DETAILED ACTION
This action is responsive to claims filed 11/15/2024.
Claims 1–20 are pending for examination.
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 .
Information Disclosure Statement
The information disclosure statements (IDS) submitted on 07/08/2021 and 01/04/2023 are in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statements are being considered and attached by the examiner.
Response to Arguments
In reference to 35 USC § 101
Applicant’s arguments, filed with respect to the claim § 101 rejections have been fully considered and are persuasive. The § 101 rejections have been withdrawn in view of the reopening of prosecution and amendments.
Examiner notes that while the claims recite several limitations that are abstract ideas (mental processes), 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 variationally optimizing measurement methods, applied on a hybrid quantum-classical computing system. The independent claims include limitations that require the use of specialized instruments. 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 variation 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 [0015–0023, 0081, 0082]: “the plurality of controllable quantum systems are implemented in a corresponding plurality of atoms. The atoms may implement the two-level systems in a radiative transition between a ground state and an excited state.” 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 with respect to the § 103 rejections 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 § 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.
Claims 16–17 are rejected under 35 U.S.C. 112(b) as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention.
Regarding claim 16, the claim include acronyms with no definition for the meaning of the acronym (i.e., nEn, nDe). It is unclear as to the exact meaning of those acronyms and, therefore, indefinite. Examiner is construing the acronyms as follows: nEn is number of preparation gate layers and nDe is a number of decoding gate layers.
Regarding claim 17, claim 17 depends from claim16 and therefore includes all the limitations of claim 16. Thus, claim 17 is rejected for including acronyms with no definition for the meaning as outlined in claim 16.
Appropriate correction is required.
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 1–20 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 Kaubruegger et al., (Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks," in Physical Review X, vol. 11, no. 4, 2021, https://arxiv.org/pdf/2102.05593), hereinafter “Kaubruegger”.
Regarding claim 1, Peruzzo teaches:
A method of measuring a physical quantity, the method being implemented in a hybrid classical-quantum system, the hybrid classical-quantum system comprising a parametrized quantum circuit on the basis of a plurality of controllable quantum systems and further comprising a classical computation system, the method comprising the steps of (Peruzzo pg. 1–2: “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. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. 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. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques … Our attention is restricted to the class of operators whose expectation value can be measured efficiently on S and mapped to Q”):
a) initializing the plurality of controllable quantum systems in an initial state (Peruzzo pg. 5, III. State Parameterization and Preparation: “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”—[wherein the state of more than one class is prepared]);
b) applying a set of preparation gates to the plurality of controllable quantum systems for preparing the plurality of controllable quantum systems in a non-classical state (Peruzzo pg. 10, C. Unitary coupled cluster: “Moreover if one allows values of different parameters at different Trotter steps, one may perform arbitrary 1 and 2 qubit gates at k=2, which forms a universal gate set and the ansatz can be made equivalent to an arbitrary quantum circuit with a sufficient number of Trotter steps …. thus its exponential exp(O) can be used to form an arbitrary two qubit gate on any two qubits, or said differently, an arbitrary element of SU(4) on any two qubits. Arbitrary two qubit gates on any qubit are known to constitute a universal gate set [77], and then clearly can be used to construct any desired universal gate set such as the Clifford+T set”—[wherein the universal gate set is made to be an arbitrary quantum circuit that can be used to construct any desired universal gate set]),
c) evolving the non-classical state over a time period for obtaining an evolved state of the plurality of controllable quantum systems (Peruzzo pg. 5–8. B Adiabatically parameterized states: “In a noiseless coherent situation at 0K, the unitarity of evolution dictates that the final state of the evolution is uniquely determined by the path f”—[wherein the states evolve according to a path over a period of time]);
e) performing a measurement of the plurality of controllable quantum systems (Peruzzo pg. 2–3, II. Background and Notation, pg. 14–15, B. Cost Reduction: “As terms within a commuting set are measured on the same state within each pass of the procedure”); and
f) determining a derived value of the physical quantity based on a mapping function between an outcome of the measurement and the physical quantity on the classical computation system (Peruzzo pg. 10, D. Fermionic UCC, pg. 14–15, B. Cost Reduction: “We can understand the equivalent action on qubits by mapping the fermion operators to spin operators” and “As terms within a commuting set are measured on the same state within each pass of the procedure, two operators within a set may be correlated such that the estimators of their average may have non-zero covariance i.e. Cov[Hα , Hβ ]= 0. This additional covariance can either require more measurements for the set of terms if the covariance is positive, or less if it is negative in analogy to the method of antithetic variables or correlated sampling in classical Monte Carlo simulations”—[wherein the covariance is determined based on mapping after measuring and is performed classically using correlated sampling]);
wherein the set of preparation gates and the set of decoding gates each comprise non- linear quantum gates suitable for generating a non-classical state of the plurality of controllable quantum systems (Peruzzo pg. 15–16, V. Optimization of
θ
→
: “The final piece of the variational quantum eigensolver is a method for updating the parameters θ based on the measured value of the objective function of interest. The dependence of the objective function on the parameters will, of course, depend upon the ansatz being used and will in general be non-linear and non-convex … The field of non-linear optimization is well developed with many tools both general and more specialized methods to different optimization problems”—[wherein ansatz (i.e., prepared state) is non-linear and generated by the non-linear universal gate set])
each comprise variational quantum gates characterized by variable actions onto controllable quantum systems of the plurality of controllable quantum systems (Peruzzo pg. 5–8, B. Adiabatically parameterized states: “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 con text where the maximum evolution time τ is limited. In this problem, the Hamiltonian the initial and problem Hamiltonians are given by”—[wherein the quantum system includes gates characterized by adiabatic quantum computational methods that control the time schedule]); and
wherein the variable actions are variationally optimized to find an extremal value of a cost function, wherein the cost function averages an estimation error of the derived value over a pre-defined expected prior distribution of the physical quantity (Peruzzo Figs. 2–3, pg. 5–8, B. Adiabatically parameterized states: “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). 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. We use as an initial condition θ1 = .15τ and θ2 = .85τ in the optimization, which corresponds to the linear path”—[wherein the non-linear minimization includes a cost function finds the extremal value (e.g., minimization) that the expectation value of the final state using a fixed maximum evolution time and initial conditions (i.e., a pre-defined expected prior distribution)]).
Peruzzo does not appear to explicitly teach:
d) applying a set of decoding gates to the plurality of controllable quantum systems in the evolved state.
