DETAILED ACTION
This action is responsive to the claims filed on 08/07/2026. Claims 1-20 are pending for examination.
This action is Final.
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 .
Arguments and Remarks
Applicant’s arguments regarding the rejection under 35 U.S.C. § 101 have been considered but are not persuasive. Applicant argues that the amended limitation requiring that “a Fourier transform of the filter function has an exponentially decaying tail” integrates the judicial exception into a practical application because the Specification explains that such a filter may be approximated by a band-limited function and may reduce or decouple quantum-circuit depth from target accuracy. However, the newly added limitation itself recites a mathematical property of the filter function and its Fourier transform and therefore remains within the mathematical-concepts grouping of abstract ideas. The claims do not positively recite performing a band-limited approximation, reducing a maximum Hamiltonian evolution time, reducing circuit depth as a result of the recited Fourier-tail property, or otherwise modifying the operation or architecture of the quantum computing component in a particular manner that produces the asserted technological improvement. Rather, the alleged advantages relied upon by Applicant are described in the Specification and remarks but are not reflected as additional technological limitations in the claims. Accordingly, the amendment does not demonstrate that the additional elements integrate the recited mathematical concepts into a practical application under Step 2A, Prong Two. The newly recited Fourier-transform property forms part of the abstract mathematical concept itself and therefore cannot, standing alone, supply the “significantly more” required by Step 2B. The remaining additional elements, individually and in combination, do not provide an inventive concept for the reasons previously set forth. Accordingly, the rejection of claims 1-20 under 35 U.S.C. § 101 is maintained
Applicant’s arguments with respect to the 35 U.S.C. §102/103 rejection of the claims 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 § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Statutory Categories
Claims 1-10 is directed to a method.
Claims 11-20 is directed to a system.
Independent Claims – Claim 1 and 11
Step 2A Prong 1: Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes. Independent claim 1 and 11 recites limitations that are abstract ideas in the form of mental processes:
Claim 1 recites:
evaluating a convolution of a spectral measure and a filter function from the outcome samples; (this limitation merely evaluating a convolution, which is stated at a high level of generality using a spectral measure and filter function such that it is being considered mental processes of evaluation which can reasonably be performed in human mind or with aid additional aid of pen and paper)
inferring an estimate of the ground state energy from the convolution. (this limitation merely inferring an estimate using a convolution, which is stated at a high level of generality such that is being considered mental processes of evaluation which can reasonably be performed in human mind or with aid additional aid of pen and paper)
wherein a Fourier transform of the filter function has an exponentially decaying tail; (this limitation merely recites mathematical concepts in the form of mathematical formulas, algorithms, or calculation. See specification pages 10-15 for the related mathematical disclosure.)
Claim 1 also recites the following additional elements for the purposes of Step 2A Prong Two
analysis:
A method, performed on a computer system, for estimating a ground state energy of a Hamiltonian that characterizes a physical system, the computer system comprising a quantum computing component and a classical computing component, the quantum computing component comprising a plurality of qubits; (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
the classical computing component comprising a classical processor and a non-transitory computer-readable memory, the non-transitory computer-readable memory storing computer instructions, which, when executed by the classical processor, perform the method, (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
the method comprising: causing the quantum computing component to derive outcome samples from a plurality of Hadamard tests in which a unitary is a time evolution of the Hamiltonian; (computer components, Hadamard tests, and Hamiltonians, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
on the classical computing component, (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
and on the classical computing component, (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
The additional limitations fail step 2A Prong 2 of the 101 analysis because they do not transform the claim into a practical application. These limitations are too abstract or lack technical improvement that would make the concept practically useful. Without clear utility or integration into a specific field, the claim does not relate to any particular application. It does not meet the requirements of Step 2A Prong 2, as it fails to make the concept meaningfully applicable in practice.
Since the claim as a whole, looking at the additional elements individually and in combination, does not contain any other additional elements that are indicative of integration into a practical application, the claim is “directed” to an abstract idea.
