Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Status of the Claims
Claims 1-2,4-14 and 16-22 are currently pending and under exam herein.
Claims 1-2,4-14 and 16-22 are rejected.
Priority
The instant application claims priority from provisional application 63/344,629 filed on 05/22/2022. Thus, the effective filing date of the instant application is 05/22/2022.
Drawings
The Drawings filed on 10/20/2022 and 12/12/2022 were considered in the previous office action.
Information Disclosure Statement
The information disclosure statements (IDS) submitted on 2/15/2024 and 1/20/2026 are in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statements have been considered by the examiner in the previous office action.
Response to Arguments 101
Applicants’ amendments sufficiently overcome the previous 101 rejection. The claims are deemed eligible under 101.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (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 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.
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.
Claim 1,2, 4-14, 16-22, are rejected under 35 U.S.C. 103 as being unpatentable over Elfving et al. (US20230020166A1) in further view of Anand et al. (Anand et al., A Quantum Computing View on Unitary Coupled Cluster Theory, arxiv, 9/30/2021). in view of Romero et al. (Romero et al. Strategies for Quantum Computing Molecular Energies Using the Unitary Coupled Cluster Ansatz. Quantum Science and Technology 2018, 4 (1), 014008) in view of Lee et al. (Lee et al. Generalized Unitary Coupled Cluster Wave Functions for Quantum Computation. Journal of Chemical Theory and Computation 2018, 15 (1)) in further view of Barkoutsos et al. (Barkoutsos et al. Quantum Algorithms for Electronic Structure Calculations: Particle-Hole Hamiltonian and Optimized Wave-Function Expansions. Physical Review A 2018, 98 (2)) in view of Whitfield et al. (Whitfield et al. Simulation of Electronic Structure Hamiltonians Using Quantum Computers. Molecular Physics 2011, 109 (5), 735–750.)in further view of Elfving et al.(Arxiv) (arxiv, Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers, 11/30/2020) in further view of Sugisaki et al. (Sugisaki, K.; Nakazawa, S.; Toyota, K.; Sato, K.; Shiomi, D.; Takui, T. Quantum Chemistry on Quantum Computers: A Method for Preparation of Multiconfigurational Wave Functions on Quantum Computers without Performing Post-Hartree–Fock Calculations. ACS Cent. Sci. 2019, 5 (1), 167–175) The italicized text corresponds to the instant claim limitations.
With respect to the limitations of Claims 1, 13 and 20, Elfving et al. teaches efficient simulation of quantum chemistry using gate-based qubit quantum devices and, in particular, though not exclusively, to methods and systems for simulating quantum chemistry using gate-based qubit quantum devices, and a computer program product enabling gate-based qubit quantum devices to perform such simulation methods (specification paragraph 2, a hybrid quantum-classical computing system configured for implementing a simulation of a chemical system, wherein the hybrid quantum-classical computing system comprises a classical computing component coupled to a quantum computing component, wherein the hybrid quantum-classical computing system is configured to (Claim 1) A method for using a hybrid quantum-classical computing system to implement a simulation of a chemical system, wherein the hybrid quantum-classical computing system comprises a classical computing component coupled to a quantum computing component, wherein the method comprises(Claim 13) A computer program product comprising at least one non-transitory computer- readable medium storing executable instructions, the executable instructions configured to, when executed by a hybrid quantum-classical computing system, cause the hybrid quantum- classical computing system to perform (Claim 20)) Elfving et al. also teaches receiving or determining, by the classical computer, information on a Hamiltonian describing the quantum chemistry system, the Hamiltonian being a hard core bosonic Hamiltonian, which restricted to electron singlet state configurations (Claim 1, determine characterizing parameters that describe the chemical system, wherein the characterizing parameters are at least partially based on a chemical structure of the chemical system; (Claim 1) (Claim 13) (Claim 20) Elfving et al. also teaches receiving or determining, by the classical computer, information on a paired-electron unitary coupled cluster with double excitations (pUCCD) ansatz, the ansatz being restricted to electron singlet state configurations (Claim 1, (ii) generate an operator representation of the chemical system, including single electron excitation operators and double electron excitation operators; (Claim 1) (Claim 13) (Claim 20)).