However, Kaubruegger teaches:
d) applying a set of decoding gates to the plurality of controllable quantum systems in the evolved state (Kaubruegger Figs. 2, 10, pg. 4: “The most general circuits satisfying the x-parity constraint for a fixed number nEn and nDe of layers of entangling and decoding gates … Performance of the variationally enhanced interferometer with N = 64 particles. Performance is shown in terms of the posterior phase distribution width relative to the prior width, ∆φ/δφ, for a given prior, that is, for a given dynamic range of the interferometer. Colored lines show the performance of variationally optimized circuits for the depth (nEn,nDe) of entangling and decoding layers as indicated. The number of variational parameters is given by 3(nEn+nDe). The performance of the optimal quantum interferometer (OQI) [31] is indicated by the dotted line. The shaded areas indicate the classically accessible (purple) and the quantum mechanically forbidden (gray) regions (for N = 64). Related results applied to atomic clocks are shown in Fig. 10”).
The methods of Peruzzo, the teachings of Kaubruegger, and the instant application are analogous art because they pertain to variationally evolving quantum systems to make measurements.
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 Kaubruegger to provide gates that allow for measurement in the evolved state. One would be motivated to do so to aid in the optimization of the variational quantum gates system (Kaubruegger Figs. 2, 10, pg. 4: “Performance of the variationally enhanced interferometer with N = 64 particles. Performance is shown in terms of the posterior phase distribution width relative to the prior width, ∆φ/δφ, for a given prior, that is, for a given dynamic range of the interferometer. Colored lines show the performance of variationally optimized circuits for the depth (nEn,nDe) of entangling and decoding layers as indicated. The number of variational parameters is given by 3(nEn+nDe). The performance of the optimal quantum interferometer (OQI) [31] is indicated by the dotted line. The shaded areas indicate the classically accessible (purple) and the quantum mechanically forbidden (gray) regions (for N = 64). Related results applied to atomic clocks are shown in Fig. 10”).
Regarding claim 2, Peruzzo in view of Kaubruegger teaches all the limitations of claim 1.
Peruzzo teaches:
wherein the cost function is mathematically equivalent to
C
=
∫
d
ϕ
ϵ
ϕ
P
ϕ
wherein ϕ is the physical quantity, ϵ(ϕ) is the average estimation error for a given value of the physical quantity, and P(ϕ) is the pre-defined expected prior distribution of the physical quantity (Peruzzo pg. 12–15, IV. Operator Averaging: “Once a trial state |Ψ(θ) has been prepared, the next crucial step in the VQE is the evaluation of the objective function corresponding to the problem operator H, {H} (θ)={Ψ(θ)|H|Ψ(θ)}. One possibility is to use the quantum phase estimation algorithm[6–8]. If |Ψ(θ) is an eigenstate, then the value is obtained after a single state preparation with a cost in the desired precision of O(1/e). Unfortunately, to achieve this precision, all of the operations must be coherent which is a prohibitive technological requirement for current and near-term quantum computers. Moreover, if the state is instead a mixture of many eigenstates, it will still require O(1/2) repetitions of the entire procedure to converge the value H (θ)to a precision e”).
Regarding claim 3, Peruzzo in view of Kaubruegger teaches all the limitations of claim 2.
Peruzzo teaches:
wherein the estimation error ϵ(ϕ) is the average mean square error of the derived value with respect to an actual value of the physical quantity (Peruzzo pg. 14, B. Cost Reduction: “As the estimator is now biased, one must consider the bias-variance trade off to maintain the desired accuracy. In order to achieve an expected mean-square-error of in the final answer”).
Regarding claim 4, Peruzzo in view of Kaubruegger teaches all the limitations of claim 3.
Peruzzo teaches:
wherein the cost function is mathematically equivalent to
ϵ
ϕ
=
∫
d
x
ϕ
-
ϕ
e
s
t
x
2
p
x
|
ϕ
wherein x is the outcome, ϕest(x) is the mapping function mapping the outcome x to the derived value of the physical quantity, ϕ is the actual value of the physical quantity, and p(x|ϕ) is the conditional probability of measuring the outcome x when the actual value of the physical quantity is ϕ (Peruzzo pg. 12–15, IV. Operator Averaging: “Using the formulas from the previous section to compute the expected number of state preparations for each grouping of operators to a precision , we may proceed as follows … The sum of these measurements for all the operators is defined to be the new measurement qi = γxγi, and the estimator for the average over many realizations is simply the arithmetic mean … allowing one to more conveniently estimate only variance of uncorrelated estimators to determine the un-certainty in the final estimate and fix the desired tolerances per term when measuring … Finally we note that the method of calculating operator averages outlined in this section often yields additional information besides the original designed expectation value. For example, in the case of quantum chemistry, the individual operators measured that compose the Hamiltonian are the reduced 1 and 2 electron density matrices”).
Regarding claim 5, Peruzzo in view of Kaubruegger teaches all the limitations of claim 1.
Peruzzo teaches:
wherein the pre-defined expected prior distribution approximates or is mathematically equivalent to a Normal distribution centered around an expected mean value of the physical quantity or the derived value (Peruzzo pg. 12–15, IV. Operator Averaging: “Once the probability distribution P({H}) is known, one may numerically bracket the desired confidence interval to determine the precision of the approach. Practically speaking, the convergence of this final probability distribution to a normal distribution is quite rapid, and thus the normal approximation relying on the variance is the standard procedure … In order to achieve an expected mean-square-error of in the final answer, we must decrease the variance of the estimator on the remaining terms such that C2 2 + M−k∗ γ Var[Hγ ] < 2. This may be achieved by changing the per-term variance threshold for each Hγ to be (1−C2) 2/(M −k∗). This results in a new expected number of measurements M−k∗ n∗ expect = γ (M −k∗)Var[Hγ] (1 −C2) 2. One is free to choose a value of C ∈ [0,1) to maximize computational efficiency according to the particular constraints of experiment and the distribution of operators in the sum”).
Regarding claim 6, Peruzzo in view of Kaubruegger teaches all the limitations of claim 1.