This claim recites the following additional elements for the purposes of Step 2B analysis:
A method, performed on a computer system, for estimating a ground state energy of a Hamiltonian that characterizes a physical system, the computer system comprising a quantum computing component and a classical computing component, the quantum computing component comprising a plurality of qubits; (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
the classical computing component comprising a classical processor and a non-transitory computer-readable memory, the non-transitory computer-readable memory storing computer instructions, which, when executed by the classical processor, perform the method, (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
the method comprising: causing the quantum computing component to derive outcome samples from a plurality of Hadamard tests in which a unitary is a time evolution of the Hamiltonian; (computer components, Hadamard tests, and Hamiltonians, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
on the classical computing component, (computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
and on the classical computing component, (computer components, stated at a high level of generality, is being considered as mere instructions.
The claim also fails Step 2B of the analysis because the additional limitations do not amount to significantly more than the abstract idea itself. The additional limitations do not enhance the claim in a way that would move it beyond its abstract ideas as they minimally elaborate on the core concept without adding any inventive or technical substance. Considering the additional elements individually and in combination, and the claim as a whole, the additional elements do not provide significantly more than the abstract idea. Therefore, the claim is not patent eligible.
Claim 11 recites limitations substantially identical to claim 1 as such a similar analysis under 101 applies.
Dependents of Claims 1 and 11
The remaining dependent claims corresponding to independent claims 1 and 11 do not recite additional elements, whether considered individually or in combination, that are sufficient to integrate the judicial exception into a practical application or amount to significantly more than the judicial exception. The analysis of which is shown below:
The claims below recite additional limitations which fail step 2A Prong 2 of the 101 analysis because they do not transform the claim into a practical application. These limitations are too abstract or lack technical improvement that would make the concept practically useful. Without clear utility or integration into a specific field, the claim does not relate to any particular application. It does not meet the requirements of Step 2A Prong 2, as it fails to make the concept meaningfully applicable in practice.
The claims also fails Step 2B of the analysis because the additional limitations do not amount to significantly more than the abstract idea itself. The additional limitations do not enhance the claim in a way that would move it beyond its abstract ideas as they minimally elaborate on the core concept without adding any inventive or technical substance. The claims are unpatentable.
Claim 2 recites the additional limitation of:
The method of claim 1, wherein the physical system comprises a molecule. (Under Step 2A Prong II and Step 2B: this limitation is merely directing the aforementioned judicial exception into a field of use of molecular systems, see MPEP 2106.05(h))
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 3 recites the additional limitation of:
The method of claim 1, wherein the physical system comprises a physical material. (Under Step 2A Prong II and Step 2B: this limitation is merely directing the aforementioned judicial exception into a field of use of physical materials, see MPEP 2106.05(h))
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 4 recites the additional limitation of:
The method of claim 1, wherein the quantum computing component comprises a fault-tolerant quantum computer. (Under Step 2A Prong II and Step 2B: computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 5 recites the additional limitation of:
The method of claim 1, wherein the quantum computing component includes a low-depth quantum circuit having an initial overlap. (Under Step 2A Prong II and Step 2B: computer components, stated at a high level of generality, is being considered as mere instructions to apply an exception using generic computer components, see MPEP 2106.05(f))
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 6 recites the additional limitation of:
The method of claim 5, further comprising selecting a target accuracy for the estimate of the ground state energy. (a mental process of selection, stated at a high level of generality, which can reasonably be performed in human mind or with additional aid of pen and paper)
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 7 recites the additional limitation of:
The method of claim 6, wherein the Hamiltonian has an inverse spectral gap of the Hamiltonian; wherein the target accuracy has an inverse of the target accuracy; and wherein the initial overlap has an inverse of the initial overlap. (this limitation is merely reciting mathematical concepts in the form of algorithms, calculations, or formulas, pages 13-26 of the specification contain the related mathematical disclosure)
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 8 recites the additional limitation of:
The method of claim 7, wherein the low-depth quantum circuit has a depth that is linear in the inverse spectral gap of the Hamiltonian and poly-logarithmic in the inverse of the target accuracy and the inverse of the initial overlap. (this limitation defines linear and poly-logarithmetic relationships to variables in a Halmiltonian system which is being considered as merely reciting the abstract idea of mathematical calculation, pages 13-26 of the specification contain the related mathematical disclosure)
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 9 recites the additional limitation of:
The method of claim 7, wherein a runtime of the method is polynomial in the inverse spectral gap of the Hamiltonian, the inverse of the target accuracy, and the inverse of the initial overlap. (this limitation defines polynomial relationships to variables in a Halmiltonian system which is being considered as merely reciting the abstract idea of mathematical calculation, pages 13-26 of the specification contain the related mathematical disclosure)
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claim 10 recites the additional limitation of:
The method of claim 1, further comprising inferring, from the estimate of the ground state energy, a property of the Hamiltonian. (a mental process of estimating a property of a Hamiltonian using a predetermined estimate of the ground state energy which can reasonably be performed in human mind or with aid of pen and paper)
Since the claim does not recite additional elements that either integrate the judicial exception into a practical application, nor provide significantly more than the judicial exception, the claim is not patent eligible.