With respect to the limitations of Claim 10, Elfving et al. teaches that determining an energy of the quantum chemistry system based on the trial state and the restricted Hamiltonian (specification paragraph 36) and the trial state and the energy may be determined based on a variational scheme, preferably a variational quantum eigenvalue (VQE) system (specification paragraph 24, wherein the hybrid quantum-classical computing system is further configured to, based at least in part on a result of implementing the simulation, determine at least one of. a wavefunction of the chemical system, a structural characteristic of the chemical system, a chemical interaction characteristic of the chemical system, or a response characteristic of the chemical system (Claim 10)).
With respect to the limitations of Claims 1, 13, Elfving et al. teaches the paired-electron unitary coupled cluster with double-excitations (pUCCD) ansatz may be defined in terms of electron-pair annihilation operators, hard-core bosonic annihilation operators (specification paragraph 19) and Fermionic Hamiltonians known from the prior art, cannot be mapped to qubits directly/naturally, whereas the hard-core bosonic Hamiltonian is directly supported on qubits due to the matching commutation relations of the shared SU(2) group (specification paragraph 13, (iii) by generating a spatial excitation synthesis of the chemical system from the quantum state synthesis using hard-core bosonic operators (claim 1) (claim 13)) Elfving et al. also teaches the quantum state preparation module and energy estimation module may be implemented as a gate-based qubit quantum circuit comprising N qubits which may be configured in an initial state. In an embodiment, the measuring of the energy may include determining the quantum state of the qubits by applying a unitary ansatz to the initial state (specification paragraph 26) and the electron singlet state may be configured to only include molecular orbitals that are occupied or not occupied by electron pairs, preferably a qubit includes a first qubit state (specification paragraph 16, (v) by introducing spin orbitals on the at least one quantum circuit (Claim 1) (Claim 13)
With respect to the limitations of Claim 6, 16, Elfving et al. teaches the invention may relate to a method for simulating a quantum chemistry system comprising: determining a Hamiltonian describing the quantum chemistry system, the Hamiltonian being restricted to molecular orbitals that are occupied or not occupied by electron pairs; determining a paired-electron unitary coupled cluster with double excitations (pUCCD) ansatz, the ansatz being restricted to molecular orbitals that are occupied or not occupied by electron pairs (specification paragraph 11) and determining a trial state may include: initializing qubits of the quantum computer based on parameters, preferably coupled cluster amplitudes, which are computed on information of the quantum chemistry system (specification paragraph 27). This is equivalent to double occupied and virtual spatial orbitals (wherein generating the quantum state synthesis of the chemical system comprises generating a reference state based on the double occupied and virtual spatial orbitals of the chemical system (Claim 6) generating the quantum state synthesis of the chemical system comprises generating a reference state based on the double occupied and virtual spatial orbitals of the chemical system (Claim 16)).
With respect to the limitations of Claim 7, 16, Elfving et al. teaches the gate operation may be a singlet-state simulation (SSS) gate operation, including a partial-swap gate operation, partial-swap gate performs an entangling operation which simulates partially distributing an electron pair among two molecular orbitals (specification paragraph 30) and the Hamiltonian may describe a quantum chemistry (electronic structure) system that is defined in terms of electron-pair annihilation operators, preferably hard-core bosonic annihilation operators (specification, paragraph 17, wherein generating the spatial excitation synthesis comprises transforming spatial orbital to spatial orbital operators to double excitation spatial-to-spatial qubit operators (Claim 7) generating the spatial excitation synthesis comprises transforming spatial orbital to spatial orbital operators to double excitation spatial-to-spatial qubit operators (Claim 16)).