Peruzzo teaches:
wherein the derived value is a periodic function with respect to changes of the physical quantity, and the pre-defined expected prior distribution is associated with a standard deviation δϕ smaller than a period of the periodic function (Peruzzo pg. 12–15, IV. Operator Averaging: “Once the probability distribution P({H}) is known, one may numerically bracket the desired confidence interval to determine the precision of the approach. Practically speaking, the convergence of this final probability distribution to a normal distribution is quite rapid, and thus the normal approximation relying on the variance is the standard procedure … with e0 defined to be 0, that defines the maximal bias introduced by truncating the k smallest terms. Using this sequence, one may choose a constant C ∈ [0,1) and re move the k∗ lowest terms by finding the maximal index k∗ in the sequence such that ek∗ < Ce … In order to achieve an expected mean-square-error of in the final answer, we must decrease the variance of the estimator on the remaining terms such that C2 2 + M−k∗ γ Var[Hγ ] < e2. This may be achieved by changing the per-term variance threshold for each Hγ to be (1−C2) 2/(M −k∗). This results in a new expected number of measurements M−k∗ n∗ expect = γ (M −k∗)Var[Hγ] (1 −C2) 2. One is free to choose a value of C ∈ [0,1) to maximize computational efficiency according to the particular constraints of experiment and the distribution of operators in the sum”—[wherein the confidence interval is derived from a period function with respect to the distribution represented by the Hamiltonians associated with the pre-defined variance associated with a standard deviation less than the period of the function (e.g., ek∗ < Ce)]).
Regarding claim 7, Peruzzo in view of Kaubruegger teaches all the limitations of claim 1.
Peruzzo teaches:
wherein the derived value is a periodic function with respect to changes of the physical quantity (Peruzzo pg. 12–15, IV. Operator Averaging: “In practical implementations these issues are often left unaddressed rigorously in stochastic sampling methods and a reasonable minimum number of measurements is chosen such as n = 1000 or n = 10000 before the estimates of Var[Hγ]({xi}) are taken to be reliable, trusting that after a number of samples that it is well represented by a normal distribution and the higher moments associated with errors in estimates of the variance vanish rapidly”—[wherein the stochastic method is proportional to the number of the number of measurements of the quantity]), and
Kaubruegger teaches:
the pre-defined expected prior distribution is associated with a standard deviation δϕ greater than 1/N of the period of the periodic function, wherein N is the number of controllable quantum systems (Kaubruegger Figs. 7, 10, pg. 8: “Plot of ΔϕM N, i.e. the standard deviation of an effective measurement rescaled by the ensemble size N, vs. prior width δϕ. Solid lines show results for the optimized interferometer with circuit depth (nEn; nDe) = (2, 5) in comparison to the analytic expression describing a GHZ-state interferometer [Eq. (21)] shown with dashed lines and the π-corrected Heisenberg limit including phase slips [Eq. (22)] shown with dotted lines. The Heisenberg limit and the π -corrected Heisenberg limit are indicated with dotted horizontal lines”—[wherein the standard deviation δϕ is rescaled by the ensemble size N to be greater than 1/N of the period]).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 1, is equally applicable to claim 7.
Regarding claim 8, Peruzzo in view of Kaubruegger teaches all the limitations of claim 1.
Peruzzo teaches:
wherein the plurality of controllable quantum systems implement a plurality of two-level-systems, each controllable quantum system implementing one two-level system of the plurality of two-level systems, and wherein the mapping function maps a difference between the number of controllable quantum systems in an excited state and in a ground state of the plurality of two-level-systems to the derived value of the physical quantity (Peruzzo pg. 8, pg. 10, C. Unitary coupled cluster, pg. 14–15, B. Cost Reduction: “here we document its generalization to generic collections of interacting two level quantum systems” and “Moreover if one allows values of different parameters at different Trotter steps, one may perform arbitrary 1 and 2 qubit gates at k=2, which forms a universal gate set and the ansatz can be made equivalent to an arbitrary quantum circuit with a sufficient number of Trotter steps …. thus its exponential exp(O) can be used to form an arbitrary two qubit gate on any two qubits, or said differently, an arbitrary element of SU(4) on any two qubits. Arbitrary two qubit gates on any qubit are known to constitute a universal gate set [77], and then clearly can be used to construct any desired universal gate set such as the Clifford+T set” and “As terms within a commuting set are measured on the same state within each pass of the procedure, two operators within a set may be correlated such that the estimators of their average may have non-zero covariance i.e. Cov[Hα , Hβ ]= 0. This additional covariance can either require more measurements for the set of terms if the covariance is positive, or less if it is negative in analogy to the method of antithetic variables or correlated sampling in classical Monte Carlo simulations”—[wherein the covariance is determined based on mapping after measuring and is performed on 1 and 2 qubit gates at k=2).
Regarding claim 9, Peruzzo in view of Kaubruegger teaches all the limitations of claim 8.
Kaubruegger teaches:
wherein the mapping function is mathematically equivalent to a linear function of the difference at least over a standard deviation of the pre-defined expected prior distribution (Kaubruegger Pg. 3–4, II. Quantum Variational Optimization Of Ramsey Interferometry, pg. 6, C. Results of optimization: “To be specific, we assume for the prior a normal distribution Pδϕ(ϕ) with standard deviation δϕ [see Eq. (3)]. In addition, (10) assumes a linear estimator ϕest(m) = am which is close to optimal, as shown below. We note that it is possible to use the optimal Bayesian estimator, which however is computationally demanding” and “The estimator expectation value of the (0, 0)- and (1, 0)- circuit (CSS and SSS interferometer) is given by a sine function [purple and orange line in panel (a)], thus, it can unambiguously map the estimated phase to the actual phase in the range between -π/2 = 2 and π/2 = 2 … Finally, more complex decoding operations employed by the (1, 3)- and (2, 5)- circuit (red and green lines) allow to approach the performance of the optimal interferometer (black dotted lines). The linear regime of ϕest extends almost to the full 2π range, and the estimator error is well suppressed for phases deeply within the tails of the prior”—[wherein the mapping function is mathematically equivalent to a linear function with a standard deviation of the prior distribution]).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 1, is equally applicable to claim 9.
Regarding claim 10, Peruzzo in view of Kaubruegger teaches all the limitations of claim 1.