Claims 12-20 recite limitations substantially identical to claims 2-10, as such a similar analysis applies.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The text of those sections of Title 35, U.S. Code not included in this action can be found in a prior Office action.
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 non-obviousness.
This application currently names joint inventors. In considering patentability of the claims the examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the examiner to consider the applicability of 35 U.S.C. 102(b)(2)(C) for any potential 35 U.S.C. 102(a)(2) prior art against the later invention.
Claims 1-6 and 11-16 are rejected under 35 U.S.C. 103 as being unpatentable by Lin et al., (Lin, L., & Tong, Y. (2022). Heisenberg-limited ground-state energy estimation for early fault-tolerant quantum computers. PRX quantum, 3(1), 010318.), hereafter referred to as Lin, in view of He et al., (He, M.-Q., Zhang, D.-B., & Wang, Z. D. (2021). Quantum Gaussian filter for exploring ground-state properties. Physical Review A, 106(3). https://doi.org/10.1103/physreva.106.032420), hereafter referred to as He.
Claim 1: Lin teaches the following:
A method, performed on a computer system, for estimating a ground state energy of a Hamiltonian that characterizes a physical system, (Lin, page 1, paragraph 1, “We assume we can access the Hamiltonian H through the time evolution operator e−iτH for some fixed τ. Our goal is to estimate the ground state energy λ0 to within additive error .”
page 3, paragraph 2, “To our best knowledge our algorithm is the first to satisfy all three requirements. In our algorithm, we sample from a simple quantum circuit, and use the samples to approximately reconstruct the cumulative distribution function (CDF) of the spectral measure associated with the Hamiltonian. We then use classical post-processing to estimate the ground state energy with high confidence.”, Lin proposes a method to estimate the ground-state energy of a Hamiltonian. It further places the work in the context of condensed matter physics and quantum chemistry, which are physical-system applications, thereby teaching a Hamiltonian that characterizes a physical system. The introduction also states that the “goal is to estimate the ground state energy λ0” of the Hamiltonian H, which directly matches the claimed objective.)
the computer system comprising a quantum computing component and a classical computing component, the quantum computing component comprising a plurality of qubits; the classical computing component comprising a classical processor and a non-transitory computer-readable memory, the non-transitory computer-readable memory storing computer instructions, which, when executed by the classical processor, perform the method, (Lin, page 8, section 2, “We want to keep the quantum circuit we use as simple as possible. In this work we use the following
circuit
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where H is the Hadamard gate. We choose W = I or W = S† where S is the phase gate, depending on the quantity we want to estimate. The quantum circuit is simple and uses only one ancilla qubit as required.”
