detection events]).
Regarding claim 54, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein (c) comprises obtaining a qubit Hamiltonian of at least one of said first Hamiltonian and said second Hamiltonian (McClean Pg. 7, 1. Variational Adiabatic Path Example: “To further illustrate the utility of a variational perspective on adiabatic quantum computational methods in a resource constrained setting, we consider here a simple 1-qubit problem first studied in the adiabatic context in the original work of Farhi et al [54]. In particular, we will consider this problem in a resource constrained context where the maximum evolution time τ is limited. In this problem, the Hamiltonian the initial and problem Hamiltonians”]).
The same motivation that was utilized for combining Peruzzo and McClean, as set forth in claim 37, is equally applicable to claim 54.
Regarding claim 55, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein said implementing in (c) comprises preparing an initial state of one or more qubits of said at least one non-classical computer and wherein said adiabatic evolution comprises performing adiabatic quantum computation on an optimization device (McClean Pg. 1, Abstract: “We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device” and McClean Pg. 1, I. Introduction: “The VQE has the notable property that it can run on any quantum device, making it a candidate for exploring the performance of early quantum computers … This will allow for straightforward determination of expectation values of O on Q by weighted summation of projective measurements on the quantum device S” and McClean Pg. 7, 1. Variational Adiabatic Path Example: “In this simple example we use the Nelder Mead simplex method to perform a derivative free optimization of θi , in analogy to how it might be performed on a quantum device”).
The same motivation that was utilized for combining Peruzzo and McClean, as set forth in claim 37, is equally applicable to claim 55.
Regarding claim 57, Peruzzo in view of McClean teaches all the limitations of claim 55.
McClean teaches:
wherein (c) comprises generating a result state of said one or more qubits and obtaining one or more measurements of said result state, thereby obtaining said first solution to said final Hamiltonian (McClean Pg., 13, A. Bayesian Perspective: “In a Bayesian perspective, we start from an uninformative prior for the distribution Hγi. In the case of two measurement outcomes, the likelihood function is the binomial likelihood, and the posterior distributions after measurement can be worked out analytically when used with a conjugate Beta prior. These distributions are well defined even for small numbers of measurements or when ρ is close to an eigenstate of Hγ, resulting in potentially unobserved events in a sequence of measurements”).
The same motivation that was utilized for combining Peruzzo and McClean, as set forth in claim 55, is equally applicable to claim 57.
Regarding claim 58, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo teaches:
wherein said non-classical computer is a quantum computer, a quantum-ready or a quantum-enabled computer (Peruzzo Pg. 2, Abstract: “We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer”—[wherein the BRI of quantum-ready and quantum-enabled is a quantum computer coupled with a digital computer (see present disclosure ¶ 0102)]).
Regarding claim 59, Peruzzo in view of McClean teaches all the limitations of claim 37.
McClean teaches:
wherein said optimization problem comprises one or more members selected from the group consisting of a non-classical optimization problem and a classical optimization problem (McClean Pg. 1, Introduction: “Since the initial proposal by Richard Feynman [5], a number of advances have been made in understanding how to use a quantum computer to help solve eigenvalue and optimization problems … To this end, in 2014 Peruzzo and McClean et al. developed the variational quantum eigensolver (VQE), a hybrid quantum-classical algorithm designed to utilize both quantum and classical resources to find variational solutions to eigenvalue and optimization problems not accessible to traditional classical computers [1].” and McClean Pg. 2, A. General Quantum Systems and the Variational Principle: “This Hamiltonian could be derived from a physical system such as a collection of interacting spins or the discretization of an interacting electronic system. Similarly it could come from the encoding of an optimization problem or the problem Hamiltonian in adiabatic quantum computation”).
The same motivation that was utilized for combining Peruzzo and McClean, as set forth in claim 37, is equally applicable to claim 59.
Claims 50 and 61 are rejected under 35 U.S.C. 103 as being unpatentable over Peruzzo in view of McClean and further in view of Albash et al., ("Adiabatic quantum computation," in Reviews of Modern Physics, vol. 90, no. 1, 2018., https://arxiv.org/pdf/1611.04471.pdf), hereinafter “Albash”.
Regarding claim 50, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo in view of McClean does not appear to explicitly teach:
wherein (a) comprises using one or more artificial intelligence (AI) algorithms to determine said one or more parameters of said first Hamiltonian.