Kaubruegger teaches:
wherein the physical quantity is an oscillating frequency of electromagnetic radiation interacting with the plurality of controllable quantum systems prior to and after step c), and wherein the derived value is a phase originating from a difference in the oscillating frequency and a resonant frequency of the plurality of controllable quantum systems (Kaubruegger pg. 1–2, 17: “Examples include the development of optical clocks [1], atom [2] and light [3] interferometers, and magnetic _eld sensing [4]. These achievements have opened the door to novel applications from the practical to the scientific … In the continuing effort to push the boundaries of quantum sensing, entanglement as a key element of quantum physics gives the opportunity to reduce quantum fluctuations inherent in quantum measurements below the standard quantum limit (SQL), i.e. what is possible with uncorrelated constituents [12]. Squeezed light improves gravitational wave detection [13], allows lifescience microscopy below the photodamage limit [14], further, squeezing has been demonstrated in atom interferometers [15{30]. However, beyond the SQL, quantum physics imposes ultimate limits on quantum sensing, and one of the key challenges is to identify, and in particular devise experimentally realistic strategies defining optimal quantum sensors … Our discussion of optimal single-shot Ramsey interferometry [75] has immediate relevance for atomic clocks [12, 76–79]. An optical atomic clock operates by locking the frequency of an oscillator, represented by a classical laser field with fluctuating frequency ωL(t), to the transition frequency ωA of an ensemble of N isolated atoms [1]. The locking of the laser to the atomic transition is achieved by repeatedly measuring the accumulated phase ϕ = R T 0 dt[!L(t) !A] in Ramsey interferometry with interrogation time T. Importantly, the width δϕ of the distribution of this phase increases with the Ramsey time T” and “To stabilise the laser frequency for long averaging times t >> T a feedback correction is applied to the laser frequency at the end of each cycle. In the simulations, the estimated frequency deviation yest;k =mk=(2!AT@- m(-)j-=0) obtained from measurement result mk at tk is multiplied by a gain factor 0 < g <= 1 and subtracted from the true laser frequency. This integrating servo corrects frequency errors over ~ 1/g cycles and is sufficient to achieve a robust stabilization at t=T >> 1/g for flicker noise limited lasers [79]”).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 1, is equally applicable to claim 10.
Regarding claim 11, Peruzzo teaches:
a plurality of controllable quantum systems implementing a corresponding plurality of two-level systems, each controllable quantum system implementing one two-level system of the plurality of two-level systems, (Peruzzo pg. 10, C. Unitary coupled cluster: “Moreover if one allows values of different parameters at different Trotter steps, one may perform arbitrary 1 and 2 qubit gates at k=2, which forms a universal gate set and the ansatz can be made equivalent to an arbitrary quantum circuit with a sufficient number of Trotter steps …. thus its exponential exp(O) can be used to form an arbitrary two qubit gate on any two qubits, or said differently, an arbitrary element of SU(4) on any two qubits. Arbitrary two qubit gates on any qubit are known to constitute a universal gate set [77], and then clearly can be used to construct any desired universal gate set such as the Clifford+T set”—[wherein the universal gate set is made to be an arbitrary quantum circuit that can be used to construct any desired universal gate set and is performed on 1 and 2 qubit gates at k=2 (i.e., two-level systems)]);
a controller configured to (Peruzzo 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”—[wherein the pre-threshold device is a quantum computing systems that operate within a regime]):
a) initialize the plurality of controllable quantum systems in an initial state (Peruzzo pg. 5, III. State Parameterization and Preparation: “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”—[wherein the state of more than one class is prepared]);
b) apply a set of preparation gates to the plurality of controllable quantum systems (Peruzzo pg. 10, C. Unitary coupled cluster: “Moreover if one allows values of different parameters at different Trotter steps, one may perform arbitrary 1 and 2 qubit gates at k=2, which forms a universal gate set and the ansatz can be made equivalent to an arbitrary quantum circuit with a sufficient number of Trotter steps …. thus its exponential exp(O) can be used to form an arbitrary two qubit gate on any two qubits, or said differently, an arbitrary element of SU(4) on any two qubits. Arbitrary two qubit gates on any qubit are known to constitute a universal gate set [77], and then clearly can be used to construct any desired universal gate set such as the Clifford+T set”—[wherein the universal gate set is made to be an arbitrary quantum circuit that can be used to construct any desired universal gate set]),
c) permit an evolution of the plurality of controllable quantum systems over a time period (Peruzzo pg. 5–8. B Adiabatically parameterized states: “In a noiseless coherent situation at 0K, the unitarity of evolution dictates that the final state of the evolution is uniquely determined by the path f”—[wherein the states evolve according to a path over a period of time]);
e) determine a measurement outcome of the plurality of controllable quantum systems (Peruzzo pg. 2–3, II. Background and Notation, pg. 14–15, B. Cost Reduction: “As terms within a commuting set are measured on the same state within each pass of the procedure”); and
f) determine a feedback onto the oscillator based on a mapping function between the measurement outcome and a derived frequency difference between the oscillator frequency and the target clock frequency associated with the plurality of two-level systems (Peruzzo pg. 10, D. Fermionic UCC, pg. 14–15, B. Cost Reduction: “We can understand the equivalent action on qubits by mapping the fermion operators to spin operators” and “As terms within a commuting set are measured on the same state within each pass of the procedure, two operators within a set may be correlated such that the estimators of their average may have non-zero covariance i.e. Cov[Hα , Hβ ]= 0. This additional covariance can either require more measurements for the set of terms if the covariance is positive, or less if it is negative in analogy to the method of antithetic variables or correlated sampling in classical Monte Carlo simulations”—[wherein the equivalent action is feedback and the covariance is determined based on mapping after measuring and is performed classically using correlated sampling]);
wherein before and after the evolution of the plurality of controllable quantum systems over the time period, the controller drives a state rotation of each of the plurality of controllable quantum systems [using the electromagnetic radiation of the oscillator to implement a Ramsey interferometer] (Peruzzo pg. 12: “As a result, all that is required is the weighted sum of the results from simple Pauli measurements. This is an operation requiring coherence time O(1) assuming parallel qubit rotation and readout are possible, otherwise the coherence time required is O(k) where k is the locality of the term to be measured”—[wherein the system controls the qubit rotation based on the schedule of coherence time]); and
wherein the set of preparation gates and the set of decoding gates each comprise non- linear quantum gates suitable for generating a non-classical state of the plurality of controllable quantum systems (Peruzzo pg. 15–16, V. Optimization of
θ
→
: “The final piece of the variational quantum eigensolver is a method for updating the parameters θ based on the measured value of the objective function of interest. The dependence of the objective function on the parameters will, of course, depend upon the ansatz being used and will in general be non-linear and non-convex … The field of non-linear optimization is well developed with many tools both general and more specialized methods to different optimization problems”—[wherein ansatz (i.e., prepared state) is non-linear and generated by the non-linear universal gate set]) and
each comprise variational quantum gates characterized by variable actions onto at least one of the plurality of controllable quantum systems (Peruzzo pg. 5–8, B. Adiabatically parameterized states: “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 con text where the maximum evolution time τ is limited. In this problem, the Hamiltonian the initial and problem Hamiltonians are given by”—[wherein the quantum system includes gates characterized by adiabatic quantum computational methods that control the time schedule]); and
wherein values of the variable actions are the result of a variational optimization of the variable actions based on a cost function, wherein the cost function averages an estimation error of the derived value over a pre-defined expected prior distribution of the physical quantity (Peruzzo Figs. 2–3, pg. 5–8, B. Adiabatically parameterized states: “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). 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. We use as an initial condition θ1 = .15τ and θ2 = .85τ in the optimization, which corresponds to the linear path”—[wherein the non-linear minimization includes a cost function finds the extremal value (e.g., minimization) that the expectation value of the final state using a fixed maximum evolution time and initial conditions (i.e., a pre-defined expected prior distribution)]).