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Figure 2 of Lin
Lin expressly discloses a quantum circuit together with a classical post-processing procedure, and Figure 2 later describes the “classical and quantum components” of the algorithm. The introduction states that the Hamiltonian acts on n qubits, which teaches a quantum computing component comprising a plurality of qubits. The paper does not use the exact structural words “classical processor” and “non-transitory computer-readable memory,” but a classical computer performing post-processing inherently uses a processor executing stored instructions.)
the method comprising: causing the quantum computing component to derive outcome samples from a plurality of Hadamard tests in which a unitary is a time evolution of the Hamiltonian; (Lin, page 8, section 2, “We want to keep the quantum circuit we use as simple as possible. In this work we use the following
circuit
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where H is the Hadamard gate. We choose W = I or W = S† where S is the phase gate, depending on the quantity we want to estimate. The quantum circuit is simple and uses only one ancilla qubit as required... This circuit requires controlled time evolution, which can be non-trivial to implement. The idea of removing controlled operation in phase estimation has also been considered in [13]. Here we can use ideas from Refs. [31, 43, 49, 59] to remove the need to perform controlled time evolution. But this type of approach requires an eigenstate of H with known eigenvalue that is easy to prepare. In a second-quantized setting we can simply use the vacuum state. We will discuss this in detail in Appendix E.”,
Lin, page 8, paragraph 5, “We can define a spectral measure of τH associated with ρ. The spectral measure is
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”, Section 2 discloses an ancilla-based interference circuit having Hadamard gates and a controlled time-evolution unitary e^{-ij\tau H}. The paper then defines random variables X_j and Y_j from the measurement outcomes of that circuit, and later discusses sampling them repeatedly. That teaches deriving outcome samples from a plurality of Hadamard-test-type runs in which the unitary is time evolution of the Hamiltonian.)
on the classical computing component, evaluating a convolution of a spectral measure and a filter function from the outcome samples; (Lin, page 8, paragraph 5, “We can define a spectral measure of τH associated with ρ. The spectral measure is
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”,
Lin, page 9, paragraph 2, “Therefore instead of the usual definition, we define C(x) = (H ∗p)(x), where ∗ denotes convolution… With this F(x) we define the ACDF by C(x) = (F ∗p)(x)”, Lin expressly defines a spectral measure p(x), then defines the usual CDF as C(x)=(H*p)(x), and then defines an approximate filter F(x) and the approximate CDF (Lin pages 9-10). That is an explicit disclosure of a convolution of a spectral measure and a filter function. The paper then explains how to evaluate that quantity from the sampled circuit outcomes: Figure 2 describes generating samples and computing G(x), and Eq. (10) on page 10 expands the approximate CDF directly in terms of
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, which the paper states are estimated from the sampled quantum outcomes. This matches the claimed classical evaluation of the convolution from the outcome samples. Here, F(x) is considered the claimed filter function because Lin defines F(x) as an approximate Heaviside function and then uses it in the convolution C(x)=(H*p)(x). The convolution is “from the outcome samples” not because F(x) is derived from the samples, but because Lin evaluates C(x) by rewriting it in terms of Tr[ρe−ijτH], which Lin states is estimated from sampled measurement outcomes X_j and Y_j, and then forms the sample-based estimator G(x;J,Z)and ¯ G(x).)
and on the classical computing component, inferring an estimate of the ground state energy from the convolution. (Lin, page 9, paragraph 5, “We prove these inequalities in Appendix B. Given the statistical estimation of the ACDF C(x), these inequalities enable us to estimate where the jumps of the CDF occur, which leads to an estimate of the ground state energy… By approximately evaluating the ACDF C(x) for certain chosen x, and through Eq. (9), we can perform a binary search to locate the ground state energy in smaller and smaller intervals.”, once the ACDF C(x)is statistically estimated, the jumps of the CDF can be located, which “leads to an estimate of the ground state energy,” and the paper then uses binary-search-based classical post-processing to do exactly that. Since the ACDF is expressly defined as the convolution (F*p)(x), the reference teaches inferring an estimate of the ground-state energy from the convolution. The claim language is therefore met by the paper’s disclosed workflow of evaluating \widetilde{C}(x) and then using it to locate the ground-state energy.)