With respect to the limitations of Claim 9, 17, Elfving et al. teaches the pUCCD protocol enables efficient use of the swap network for simulation, such that the qubit lattice connectivity requirement is relaxed considerably as compared to previous UCC proposals. Only a single linear chain needs to be defined across the lattice to reach the proven-to-be-minimal linear gate depth (specification, paragraph 33) and the restricted Hamiltonian method can readily be extended to include higher-order excitations as desired for accuracy reasons, interpolating towards fully un-restricted, where the trade-off should be made by including higher-order terms for accuracy at a cost of increased run-time due to circuit depth and additional sets of non-commuting operators in the Hamiltonian (specification paragraph 23, wherein the hybrid quantum-classical computing entity is configured to compile the quantum circuit synthesis into an at least one quantum circuit, wherein the quantum circuit synthesis comprises, in order, the double excitation spatial-to-spatial qubit operators (Claim 9) wherein the quantum circuit synthesis comprises, in order, the double excitation spatial-to-spatial qubit operators, the Jordan- Wigner encoded arbitrary double excitation qubit operators, and single excitation qubit operators. (Claim 17)).
With respect to the limitations of Claims 2, 14, Elfving et al. teaches the Hamiltonian may describe a quantum chemistry (electronic structure) system that is defined in terms of electron-pair annihilation operators, preferably hard-core bosonic annihilation operators (specification, paragraph 17) and Fermionic Hamiltonians known from the prior art, cannot be mapped to qubits directly/naturally, whereas the hard-core bosonic Hamiltonian is directly supported on qubits due to the matching commutation relations of the shared SU(2) group (specification, paragraph 13, wherein the hybrid quantum-classical computing system is configured to reconfigure the order of occurrence of the single electron excitation operators and the double electron excitation operators to: (i) double excitation operators corresponding to double excitations from a spatial orbital to a corresponding spatial orbital (Claim 2) wherein the order of occurrence of the single electron excitation operators and the double electron excitation operators is reconfigured to:(i) double excitation operators corresponding to double excitations from a spatial orbital to a corresponding spatial orbital (Claim 14)
Elfving et al. does not explicitly teach
reconfigure an order of occurrence of the single electron excitation operators and the double electron excitation operators in the operator representation as a function of the characterizing parameters, such that the simulation is executable with a lower count of two- qubit quantum gates used in at least one quantum circuit executable on the quantum computing component that is used to implement the simulation (claim 1) (Claim 13) (Claim 20)
(ii) by generating a quantum state synthesis of the chemical system based on the degree of symmetry (Claim 3) (Claim 15)
(iv) by processing the spatial excitation synthesis by transforming from spatial orbitals to spin orbitals therein (Claim 3) (Claim 15)
wherein generating the quantum circuit synthesis comprises transforming the double excitation operators of the chemical system that correspond to double excitations other than spatial orbital to spatial orbital double excitations to Jordan-Wigner encoded arbitrary double excitation qubit operators configured to act on 4-qubits or more (Claim 8)
the Jordan- Wigner encoded arbitrary double excitation qubit operators (Claim 9) (Claim 17)).
(ii) arbitrary double excitation operators (Claim 2) (Claim 14)
wherein the hybrid quantum-classical computing system is configured to reconfigure the order of occurrence of the single electron excitation operators and the double electron excitation operators to: (i) double excitation operators corresponding to double excitations from a spatial orbital to a corresponding spatial orbital (Claim 2)
wherein the order of occurrence of the single electron excitation operators and the double electron excitation operators is reconfigured to:(i) double excitation operators corresponding to double excitations from a spatial orbital to a corresponding spatial orbital (Claim 14)
wherein the hybrid quantum-classical computing system is further configured to cause the classical computing component to cause at least one of (a) display of a graphical representation of at least a portion of the simulation of the chemical system or (b) generation and storage in a classical memory of a file comprising one or more parameters of the simulation of the chemical system (Claim 11) (Claim 18))
wherein the operator representation is generated using a unitary coupled cluster singles and doubles (UCCSD) ansatz (Claim 12) (Claim 19)
(iii) arbitrary single excitation operators (Claim 2) (Claim 14))
(wherein the hybrid quantum-classical computing system is further configured to cause the classical computing component to cause at least one of (a) display of a graphical representation of at least a portion of the simulation of the chemical system or (b) generation and storage in a classical memory of a file comprising one or more parameters of the simulation of the chemical system (Claim 11) further comprising determining by the quantum computing component at least one of a wavefunction of the chemical system, a structural characteristic of the chemical system, a chemical interaction characteristic of the chemical system, or a response characteristic of the chemical system via implementing the simulation; and causing, by the classical computing component, at least one of (a) display of a graphical representation of at least a portion of the model of the chemical system or (b) generation and storage in a classical memory of a file comprising one or more parameters of the model of the chemical system. (Claim 18))
wherein the hybrid quantum-classical computing system is configured to determine the characterizing parameters that describe the chemical system and generate a corresponding operator representation: (i) by applying symmetry filtering to the operator representation of the chemical system to assess its structural degree of symmetry (claim 1)
wherein the system is configured to determine the characterizing parameters that describe the chemical system and generate a corresponding operator representation: (i) by applying symmetry filtering to the operator representation of the chemical system to assess its structural degree of symmetry (Claim 13)
and (vi) by using commuting sets of double excitation operators and single excitation operators to synthesize the at least one quantum circuit, such that double excitation operators appear in the at least one quantum circuit before the single excitation operators appear in the at least one quantum circuit and each commuting set corresponds to an excitation of the chemical system (claim 1) (Claim 13)).