Peruzzo does not appear to explicitly teach:
A clock comprising:
an oscillator for generating electromagnetic radiation associated with an oscillator frequency; wherein an energy difference of the two-level systems corresponds to a target clock frequency of the clock;
d) apply a set of decoding gates to the plurality of controllable quantum systems; and
[wherein before and after the evolution of the plurality of controllable quantum systems over the time period, the controller drives a state rotation of each of the plurality of controllable quantum systems] using the electromagnetic radiation of the oscillator to implement a Ramsey interferometer
However, Kaubruegger teaches:
A clock comprising:
an oscillator for generating electromagnetic radiation associated with an oscillator frequency (Kaubruegger Fig. 10, pg. 2, 11, 14: “An optical atomic clock operates by locking the frequency of an oscillator, represented by a classical laser field with fluctuating frequency ωL(t), to the transition frequency ωA of an ensemble of N isolated atoms [1]” and “Larger interrogation times correspond to wider prior phase distributions hence the π-corrected HL becomes the limiting factor, σπHL = πN−1(bαT)−1/2 (green dashed line). The optimal quantum clock instability in the limit of large number of atoms, N → ∞, is fundamentally restricted by the interplay between the σπHL and σOQC CTL as we will discuss below. The instabilities of clocks based on variationally optimized interferometers employing quantum circuits of various complexities are shown in Fig. 10(b)” and “we optimize quantum circuits in view of an ‘optimal measurement’ cost function, and it is the (potentially large scale) entanglement represented by the variational many particle wavefunction in N-atom quantum memory”).
Examiner notes that Peruzzo on at least pg. 11, E. Quantum Error Suppression and Symmetries, teaches: “In a pre-threshold, non-error corrected quantum device, there can be a distinction between the formal specification of the ansatz preparation Ua(θ) as a gate or operation sequence and the operation sequence actually performed on the system with inputs θ, which we will denote ˜Ua(θ). We call an error in such an implementation suppressible if there exists a correction input vector β such that ||Ua(θ)− ˜Ua(θ+β)|| < for a specified > 0, and further denote it variationally suppressible if the corrected vector θ+β also corresponds to an optimum on the parameter surface. In such a case, the variational quantum eigensolver can suppress these errors naturally without detailed knowledge of the error mechanism.”
However, Kaubruegger teaches:
wherein an energy difference of the two-level systems corresponds to a target clock frequency of the clock (Kaubruegger Fig. 10, pg. 11: “Larger interrogation times correspond to wider prior phase distributions hence the π-corrected HL becomes the limiting factor, σπHL = πN−1(bαT)−1/2 (green dashed line). The optimal quantum clock instability in the limit of large number of atoms, N → ∞, is fundamentally restricted by the interplay between the σπHL and σOQC CTL as we will discuss below. The instabilities of clocks based on variationally optimized interferometers employing quantum circuits of various complexities are shown in Fig. 10(b)”—[wherein the larger interrogation times correspond wider distributions optimized by the variational method of the two-level systems which may correspond to an optimal quantum clock frequency]);
d) apply a set of decoding gates to the plurality of controllable quantum systems (Kaubruegger Figs. 2, 10, pg. 4: “The most general circuits satisfying the x-parity constraint for a fixed number nEn and nDe of layers of entangling and decoding gates … Performance of the variationally enhanced interferometer with N = 64 particles. Performance is shown in terms of the posterior phase distribution width relative to the prior width, ∆φ/δφ, for a given prior, that is, for a given dynamic range of the interferometer. Colored lines show the performance of variationally optimized circuits for the depth (nEn,nDe) of entangling and decoding layers as indicated. The number of variational parameters is given by 3(nEn+nDe). The performance of the optimal quantum interferometer (OQI) [31] is indicated by the dotted line. The shaded areas indicate the classically accessible (purple) and the quantum mechanically forbidden (gray) regions (for N = 64). Related results applied to atomic clocks are shown in Fig. 10”); and
using the electromagnetic radiation of the oscillator to implement a Ramsey interferometer (Kaubruegger pg. 1, I. Introduction: “In our discussion below we will focus on optimal Ramsey interferometry”).
The methods of Peruzzo, the teachings of Kaubruegger, and the instant application are analogous art because they pertain to variationally evolving quantum systems to make measurements.
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 Kaubruegger to provide a clock with a frequency, gates that allow for measurement in the evolved state, and measurements corresponding to a target. One would be motivated to do so to aid in the optimization of the variational quantum gates system (Kaubruegger Figs. 2, 10, pg. 4: “Performance of the variationally enhanced interferometer with N = 64 particles. Performance is shown in terms of the posterior phase distribution width relative to the prior width, ∆φ/δφ, for a given prior, that is, for a given dynamic range of the interferometer. Colored lines show the performance of variationally optimized circuits for the depth (nEn,nDe) of entangling and decoding layers as indicated. The number of variational parameters is given by 3(nEn+nDe). The performance of the optimal quantum interferometer (OQI) [31] is indicated by the dotted line. The shaded areas indicate the classically accessible (purple) and the quantum mechanically forbidden (gray) regions (for N = 64). Related results applied to atomic clocks are shown in Fig. 10”).
Regarding claim 12, Peruzzo in view of Kaubruegger teaches all the limitations of claim 11.
Peruzzo teaches:
wherein the plurality of controllable quantum systems are implemented in a corresponding plurality of atoms (Peruzzo pg. 3, II. Background and Notation: “Given a set of nuclear charges Zi and a number of electrons, the standard form of the electronic structure problem is to solve for the eigenvectors and eigenvalues of the electronic Hamiltonian H, written as where atomic units have been used, Ri are nuclear positions, ri electronic positions, and Mi are nuclear masses”).
Regarding claim 13, Peruzzo in view of Kaubruegger teaches all the limitations of claim 11.
Kaubruegger teaches:
wherein the controller drives a global rotation of the states of the plurality of controllable quantum systems by an angle of substantially π/2 to implement the Ramsey interferometer (Kaubruegger Fig. 1, pg. 2: “Quantum circuit representation of Ramsey interferometer with uncorrelated atoms … We illustrate the approach with a variational circuit built from global spin rotations Rx and one-axis-twisting gates Tx,z available in neutral atom and ion quantum simulation platforms, as discussed in Sec. IIB. The circuits optimization, shown as a feedback loop (in red), can be performed on a classical computer, or, if the complexity of underlying quantum many-body problem exceeds capabilities of classical computers, on the sensor itself, thus, leading to a (relevant) quantum advantage, see Sec. IIG”).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 11, is equally applicable to claim 13.