He, in the same field of quantum ground-state estimation using hybrid quantum-classical processing, teaches the following which Lin fails to teach:
wherein a Fourier transform of the filter function has an exponentially decaying tail; (He, page 1, Abstract; page 2, Section II, Eq. (2), “Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian function of system Hamiltonian. A hybrid quantum-classical algorithm feasible on near-term quantum computers is developed, which implements the quantum Gaussian filter as a linear combination of Hamiltonian evolution at various times. Remarkably, the linear combination coefficients are determined classically and can be optimized in the post-processing procedure.”; “Since the Gaussian filter operator
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It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the ground-state-energy estimation method of Lin to employ the Gaussian filtering technique taught by He. Lin teaches estimating a ground-state energy by obtaining outcome samples from Hamiltonian time evolutions, evaluating a convolution of a spectral measure and filter function, and inferring the ground-state energy from the convolution, while also recognizing circuit depth and maximal evolution time as important resource considerations for early fault-tolerant quantum computing. He similarly addresses ground-state estimation using a hybrid quantum-classical technique, but teaches employing a Gaussian filter represented by a Fourier approximation comprising a weighted linear combination of Hamiltonian time evolutions, wherein the Fourier weights decay according to a Gaussian factor. He explains that filter-based approaches can reduce quantum resources and further relates circuit depth to the maximum Hamiltonian evolution time. One of ordinary skill in the art would therefore have been motivated to substitute He’s known Gaussian filter for Lin’s Heaviside-type filter in order to suppress long-time Fourier contributions and reduce the quantum resources associated with implementing the filtering operation while retaining Lin’s known spectral-measure-based ground-state-energy estimation framework. Such a modification represents the predictable use of a known ground-state filtering technique for its established purpose and yields the predictable result of Lin’s ground-state estimation method employing a filter whose Fourier transform has an exponentially decaying tail.
Claim 2: Lin and He teaches the limitations of claim 1, Lin further teaches the following:
The method of claim 1, wherein the physical system comprises a molecule. (Lin, page 1, paragraph 2, “At least for relatively small molecular systems, the Hartree-Fock state can often have a large overlap with the exact ground state [68]. Therefore we may use the Hartree-Fock solution as ρ in this setting.”, Lin states that, in quantum chemistry, the Hartree-Fock method yields an approximate ground state and that, for relatively small molecular systems, the Hartree-Fock state can have a large overlap with the exact ground state, and that the Hartree-Fock solution is used in that setting.)
Claim 3: Lin and He teaches the limitations of claim 1, Lin further teaches the following:
The method of claim 1, wherein the physical system comprises a physical material. (Lin, page 1, paragraph 1, “Estimating the ground state energy of a quantum Hamiltonian is of immense importance in condensed matter physics, quantum chemistry, and quantum information.”, Lin expressly identifies condensed matter physics as one of the central application areas for estimating the ground-state energy of a quantum Hamiltonian. It also uses the Hubbard-model setting as an example later in the paper. A person of ordinary skill would understand that condensed matter and Hubbard-model applications are directed to physical materials.)
Claim 4: Lin and He teaches the limitations of claim 1, Lin further teaches the following:
The method of claim 1, wherein the quantum computing component comprises a fault-tolerant quantum computer. (Lin, abstract, “Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classical post-processing procedure.”, Lin expressly implements its methods on fault-tolerant quantum computers in a less expensive way compared to quantum phase estimation methods.)