However, Albash teaches:
wherein (a) comprises using one or more artificial intelligence (AI) algorithms to determine said one or more first variational parameters of said first Hamiltonian (Albash Pg. 44, 7. Machine learning: “Another idea is to learn the weights of a Boltzmann machine or, after the introduction of a hidden layer, a reduced Boltzmann machine (Hinton et al., 2006). The latter forms the basis for various modern methods of deep learning. StoqAQC approaches for this problem were developed in (Adachi and Henderson, 2015; Amin et al., 2016; Benedetti et al., 2016)”—[wherein the BRI of AI algorithm is any machine learning technique (see ¶0070 of the present disclosure) and wherein a reduced Boltzmann machine is a method of deep learning (i.e., a machine learning algorithm)]).
The methods of Peruzzo in view of McClean, the teachings of Albash, and the instant application are analogous art because they pertain to solving optimization problems using Hamiltonians.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Peruzzo in view of McClean with the teachings of Albash to provide various members, groups, algorithms, and cost analyses. One would be motivated to do so to efficiently check the problem using a quantum computer (Albash Pg. 25, Left Col., 4th ¶: “In some cases this problem is easy, and in other cases it turns out to be so hard that we do not hope to solve it efficiently even on a quantum computer. Characterizing which types of local Hamiltonians fall into the latter category is the subject of QMA-completeness”—[wherein the theory of QMA completeness deals with decision problems that are efficiently checkable using quantum computers (see Albash Pg. 5, Left Col. 1st ¶)]).
Regarding claim 61, Peruzzo in view of McClean teaches all the limitations of claim 37.
Peruzzo teaches:
or (ii) if said value does not meet a threshold value, repeating (e) with updated one or more second variational parameters at least one time (Peruzzo Fig. 1, Pg. 3, Architecture of the quantum-variational eigensolver: “In QEE, quantum states that have been previously prepared are fed into the quantum modules, which compute ‹Hi›, where Hi is any given term in the sum defining H. The results are passed to the CPU, which computes ‹H›. In the quantum variational eigensolver, the classical minimization algorithm, run on the CPU, takes ‹H› and determines the new state parameters, which are then fed back to the QPU”—[wherein Peruzzo teaches that parameters are fed back into the system (i.e., one or more second parameters) to reconfigure the Hamiltonians (see Fig. 1)]).
Peruzzo in view of McClean does not appear to explicitly teach:
subsequent to (e): (i) if a value of a cost function of said solution of said optimization problem meets a threshold value, outputting a result, wherein said second solution to said final Hamiltonian is indicative of said solution of said optimization problem.
However, Albash teaches:
subsequent to (e): (i) if a value of a cost function of said solution of said optimization problem meets a threshold value, outputting a result, wherein said second solution to said final Hamiltonian is indicative of said solution of said optimization problem (Albash Pg. 25, Left Col., ¶3–4: “How far can gap amplification methods go? It was shown in (Schaller, 2008) that for the one-dimensional transverse-field quantum Ising model, and for the preparation of cluster states (Raussendorf and Briegel, 2001), it is possible to use a series of straight-line interpolations in order to generate a schedule along which the gap is always greater than a constant independent of the system size, thus avoiding the quantum phase transition. However, there exists an efficient method to compute the ground state expectation values of local operators of 2D lattice Hamiltonians undergoing exact adiabatic evolution, and this implies that adiabatic quantum algorithms based on such local Hamiltonians, with unique ground states, can be simulated efficiently if the spectral gap does not scale with the system size. In this section we review Hamiltonian quantum complexity theory from the perspective of QMA completeness. This theory naturally incorporates decision problems of the type that motivate AQC. Essentially, it concerns a problem involving the ground state of a local Hamiltonian, whose ground state energy is promised to either be below a threshold a or above another threshold b > a, and where b − a is polynomially small in the system size”—[wherein the Hamiltonians are simulated (i.e., outputting a result indicative of said solution) wherein the ground state energy (e.g., solution) is below or above a threshold (i.e., meets a threshold)]).