wherein the hybrid quantum-chemical computing system is configured to reduce a number of quantum gates required in the quantum circuit synthesis as a function of the structural degree of symmetry of the chemical system (Claim 4)
wherein applying the symmetry filtering to the operator representation comprises at least one of: defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that do not commute with one or more symmetries of the set of symmetries, or defining an abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the abelian point group (Claim 5)
wherein at least one of: the hybrid quantum-chemical computing system is configured to reduce a number of controlled-NOT gates required in the quantum circuit synthesis as a function of the structural degree of symmetry of the chemical system, applying the symmetry filtering to the operator representation comprises defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that do not commute with one or more symmetries of the set of symmetries, applying the symmetry filtering to the operator representation comprises defining an abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the abelian point group (Claim 16))
and single excitation qubit operators (Claim 9) (Claim 17)).
wherein generating the quantum state synthesis of the chemical system based on the degree of symmetry comprises: generating a double occupation of spatial orbitals reference state by processing a reference state of the chemical system; and mapping spatial orbital occupations provided the double occupation of spatial orbitals reference state to qubits. (Claim 21)
and (v) execute the at least one quantum circuit executable to cause a controlled quantum state evolution of qubits of the quantum computing component to implement the simulation, wherein determining the characterizing parameters that describe the chemical system and generating the corresponding operator representation comprises (Claim 1) (Claim 13) (Claim 20)
wherein introducing the spin orbitals on the at least one quantum circuit comprises: mapping spatial orbitals that are singly occupied in a reference state of the chemical system to respective qubits; and inserting operations into the at least one quantum circuit to toggle the respective qubits to a qubit state indicating occupation of the spin orbitals. (Claim 22)
wherein generating the quantum state synthesis of the chemical system based on the degree of symmetry comprises: generating a double occupation of spatial orbitals reference state by processing a reference state of the chemical system; and mapping spatial orbital occupations provided the double occupation of spatial orbitals reference state to qubits. (Claim 21)
However, these limitations were known in the art at the time as taught by Anand et al. in view of Romero et al. in view of Lee et al. in view of Barkoutsos et al. in view of Whitfield et al.
With respect to the limitations of Claims 1, 13, 20 Anand et al. investigated the influence of operator ordering in a Trotterised UCCSD ansatz. This paper shows that especially in the case of static correlation, particular orderings lead to chemically meaningful improvements in energies. A simple example of an unfavourable or inefficient ordering is starting with an excitation that does not include occupied reference orbitals (pg. 14, paragraph 6) Single excitations can only occur between orbitals belonging to the same irreducible representation. Double excitations occur when the (tensor) product of the irreducible representations of the occupied orbitals is equal to the product of the irreducible representations of the virtual orbitals. These operators yield the same numerical results and greatly reduce the number of excitations needed to encode in a quantum computer, reducing the two-qubit gate count too as well as the number of parameters in a subsequent optimization procedure (pg. 28, paragraph 3-4) However, due to its structure, a simple compilation of UCCSD operators can be performed based on the tableau representation, which reduces the CNOT gate count significantly (pg. 38, paragraph 2, (iii) reconfigure an order of occurrence of the single electron excitation operators and the double electron excitation operators in the operator representation as a function of the characterizing parameters, such that the simulation is executable with a lower count of two- qubit quantum gates used in at least one quantum circuit executable on the quantum computing component that is used to implement the simulation (claim 1) (Claim 13) (Claim 20)).