Regarding claim 14, Peruzzo in view of Kaubruegger teaches all the limitations of claim 11.
Peruzzo teaches:
wherein the pre-defined expected prior distribution corresponds to an expected statistical distribution of the actual value after the evolution over the time period (Peruzzo pg. 12–15, IV. Operator Averaging: “Once the probability distribution P({H}) is known, one may numerically bracket the desired confidence interval to determine the precision of the approach. Practically speaking, the convergence of this final probability distribution to a normal distribution is quite rapid, and thus the normal approximation relying on the variance is the standard procedure … with e0 defined to be 0, that defines the maximal bias introduced by truncating the k smallest terms. Using this sequence, one may choose a constant C ∈ [0,1) and re move the k∗ lowest terms by finding the maximal index k∗ in the sequence such that ek∗ < Ce … In order to achieve an expected mean-square-error of in the final answer, we must decrease the variance of the estimator on the remaining terms such that C2 2 + M−k∗ γ Var[Hγ ] < e2. This may be achieved by changing the per-term variance threshold for each Hγ to be (1−C2) 2/(M −k∗). This results in a new expected number of measurements M−k∗ n∗ expect = γ (M −k∗)Var[Hγ] (1 −C2) 2. One is free to choose a value of C ∈ [0,1) to maximize computational efficiency according to the particular constraints of experiment and the distribution of operators in the sum”—[wherein the confidence interval is derived from a period function with respect to the distribution]).
Regarding claim 15, Peruzzo in view of Kaubruegger teaches all the limitations of claim 11.
Kaubruegger teaches:
wherein the set of preparation gates and the set of decoding gates each implement global rotations of the states of the plurality of controllable quantum systems approximating the operator Rμ(θ1) = exp(-iθ1Jμ) and a variational non- linear quantum gate selected from the group of a generalized exchange coupling approximating the operator G(t) = exp[-iHt], with
H
=
∑
k
,
t
=
1
N
j
k
,
l
σ
k
μ
σ
l
v
+
∑
k
Δ
k
σ
k
p
or
H
=
∑
k
,
t
=
1
N
j
k
,
l
σ
k
μ
σ
l
μ
+
∑
k
Δ
k
σ
k
v
and with jk,l representing a generalized coupling strength between controllable quantum systems k, l, a one-axis twisting operation of the states of the plurality of controllable quantum systems approximating the operator Tv(θ2) = exp(-iθ2Jv2), and a Rydberg dressing operation approximating the unitary operator Dv(θ2) = exp (-iθ2(
H
v
D
/V0)], with
H
v
D
being the effective interaction Hamiltonian and V0 corresponding to the interaction strength, with μ, v, p specifying the axis of rotation about respective variable angles θ1, θ2, the variable angles θ1, θ2 and jk,l or a function thereof being the respective variable actions (Kaubruegger Fig. 8, 9–10, G. Finite range interactions: “Our previous discussion assumed infinite range interactions as entangling quantum resource, while e.g. neutral atoms stored in tweezer arrays feature finite range interactions. The variational optimization of the BMSE can be directly generalized to finite range interactions, which we illustrate by optimizing a sensor based on Rydberg dressing resources [97, 98] Dµ(θ) = exp[−iθ(HDµ /V0)], as is realized in alkaline earth tweezer clocks [46–48]. The effective interaction Hamiltonian we use for the optimization reads
PNG
media_image1.png
72
485
media_image1.png
Greyscale
where rk represents the position of particle k. The interaction strength at short distances V0 and interaction radius RC depend on the Rydberg level and the dressing laser used to let the particles interact [99]”).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 11, is equally applicable to claim 15.
Regarding claim 16, Peruzzo in view of Kaubruegger teaches all the limitations of claim 11.
Peruzzo teaches:
wherein each layer comprises at least one nonlinear quantum gate (Peruzzo pg. 15–16, V. Optimization of
θ
→
: “The final piece of the variational quantum eigensolver is a method for updating the parameters θ based on the measured value of the objective function of interest. The dependence of the objective function on the parameters will, of course, depend upon the ansatz being used and will in general be non-linear and non-convex … The field of non-linear optimization is well developed with many tools both general and more specialized methods to different optimization problems”—[wherein ansatz (i.e., prepared state) is non-linear and generated by the non-linear universal gate set])
Kaubruegger teaches:
wherein the set of preparation gates and the set of decoding gates each comprise a number of nEn and nDe layers of quantum gates, respectively, wherein nEn and nDe are positive integer numbers, and is parametrized by at least one variable action (Kaubruegger Fig. 1, pg. 2, 4: “Quantum circuit of a generalized Ramsey interferometer with generic entangling and decoding operations UEn and UDe, respectively. Our variational approach (c) consists of an ansatz, where optimal UEn and UDe are approximated by low-depth circuits. These are built from ‘layers’ of elementary operations, which are provided by the given platform. We specify the variationally optimized quantum sensor by circuits UEn(θ) and UDe(ϑ) [see Eqs. (6) and (7)], of depth nEn and nDe, respectively. Here θ ≡ {θi} and ϑ ≡ {ϑi} are vectors of variational parameters to be optimized for a given strategy represented by a cost function C defined here as Bayesian mean squared error (BMSE) [see Eqs. (2) and (10)]” and “The most general circuits satisfying the x-parity constraint for a fixed number nEn and nDe of layers of entangling and decoding gates are ”).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 11, is equally applicable to claim 16.
Regarding claim 17, Peruzzo in view of Kaubruegger teaches all the limitations of claim 16.
Kaubruegger teaches:
wherein nEn is equal to or smaller than nDe- (Kaubruegger Fig. 1, pg. 4: “The most general circuits satisfying the x-parity constraint for a fixed number nEn and nDe of layers of entangling and decoding gates are [eq. 6 and eq. 7] Here the subscripts on the parameters indicate the layer containing the same three gates and the superscript identifies the gate within the layer”—[emphasis added]).
The same motivation that was utilized for combining Peruzzo with Kaubruegger, as set forth in claim 11, is equally applicable to claim 17.