Claim 5: Lin and He teaches the limitations of claim 1, Lin further teaches the following:
The method of claim 1, wherein the quantum computing component includes a low-depth quantum circuit having an initial overlap. (Lin, page 1, paragraph 2, “Some assumptions are needed as otherwise this problem is QMA-hard [2, 32, 34, 50]. We assume we are given a state described by its density matrix ρ. Let pk = Tr[ρΠk]. Then if p0 (i.e. the overlap between the initial state and the ground state) is reasonably large we can solve the ground state energy estimation problem efficiently.”,
Lin, page 3, paragraph 3, “To be specific, we expect such early fault-tolerant quantum computers to have the following characteristics: (1) The number of logical qubits are limited. (2) It is undesirable to have a large number of controlled operations. (3) It is a priority to reduce the circuit depth, e.g. it is better to run a circuit of depth O(D) for O(M) times than to run a circuit of depth O(DM) for a constant number of times, even if using the shorter circuit entails some additional poly-logarithmic factors in the total runtime.”, Lin states that “p_0” is “the overlap between the initial state and the ground state,” and further explains that efficient estimation is obtained when that overlap is reasonably large. Lin also reiterates that its complexity analysis is concerned with dependence on the “initial overlap p_0,” and Table 2 states that “[t]he overlap between the initial state and the ground state is assumed to be p_0.” That teaches a quantum component operating with an initial state having an initial overlap with the ground state. Lin further states that for early fault-tolerant quantum computers “it is a priority to reduce the circuit depth,” then defines maximal evolution time as a metric that describes circuit depth, and states as one of the algorithm’s goals that the maximal evolution time is bounded by
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(Lin page 10 section 3). A person of ordinary skill would understand a simple one-ancilla circuit expressly designed to reduce circuit depth, and characterized by bounded maximal evolution time that directly corresponds to circuit depth, to be a low-depth quantum circuit. )
Claim 6: Lin and He teaches the limitations of claim 1, Lin further teaches the following:
The method of claim 5, further comprising selecting a target accuracy for the estimate of the ground state energy. (Lin, page 9, last pargraph, “By approximately evaluating the ACDF C(x) for certain chosen x, and through Eq. (9), we can perform a binary search to locate the ground state energy in smaller and smaller intervals. The algorithm to do this and the total computational cost required to estimate the ground state energy to precision ε at a confidence level 1 −ϑ are discussed in Sections 4 and 5”,
Page 1, paragraph 1, “We assume we can access the Hamiltonian H through the time evolution operator e−iτH for some fixed τ. Our goal is to estimate the ground state energy λ0 to within additive error ε.”, the goal is to estimate the ground-state energy “to within additive error ε,” and page 2 states that the computational complexity depends on the “desired precision ε.” Later sections discuss choosing parameters so as to estimate the ground-state energy to “precision \epsilon” at a desired confidence level. That teaches selecting a target accuracy for the estimate.)
Claim 11-16 recite limitations substantially identical to claims 1-6, as such a similar analysis applies.
Claims 7-10 and 17-20 are rejected under 35 U.S.C. 103 as being unpatentable over Lin in view of He, as applied to claims 1-6 and 11-16 above, and Zhang et al. (Zhang, R., Wang, G., & Johnson, P. (2022). Computing ground state properties with early fault-tolerant quantum computers. Quantum, 6, 761.), hereafter referred to as Zhang.
Claim 7: Lin and He teaches the limitations of claim 6, Zhang, in the same field of quantum processing, teaches the following which Lin and He fails to teach:
The method of claim 6, wherein the Hamiltonian has an inverse spectral gap of the Hamiltonian; wherein the target accuracy has an inverse of the target accuracy; and wherein the initial overlap has an inverse of the initial overlap. (Zhang, page 3, paragraph 1, “Theorem 1.1 (Main theorem, informal). Given a Hamiltonian H and an observable O. Suppose we have access to a unitary UI that prepares a state |φ0⟩ that has non-trivial overlap with the ground state |ψ0⟩ of H. Then, there exists an algorithm to estimate ⟨ψ0|O|ψ0⟩ with high accuracy and low-depth: the maximal Hamiltonian evolution time is e O(γ−1), where γ is the spectral gap of H.”