With respect to the limitations of Claim 1, 13, Anand et al. teaches single excitations can only occur between orbitals belonging to the same irreducible representation. Double excitations occur when the (tensor) product of the irreducible representations of the occupied orbitals is equal to the product of the irreducible representations of the virtual orbitals. Additionally, the products of irreducible representations that partake in the excitation should contain the fully symmetric irreducible representation. These operators yield the same numerical results and greatly reduce the number of excitations needed to encode in a quantum computer, reducing the two-qubit gate count too as well as the number of parameters in a subsequent optimization procedure. (pg. 28, paragraph 4-5, wherein the hybrid quantum-classical computing system is configured to determine the characterizing parameters that describe the chemical system and generate a corresponding operator representation: (i) by applying symmetry filtering to the operator representation of the chemical system to assess its structural degree of symmetry (claim 1) wherein the system is configured to determine the characterizing parameters that describe the chemical system and generate a corresponding operator representation: (i) by applying symmetry filtering to the operator representation of the chemical system to assess its structural degree of symmetry (Claim 13)). Anand et al. also teaches the compilation of UCCSD excitations is separated in two steps. First, the parity operator is factorized for a set of four commuting Pauli strings. Second, the remaining qubit excitations are diagonalized with Clifford gates (pg. 38, paragraph 3) and if the qubit operators comprising a fermionic excitation commute with each other than the exponential function of the fermionic excitation is a product of exponential functions of the qubit operators (individual Pauli strings). (pg. 13, paragraph 3) A simple example of an unfavorable or inefficient ordering is starting with an excitation that does not include occupied reference orbital(pg. 14, paragraph 7, and (vi) by using commuting sets of double excitation operators and single excitation operators to synthesize the at least one quantum circuit, such that double excitation operators appear in the at least one quantum circuit before the single excitation operators appear in the at least one quantum circuit and each commuting set corresponds to an excitation of the chemical system (claim 1) (Claim 13)).
With respect to the limitations of Claim 4-5, 16, Anand et al. teaches that single excitations can only occur between orbitals belonging to the same irreducible representation. Double excitations occur when the (tensor) product of the irreducible representations of the occupied orbitals is equal to the product of the irreducible representations of the virtual orbitals. These operators yield the same numerical results and greatly reduce the number of excitations needed to encode in a quantum computer, reducing the two-qubit gate count too as well as the number of parameters in a subsequent optimization procedure (pg. 28, paragraph 3-4) However, due to its structure, a simple compilation of UCCSD operators can be performed based on the tableau representation, which reduces the CNOT gate count significantly (pg. 38, paragraph 2, wherein the hybrid quantum-chemical computing system is configured to reduce a number of quantum gates required in the quantum circuit synthesis as a function of the structural degree of symmetry of the chemical system (Claim 4) wherein applying the symmetry filtering to the operator representation comprises at least one of: defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that do not commute with one or more symmetries of the set of symmetries, or defining an abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the abelian point group (Claim 5) wherein at least one of: the hybrid quantum-chemical computing system is configured to reduce a number of controlled-NOT gates required in the quantum circuit synthesis as a function of the structural degree of symmetry of the chemical system, applying the symmetry filtering to the operator representation comprises defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that do not commute with one or more symmetries of the set of symmetries, applying the symmetry filtering to the operator representation comprises defining an abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the abelian point group (Claim 16))
With respect to the limitations of Claims 2, 14, Romero et al. teaches the approximation up to double cluster operators provides a good compromise between cost and accuracy for applications in quantum chemistry, with a number of parameters that scales as O(N2h2). The number of parameters in the approximation determines the size of the circuit and impacts the cost of the classical optimization required for wavefunction optimization (pg. 18 paragraph 5 – pg. 19 paragraph 1, (ii) arbitrary double excitation operators (Claim 2) (Claim 14))