Regarding claim 18, Peruzzo teaches:
A method of optimizing a measurement of a physical quantity with a hybrid classical-quantum system comprising a plurality of controllable quantum systems and further comprising a classical computation system, the method being implemented in the hybrid classical-quantum system, the method comprising the steps of (Peruzzo pg. 1–2: “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. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. 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. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques … Our attention is restricted to the class of operators whose expectation value can be measured efficiently on S and mapped to Q”):
a) initializing a number of variational parameters, the variational parameters parametrizing variable actions of variational quantum gates for acting onto the plurality of controllable quantum systems (Peruzzo pg. 5, III. State Parameterization and Preparation: “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”—[wherein the state of more than one class is prepared by quantum gates variationally optimized]);
b) repeatedly implementing a measurement sequence of known values of the physical quantity using the plurality of controllable quantum systems, the measurement sequence having the steps of (Peruzzo pg. 2–3, II. Background and Notation, pg. 14–15, B. Cost Reduction: “As terms within a commuting set are measured on the same state within each pass of the procedure”):
- initializing the plurality of controllable quantum systems in an initial state (Peruzzo pg. 5, III. State Parameterization and Preparation: “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”—[wherein the state of more than one class is prepared]);
- applying a set of preparation gates to the plurality of controllable quantum systems for preparing the plurality of controllable quantum systems in a non-classical state (Peruzzo pg. 10, C. Unitary coupled cluster: “Moreover if one allows values of different parameters at different Trotter steps, one may perform arbitrary 1 and 2 qubit gates at k=2, which forms a universal gate set and the ansatz can be made equivalent to an arbitrary quantum circuit with a sufficient number of Trotter steps …. thus its exponential exp(O) can be used to form an arbitrary two qubit gate on any two qubits, or said differently, an arbitrary element of SU(4) on any two qubits. Arbitrary two qubit gates on any qubit are known to constitute a universal gate set [77], and then clearly can be used to construct any desired universal gate set such as the Clifford+T set”—[wherein the universal gate set is made to be an arbitrary quantum circuit that can be used to construct any desired universal gate set]),
- evolving the non-classical state for obtaining an evolved state of the plurality of controllable quantum systems evolved according to a select one of the known values (Peruzzo pg. 5–8. B Adiabatically parameterized states: “In a noiseless coherent situation at 0K, the unitarity of evolution dictates that the final state of the evolution is uniquely determined by the path f”—[wherein the states evolve according to a path over a period of time]); and
- determining a measurement outcome of the evolved state for the select one of the known values (Peruzzo pg. 13, A. Bayesian Perspective: “In a Bayesian perspective, we start from an uninformative prior for the distribution Hγ . 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. Consider a sequence of independent measurements X with two possible outcomes {m1,m2}, such as the quantum measurement of a Pauli operator. The likelihood of observing the sequence of measurements X is completely defined by a single variable p”);
wherein the set of preparation gates and the set of decoding gates each comprise non- linear quantum gates suitable for generating a non-classical state of the plurality of controllable quantum systems (Peruzzo pg. 15–16, V. Optimization of
θ
→
: “The final piece of the variational quantum eigensolver is a method for updating the parameters θ based on the measured value of the objective function of interest. The dependence of the objective function on the parameters will, of course, depend upon the ansatz being used and will in general be non-linear and non-convex … The field of non-linear optimization is well developed with many tools both general and more specialized methods to different optimization problems”—[wherein ansatz (i.e., prepared state) is non-linear and generated by the non-linear universal gate set]), and
each comprise variational quantum gates characterized by variable actions onto controllable quantum systems of the plurality of controllable quantum systems (Peruzzo pg. 5–8, B. Adiabatically parameterized states: “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 con text where the maximum evolution time τ is limited. In this problem, the Hamiltonian the initial and problem Hamiltonians are given by”—[wherein the quantum system includes gates characterized by adiabatic quantum computational methods that control the time schedule]);
c) mapping each of the measurement outcomes to a corresponding derived value of the physical quantity according to a mapping function (Peruzzo pg. 10, D. Fermionic UCC, pg. 14–15, B. Cost Reduction: “We can understand the equivalent action on qubits by mapping the fermion operators to spin operators” and “As terms within a commuting set are measured on the same state within each pass of the procedure, two operators within a set may be correlated such that the estimators of their average may have non-zero covariance i.e. Cov[Hα , Hβ ]= 0. This additional covariance can either require more measurements for the set of terms if the covariance is positive, or less if it is negative in analogy to the method of antithetic variables or correlated sampling in classical Monte Carlo simulations”—[wherein the covariance is determined based on mapping after measuring and is performed classically using correlated sampling]);
d) determining a cost parameter according to a cost function which averages an estimation error between the derived values and the corresponding known values over a pre-defined expected prior distribution of the physical quantity (Peruzzo pg. 12–15, IV. Operator Averaging: “The computational cost of Hamiltonian averaging can be reduced in a number of ways. In this section we will consider two methods for doing so … In order to achieve an expected mean-square-error of in the final answer we must decrease the variance of the estimator on the remaining terms … One is free to choose a value of C ∈ [0,1) to maximize computational efficiency according to the particular constraints of experiment and the distribution of operators in the sum. It has been seen previously that using this strategy in conjunction with locality information can potentially reduce the costs of quantum chemistry calculations dramatically”);
e) selecting updated variational parameters to reduce the cost parameter (Peruzzo pg. 12–15, IV. Operator Averaging: “The computational cost of Hamiltonian averaging can be reduced in a number of ways. In this section we will consider two methods for doing so … In order to achieve an expected mean-square-error of in the final answer we must decrease the variance of the estimator on the remaining terms … One is free to choose a value of C ∈ [0,1) to maximize computational efficiency according to the particular constraints of experiment and the distribution of operators in the sum. It has been seen previously that using this strategy in conjunction with locality information can potentially reduce the costs of quantum chemistry calculations dramatically”);
f) iteratively repeating steps b) to e) towards variational parameters associated with a minimized cost parameter (Peruzzo pg. 12–15, IV. Operator Averaging: “The computational cost of Hamiltonian averaging can be reduced in a number of ways. In this section we will consider two methods for doing so … In order to achieve an expected mean-square-error of in the final answer we must decrease the variance of the estimator on the remaining terms … One is free to choose a value of C ∈ [0,1) to maximize computational efficiency according to the particular constraints of experiment and the distribution of operators in the sum. It has been seen previously that using this strategy in conjunction with locality information can potentially reduce the costs of quantum chemistry calculations dramatically … In the second case, we maintain the same variance, but group commuting operators together that have 0 covariance, so the number of preparations per iteration is reduced to 3 and we find nexpect-2 = 6/2”).
Peruzzo does not appear to explicitly teach:
- applying a set of decoding gates to the plurality of controllable quantum systems in the evolved state.