Zhang, page 3, paragraph 3, “We can compare our algorithm with the straightforward approach of GSPE that first prepares the ground state and then applies quantum phase estimation (QPE) to estimate the ground state property. • In the first step, to achieve an ϵ-accuracy for the estimation, the ground state need to be prepared with fidelity at least 1 − ϵ using the methods in [12, 13], which have circuit depth e O(γ−1η−1) where η is the overlap between the initial state and the ground state. • In the second step, QPE [29, 24] requires circuit depth eO(ϵ−1) for an ϵ-accuracy estimation for the ground state property. Therefore, this straightforward approach has circuit depth e O(γ−1η−1 + ϵ−1), while our algorithm has circuit depth e O(γ−1).”,
Zhang, page 10, last paragraph, “Lemma 4.6 (Estimating p0O0). For any ϵ1,ν ∈ (0,1), p0O0 can be estimated with multiplicative error 1 ± O(ϵ1) with probability 1 − ν by runs the quantum circuit (Figure 1) e O(ϵ−2 1 η−2) times with expected total evolution time e time O(γ−1). O(γ−1ϵ−2 1 η−2) and maximal evolution”, Zhang expressly defines the problem using a Hamiltonian with spectral gap γ, an initial state with overlap at least η, and an estimation error parameter ε. Then states complexity bounds in terms of γ^-1, ε^-2, and η^-2, thereby teaching the claimed use of the inverse spectral gap, the inverse target accuracy, and the inverse initial overlap.)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have modified the teachings of Lin and He and incorporate the teachings of Zhang, a motivation of which would have been to adapt Lin’s hybrid low-depth ground-state-energy-estimation framework so that the method’s performance and suitability for early fault-tolerant quantum computing are expressly analyzed and improved with respect to the spectral gap, target accuracy, and initial ground-state overlap, as taught by Zhang. Zhang explains that its algorithm estimates ground-state properties using “low-depth quantum circuits” and provides costs “as a function of target accuracy, spectral gap, and initial ground state overlap.” Zhang further teaches that its approach has a “great advantage when the Hamiltonian’s spectral gap is much larger than the estimation accuracy,” thereby expressly identifying the practical benefit of using those parameters to characterize and improve algorithm performance for early fault-tolerant devices. A person of ordinary skill in the art would have been motivated to incorporate Zhang’s teachings into Lin because both references are in the same field of early fault-tolerant quantum algorithms for Hamiltonian-based ground-state estimation, and Zhang itself expressly builds on Lin’s energy-estimation method as a subroutine while extending the analysis to the spectral-gap.
Claim 8: Lin, He, and Zhang teaches the limitations of claim 7, Zhang further teaches:
The method of claim 7, wherein the low-depth quantum circuit has a depth that is linear in the inverse spectral gap of the Hamiltonian and poly-logarithmic in the inverse of the target accuracy and the inverse of the initial overlap. (Zhang, page 3, paragraph 2, “First, we note that the maximal evolution time, which is the maximal length of time we need to perform coherent time evolution, can roughly determine the depth of the quantum circuit. Our result achieves a nearly-linear dependence on γ−1 and only poly-logarithmic on the accuracy ϵ−1”
Zhang, page 4, last paragraph, “We propose a high-accuracy, early fault-tolerant quantum algorithm for GSPE that satisfies the following properties: • The maximal evolution time depends logarithmically on the accuracy ϵ and overlap η.”
Zhang, page 10, last paragraph, “Lemma 4.6 (Estimating p0O0). For any ϵ1,ν ∈ (0,1), p0O0 can be estimated with multiplicative error 1 ± O(ϵ1) with probability 1 − ν by runs the quantum circuit (Figure 1) e O(ϵ−2 1 η−2) times with expected total evolution time e time O(γ−1). O(γ−1ϵ−2 1 η−2) and maximal evolution”, Zhang teaches the claimed depth scaling through its express linkage between maximal evolution time and circuit depth. Zhang states that maximal evolution time can “roughly determine the depth of the quantum circuit,” and further states that the result achieves a nearly-linear dependence on γ^-1 and poly-logarithmic dependence on ε^-1. Zhang also states that the maximal evolution time depends logarithmically on accuracy ε and overlap η. Together, these passages teach a low-depth circuit whose depth is driven by the inverse spectral gap and only polylogarithmically/logarithmically by inverse target accuracy and inverse initial overlap.)