With respect to the limitations of Claims 11, 18, Romero et al. teaches a methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a ucc ansatz can be reduced without introducing significant loss of accuracy in the final wave functions and energies (abstract) The information is saved and displayed. (wherein the hybrid quantum-classical computing system is further configured to cause the classical computing component to cause at least one of (a) display of a graphical representation of at least a portion of the simulation of the chemical system or (b) generation and storage in a classical memory of a file comprising one or more parameters of the simulation of the chemical system (Claim 11) further comprising determining by the quantum computing component at least one of a wavefunction of the chemical system, a structural characteristic of the chemical system, a chemical interaction characteristic of the chemical system, or a response characteristic of the chemical system via implementing the simulation; and causing, by the classical computing component, at least one of (a) display of a graphical representation of at least a portion of the model of the chemical system or (b) generation and storage in a classical memory of a file comprising one or more parameters of the model of the chemical system. (Claim 18))
With respect to the limitations of Claims 12, 19, Romero et al. teaches that the key for retaining a polynomial number of operations to perform VQE with a UCC ansatz is to truncate the CC expansion. A popular truncation in quantum chemistry is to consider only single and double excitations (UCCSD) (pg. 7, paragraph 6, wherein the operator representation is generated using a unitary coupled cluster singles and doubles (UCCSD) ansatz (Claim 12) (Claim 19))
With respect to the limitations of Claims 2, 14, Lee et al. teaches UpCCGSD employs k products of the exponential of pair coupled cluster double excitation operators (pCCD), together with generalized single excitation operators and that k-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of O(kn), compared with O(N3) for UCCGSD (abstract, pg. 311, (iii) arbitrary single excitation operators (Claim 2) (Claim 14))
With respect to the limitations of Claims 9, 17, Lee et al. teaches UpCCGSD employs k products of the exponential of pair coupled cluster double excitation operators (pCCD), together with generalized single excitation operators and that k-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of O(kn), compared with O(N3) for UCCGSD (abstract, pg. 311, and single excitation qubit operators (Claim 9) (Claim 17)).
With respect to the limitations of Claims 1, 13, Barkoutsos et al. teaches the complexity of the problem can be reduced by the encoding of specific symmetries directly at the Hamiltonian level. For example, one can restrict the action of the SQ Hamiltonian to the sector of the Fock space that corresponds to the desired number of electrons or implement symmetry constraints. This parametrizes the trial wave function to lie within symmetry defined fock space (pg. 2, col 1., paragraph 2, (ii) by generating a quantum state synthesis of the chemical system based on the degree of symmetry (Claim 1) (Claim 13)
With respect to the limitations of Claims 1, 13, Whitfield et al. teaches the spin variable representation of second quantized Hermitian operators after performing the Jordan-Wigner transformation to yield tensor products of Pauli sigma matrices (spin variables) that have the proper anti-commutation relations (pg. 22, table a2) and Due to the anti-commutation rules, all sets of operators corresponding to a set of four distinct spin-orbitals, (p, q, r, s), are simulated using the same circuit. (pg. 13, paragraph 4, (iv) by processing the spatial excitation synthesis by transforming from spatial orbitals to spin orbitals therein (Claim 1) (Claim 13)).
With respect to the limitations of Claims 8-9, 17, Whitfield et al. teaches the spin variable representation of second quantized Hermitian operators after performing the Jordan-Wigner transformation to yield tensor products of Pauli sigma matrices (spin variables) that have the proper anti-commutation relations (pg. 22, table a2) and also teaches the double excitation operator each of the 8 quadruplets must be implemented in succession (pg. 20, table A1) and a set of four distinct spin-orbitals, (p, q, r, s), are simulated using the same circuit. This is due to the fact that the Jordan-Wigner of each operator generates same set of operators namely, the eight combinations (pg. 14, paragraph 6, wherein generating the quantum circuit synthesis comprises transforming the double excitation operators of the chemical system that correspond to double excitations other than spatial orbital to spatial orbital double excitations to Jordan-Wigner encoded arbitrary double excitation qubit operators configured to act on 4-qubits or more (Claim 8) the Jordan- Wigner encoded arbitrary double excitation qubit operators (Claim 9) wherein the quantum circuit synthesis comprises, in order, the double excitation spatial-to-spatial qubit operators, the Jordan- Wigner encoded arbitrary double excitation qubit operators, and single excitation qubit operators. (Claim 17)).