However, Kaubruegger teaches:
- applying a set of decoding gates to the plurality of controllable quantum systems in the evolved state (Kaubruegger Figs. 2, 10, pg. 4: “The most general circuits satisfying the x-parity constraint for a fixed number nEn and nDe of layers of entangling and decoding gates … Performance of the variationally enhanced interferometer with N = 64 particles. Performance is shown in terms of the posterior phase distribution width relative to the prior width, ∆φ/δφ, for a given prior, that is, for a given dynamic range of the interferometer. Colored lines show the performance of variationally optimized circuits for the depth (nEn,nDe) of entangling and decoding layers as indicated. The number of variational parameters is given by 3(nEn+nDe). The performance of the optimal quantum interferometer (OQI) [31] is indicated by the dotted line. The shaded areas indicate the classically accessible (purple) and the quantum mechanically forbidden (gray) regions (for N = 64). Related results applied to atomic clocks are shown in Fig. 10”).
The methods of Peruzzo, the teachings of Kaubruegger, and the instant application are analogous art because they pertain to variationally evolving quantum systems to make measurements.
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 Kaubruegger to provide gates that allow for measurement in the evolved state. One would be motivated to do so to aid in the optimization of the variational quantum gates system (Kaubruegger Figs. 2, 10, pg. 4: “Performance of the variationally enhanced interferometer with N = 64 particles. Performance is shown in terms of the posterior phase distribution width relative to the prior width, ∆φ/δφ, for a given prior, that is, for a given dynamic range of the interferometer. Colored lines show the performance of variationally optimized circuits for the depth (nEn,nDe) of entangling and decoding layers as indicated. The number of variational parameters is given by 3(nEn+nDe). The performance of the optimal quantum interferometer (OQI) [31] is indicated by the dotted line. The shaded areas indicate the classically accessible (purple) and the quantum mechanically forbidden (gray) regions (for N = 64). Related results applied to atomic clocks are shown in Fig. 10”).
Regarding claim 19, Peruzzo in view of Kaubruegger teaches all the limitations of claim 18.
Peruzzo teaches:
wherein selecting updated variational parameters to reduce the cost parameter comprises estimating an energy landscape or a gradient of the cost function with respect to the variational parameters (Peruzzo Fig. 5, pg. 15–16, V. Optimization of
θ
→
: “The field of non-linear optimization is well developed with many tools both general and more specialized methods to different optimization problems [83]. The objective function by design here is statistical in nature, making it difficult to directly use many of the basic tools from numerical optimization that rely on gradients … Additionally, the number of evaluations of the expectation value of the energy required to reach convergence is plotted as a function of the same precision ϵ”).
Regarding claim 20, Peruzzo in view of Kaubruegger teaches all the limitations of claim 19.
Peruzzo teaches:
wherein estimating the energy landscape or the gradient comprises repeatedly implementing the sequence b) to e) with shifted variational parameters, the shifted variational parameters comprising a subset of the variational parameters being shifted with respect to a current set of variational parameters (Peruzzo Fig. 5, pg. 15–16, V. Optimization of
θ
→
: “The final piece of the variational quantum eigensolver is a method for updating the parameters θ based on the measured value of the objective function of interest … However, in many cases local optima are sufficient and prior knowledge of a problem offers high quality starting points for the optimization … The field of non-linear optimization is well developed with many tools both general and more specialized methods to different optimization problems [83]. The objective function by design here is statistical in nature, making it difficult to directly use many of the basic tools from numerical optimization that rely on gradients … Additionally, the number of evaluations of the expectation value of the energy required to reach convergence is plotted as a function of the same precision ϵ”).
Prior Art of Record
The prior art made of record and not relied upon is considered pertinent to applicant’s disclosure.
Ronagh et al., (“Artificial intelligence-driven quantum computing”) discloses systems and methods of quantum-classical hybrid computing including optimization techniques “For instance, provided herein are systems and methods for improving the computational efficiency and/or accuracy of non-classical computations (e.g., quantum computations). Systems and methods provided herein may utilize non-classical computers (e.g., quantum computers) comprising a first non-classical or quantum subsystem (referred to herein as a “computation subsystem”) for performing a non-classical or quantum computation and a second non-classical or quantum subsystem (referred to herein as a “syndrome subsystem”) that is quantum mechanically entangled with the computation subsystem. During a non-classical or quantum computation, the syndrome subsystem may be measured while the computation subsystem is allowed to evolve to carry out the non-classical or quantum computation. Systems and methods provided herein may further allow measurement of the syndrome subsystem during the implementation of the non-classical or quantum computation to provide partial observations about the computation subsystem. Such observations may then be provided to an artificial intelligence (AI) module, such as a machine learning (ML) module or a reinforcement learning (RL) module which may be trained during or prior to the computation to determine next best choices for tunable parameters during or prior to the non-classical or quantum computation. The choice of tunable parameters may pertain to initial, intermediate or final segments of the non-classical or quantum computation.” Ronagh ¶0005.
Gokhale et al., (“System and method of partial compilation with variational algorithms for quantum computers”) discloses using variational methods to optimize quantum circuit parameters “A computing system includes a quantum processor with qubits, a classical memory including a quantum program defining a plurality of instructions in a source language, and a classical processor configured to: (i) receive a circuit of gates representing a quantum program for a variational algorithm in which computation is interleaved with compilation; (ii) identify a plurality of blocks, each block includes a subcircuit of gates, leaving one or more remainder subcircuits of the circuit of gates outside of the plurality of blocks; (iii) pre-compile each block of the plurality of blocks with a pulse generation program to generate a plurality of pre-compiled blocks including control pulses configured to perform the associated block on the quantum processor; and (iv) iteratively execute the quantum program using the pre-compiled blocks as static during runtime and recompiling the one or more remainder subcircuits on the classical processor at each iteration of execution”. Gokhale ¶Abstract.
Peruzzo et al., ("A variational eigenvalue solver on a photonic quantum processor") discloses a variational quantum-classical hybrid approach to optimization “an alternative approach that greatly reduces the requirements for coherent evolution and we combine this method with a new approach to state preparation based on ansatz and classical optimization. We have implemented the algorithm by combining a small-scale photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground state molecular energy for He–H+, to within chemical accuracy. The proposed approach, by drastically reducing the coherence time requirements, enhances the potential of the quantum resources available today and in the near future.” Peruzzo ¶Abstract.
Conclusion
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/N.B.S./Examiner, Art Unit 2126
/DAVID YI/Supervisory Patent Examiner, Art Unit 2126
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