The motivation to combine Lin with Zhang is similar to that as recited in claim 7 above.
Claim 9: Lin, He, and Zhang teaches the limitations of claim 7, Zhang further teaches:
The method of claim 7, wherein a runtime of the method is polynomial in the inverse spectral gap of the Hamiltonian, the inverse of the target accuracy, and the inverse of the initial overlap. (Zhang, page 10, last paragraph, “Lemma 4.6 (Estimating p0O0). For any ϵ1,ν ∈ (0,1), p0O0 can be estimated with multiplicative error 1 ± O(ϵ1) with probability 1 − ν by runs the quantum circuit (Figure 1) e O(ϵ−2 1 η−2) times with expected total evolution time e time O(γ−1). O(γ−1ϵ−2 1 η−2) and maximal evolution”,
Zhang, page 11, theorem 4.7, “Theorem 4.7 (Ground state property estimation with commutative observable, restate). Supposep0≥η for some known η, and let γ>0 be the spectral gap of the Hamiltonian. Then, for any ϵ,ν∈(0,1), the ground state property ⟨ψ0|O|ψ0⟩ can be estimated within additive error at most ϵ with probability1−ν, such that: 1. The number of times running the quantum circuits (Figure1 and 2) is e O(ϵ−2η−2), 2. The expected total evolution time is e O(γ−1ϵ−2η−2), 3. The maximal evolution time is e O(γ−1).”, Zhang teaches the claimed runtime relationship directly. Theorem 4.7 states that the expected total evolution time is Õ(γ^-1 ε^-2 η^-2). That is polynomial in the inverse spectral gap γ^-1, the inverse target accuracy ε^-1, and the inverse initial overlap η^-1.)
The motivation to combine Lin with Zhang is similar to that as recited in claim 7 above.
Claim 10: Lin and He teaches the limitations of claim 6, Zhang, in the same field of quantum processing, teaches the following which Lin fails to teach:
The method of claim 1, further comprising inferring, from the estimate of the ground state energy, a property of the Hamiltonian. (Zhang, page 7, paragraph 1, “In Step 1, we run [20]’s algorithm to estimate the ground state energy λ0 and the overlap between the initial state and the ground state p0. In Step 2, we construct a similar CDF function for the density P k Okpkδ(x − λk), where Ok := ⟨ψk|O|ψk⟩. If we evaluate the CDF at λ0, we can obtain an estimate of O0”, Zhang teaches using the ground-state-energy estimate to infer another property associated with the Hamiltonian’s ground state. Zhang states that in Step 1 it runs the prior algorithm to estimate the ground-state energy λ0, and then in Step 2 constructs a CDF such that evaluating the CDF at λ0 yields an estimate of O0. That is a direct teaching of inferring a further property of the Hamiltonian from the estimate of the ground-state energy.)
The motivation to combine Lin and He with Zhang is similar to that as recited in claim 7 above.
Claims 17-20 recite limitations substantially identical to claims 7-10, as such a similar analysis applies.
Conclusion
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The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Lin, L., & Tong, Y. (2020). Near-optimal ground state preparation. Quantum, 4, 372.
Lin, L., & Tong, Y. (2020). Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems. Quantum, 4, 361.
Knill, E., Ortiz, G., & Somma, R. D. (2007). Optimal quantum measurements of expectation values of observables. Physical Review A—Atomic, Molecular, and Optical Physics, 75(1), 012328.
Low, G. H., & Chuang, I. L. (2017). Optimal Hamiltonian simulation by quantum signal processing. Physical review letters, 118(1), 010501.
Kyriienko, O. (2020). Quantum inverse iteration algorithm for programmable quantum simulators. npj Quantum Information, 6(1), 7.
Ge, Y., Tura, J., & Cirac, J. I. (2019). Faster ground state preparation and high-precision ground energy estimation with fewer qubits. Journal of Mathematical Physics, 60(2).
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