With respect to the limitations of Claims 1, 13, 20, 21, Elfving et al.(Arxiv) teaches compile the at least one quantum circuit executable and they Accurate quantum chemistry simulations remain challenging on classical computers for problems of industri ally relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible. While variational quantum eigensolver (VQE) algorithms may already turn noisy interme diate scale quantum (NISQ) devices into useful machines, one has to make all efforts to use the scarce quantum resources as efficiently as possible. We combine the so-called seniority-zero, or paired-electron, approximation of computational quantum chemistry with techniques for simulating molecular chemistry on gate-based quan tum computers and obtain a very resource efficient quantum simulation algorithm. While some accuracy is lost through the paired-electron approximation, we show that using the freed-up quantum resources for increasing the basis set can lead to more accurate results and reductions in the necessary number of quantum computing runs by several orders of magnitude, already for a simple system like lithium hydride. We also discuss an error mitigation scheme based on post-selection which shows an attractive scaling when the given Hamiltonian format is considered, increasing the viability of its NISQ implementation. (abstract) To turn a chemical problem into a well defined computa tional problem, usually a series of assumptions and approxi mations are made. The first standard assumption is the Born Oppenheimer approximation, which decouples the nuclear and electronic degrees of freedom. Considering that elec trons move much faster than nuclei in molecules, the Born Oppenheimer approximation considers the latter as frozen point charges in space and their coordinates hence as classi cal parameters. At this point, an electronic structure problem comes up. This corresponds to a problem of determining the behavior of the electrons of the system in the potential cre ated by the nuclei and the background charges. For an intro duction to the electronic structure problem, and a description of classical and quantum algorithms which solves these prob lems, we refer the reader to Refs. [3, 28]. All wave function based methods require a discretization of the electronic struc ture problem, which a priori is a continuum problem of elec trons in three dimensional space. In the standard approach the electrons of the system are modeled individually and finite set of basis functions is in troduced (a so-called basis set) to discretize the problem and thereby make it amenable to a solution on a digital computer. Each basis function is considered to represent a fermionic mode. (A. Hamiltonians in computational chemistry) employ the paired-electron approximation [8] during the discretization step. This approximation effectively restricts the problem to a zero-seniority subspace of the full Hilbert space of all possible many-body electronic states that is spanned by those states in which all orbitals are either empty or occupied by an electron singlet pair (because of the Pauli exclusion principle). The paired-electron assumption is rather widespread in computational chemistry and has proved to deliver sufficient accuracy for the description of a range of chemical systems. Indeed its usage has become standard in computational chemistry. This is so, as quite often in molecular systems all the electrons are distributed in electronic pairs occupying the same spatial orbital. The connection here is that a singlet pair of electrons has even spin and thus behaves like a boson, while no more than 2 elec trons can occupy any of the molecular orbitals at once. No tice that this Hamiltonian is far simpler than the unrestricted ermionic Hamiltonian in Equation (1), but still non-trivial, as it is not quadratic in the creation and annihiliation operators. As a first consequence of using the paired-electron approx imation, the number of qubits needed to represent a given problem is halved compared with the unrestricted mapping. In the LiH example the 6 basis functions in the STO-6G ba sis map to 6 qubits instead of the usual 12. Alternatively, one may use the same qubit number with a larger basis set (this can be advantageous as we will show later). For example, in the 4-31G basis set, 11 molecular orbitals (MOs) result in 22 fermionic orbitals but only 11 qubits are needed in the paired electron approach. In this way, with 12 qubits as a quantum resource, one may either simulate LiH in unrestricted STO-6G or in paired-electron 4-31G. As the electron pair creation (B. Discretization in the paired-electron approximation)
PNG
media_image1.png
69
490
media_image1.png
Greyscale