The methods of Peruzzo in view of McClean, the teachings of Albash, and the instant application are analogous art because they pertain to solving optimization problems using Hamiltonians.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Peruzzo in view of McClean with the teachings of Albash to provide an estimated solution based on a threshold. One would be motivated to do so to efficiently check the problem using a quantum computer (Albash Pg. 25, Left Col., 4th ¶: “In some cases this problem is easy, and in other cases it turns out to be so hard that we do not hope to solve it efficiently even on a quantum computer. Characterizing which types of local Hamiltonians fall into the latter category is the subject of QMA-completeness”—[wherein the theory of QMA completeness deals with decision problems that are efficiently checkable using quantum computers (see Albash Pg. 5, Left Col. 1st ¶)]).
Claim 56 is rejected under 35 U.S.C. 103 as being unpatentable over Peruzzo in view of McClean and Albash and further in view of Amin et al., (US 20150363708 A1), hereinafter “Amin 2”.
Regarding claim 56, Peruzzo in view of McClean teaches all the limitations of claim 55.
Albash teaches:
wherein said optimization device is a quantum annealer (Albash Pg. 4, Left Col.: “This remains an area of very active research, partly due to the original (still unmaterialized) hope that the QAA would deliver quantum speedups for NP-complete problems (Farhi et al., 2001), and partly due the availability of commercial quantum annealing devices such as those manufactured by D-Wave Systems Inc”—[(emphasis added)]).
The same motivation that was utilized for combining Peruzzo and McClean with Albash, as set forth in claim 55, is equally applicable to claim 56.
Peruzzo in view of McClean and Albash does not appear to explicitly teach:
a digital annealer.
However, Amin 2 teaches:
a digital annealer (Amin 2 ¶0064: “Techniques described herein are used to operate an analog computer and a digital computer to solve a graph isomorphism problem. Some techniques described herein use an analog computer and a digital computer as a quantum annealer to post-processing solutions by performing non-monotonic evolution to improve the solutions. Some techniques described herein use an analog computer and a digital computer to draw samples from a function”—[emphasis added]).
The methods of Peruzzo in view of McClean and Albash, the teachings of Amin 2, and the instant application are analogous art because they pertain to solving optimization problems using Hamiltonians.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Peruzzo in view of McClean and Albash with the teachings of Amin 2 to provide for digital annealing. One would be motivated to do so to improve quantum computing systems and solutions (Amin 2 ¶0064: “The various embodiments described herein provide techniques to advance quantum computing systems previously associated with quantum annealing and/or adiabatic quantum computing. Techniques described herein are used in operation of an analog computer with a new evolution schedule. In some embodiments, parameters that define the problem Hamiltonian are time-dependent. In some embodiments, annealing parameters are non-monotonically varied. Techniques described herein are used to operate an analog computer and a digital computer to solve a graph isomorphism problem. Some techniques described herein use an analog computer and a digital computer as a quantum annealer to post-processing solutions by performing non-monotonic evolution to improve the solutions. Some techniques described herein use an analog computer and a digital computer to draw samples from a function”).
Claim 60 is are rejected under 35 U.S.C. 103 as being unpatentable over Peruzzo in view of McClean and further in view of Amin 2.
Regarding claim 60, Peruzzo in view of McClean does not appear to explicitly teach:
computer memory; and one or more computer processors operatively coupled to said computer memory, wherein said one or more computer processors are individually or collectively programmed to;
However, Amin 2 teaches:
computer memory; and one or more computer processors operatively coupled to said computer memory, wherein said one or more computer processors are individually or collectively programmed to (Amin 2 ¶0067: “Digital computer 105 may include at least one digital processor (such as, central processor unit 110), at least one system memory 120, and at least one system bus 117 that couples various system components, including system memory 120 to central processor unit 110”);
The methods of Peruzzo in view of McClean, the teachings of Amin 2, and the instant application are analogous art because they pertain to solving optimization problems using Hamiltonians.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Peruzzo in view of McClean with the teachings of Amin 2 to provide basic system components used in Perruzo and McClean but not explicitly recited. One would be motivated to do so to advance quantum computing systems (Amin 2 ¶0064: “The various embodiments described herein provide techniques to advance quantum computing systems previously associated with quantum annealing and/or adiabatic quantum computing”).
Regarding the remaining limitations of Claim 60, although varying in scope, the remaining limitations of claim 60 are substantially the same as the limitations of claim 37, respectively. Thus, claim 60 is rejected using the same reasoning and analysis as claim 37 above.
Conclusion
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/N.B.S./Examiner, Art Unit 2126
/DAVID YI/Supervisory Patent Examiner, Art Unit 2126