(Equation 2) wherein generating the quantum state synthesis of the chemical system based on the degree of symmetry comprises: generating a double occupation of spatial orbitals reference state by processing a reference state of the chemical system; and mapping spatial orbital occupations provided the double occupation of spatial orbitals reference state to qubits. (Claim 21) and (v) execute the at least one quantum circuit executable to cause a controlled quantum state evolution of qubits of the quantum computing component to implement the simulation, wherein determining the characterizing parameters that describe the chemical system and generating the corresponding operator representation comprises (Claim 1) (Claim 13) (Claim 20)
With respect to the limitations of Claims 1, 13 and 20, Sugisaki et al. teaches the quantum circuit starts RHF configuration preparation (specified i in Figure 1A). This step consists of NOT operations (denoted by X) to the qubits representing occupied orbitals to change the qubit states from |0⟩ to |1⟩. The second step (ii) is rotations applied to the ancilla qubits with the rotating angle θi depending on diradical characters yi: The third and following steps, iii−v, and so on, are sequential generations of di-, tetra-, hexa-, and higher-radical configurations conditional to ancilla qubits. These steps generate open shell electronic configurations if the correspond ing ancilla qubits are in state |1⟩ and adopt no operations if the ancillas are the |0⟩ state. These conditional operations produce linear combinations of open shell and closed shell electronic configurations as given in eq 6. The diradical wave function given in eq 1 can be generated using a circuit given in Figure 1B, by analogy with Bell state preparations. The diradical wave function preparation in Figure 1B consists of two single-qubit rotations and following three CNOT operations. The first three quantum gates generate the linear combination of states in which LUNO + i is doubly occupied and unoccupied. The subsequent two CNOT gates conditionally change the occupation number of the HONO − i orbital from doubly occupied to unoccupied, if the LUNO + i is doubly occupied. The wave function after diradical configuration generations specified iii in Figure 1A is given in eq 11. (pg. 170, cols 1-2) wherein introducing the spin orbitals on the at least one quantum circuit comprises: mapping spatial orbitals that are singly occupied in a reference state of the chemical system to respective qubits; and inserting operations into the at least one quantum circuit to toggle the respective qubits to a qubit state indicating occupation of the spin orbitals (Claim 22) (iv) compile the at least one quantum circuit executable; (Claim 1) (Claim 13) (Claim 20)
A person of ordinary skill in the art would modify Elfving et al. in view of Anand et al. in view of Romero et al. in view of Lee et al. in view of Barkoutsos et al. in view of Whitfield et al. because each work is in the same field of endeavor of quantum simulation and a person of ordinary skill in the art would see how other people have previous performed simulations. A person of ordinary skill in the art would modify the method of efficient quantum chemistry simulation using gate-based qubit quantum devices taught by Elfving et al. with the knowledge of quantum computing view on unitary coupled cluster theory taught by Anand et al. as both references are in the same field of hybrid quantum-classical molecular simulation. There is a motivation to modify Elfving et al. with Anand et al., as Anand et al. states that single excitations can only occur between orbitals belonging to the same irreducible representation. Double excitations occur when the (tensor) product of the irreducible representations of the occupied orbitals is equal to the product of the irreducible representations of the virtual orbitals. These operators yield the same numerical results and greatly reduce the number of excitations needed to encode in a quantum computer, reducing the two-qubit gate count too as well as the number of parameters in a subsequent optimization procedure (pg. 28, paragraph 3-4) provides the theoretical framework for modifying Anand et al. in order to reconfigure an order of occurrence of the single electron excitation operators and the double electron excitation operators in the operator representation as a function of the characterizing parameters, such that the simulation is executable with a lower count of two- qubit quantum gates. Elfving et al. provides explicit motivation for the restricted Hamiltonian method can readily be extended to include higher-order excitations as desired for accuracy reasons, interpolating towards fully un-restricted, where the trade-off should be made by including higher-order terms for accuracy at a cost of increased run-time due to circuit depth and additional sets of non-commuting operators in the Hamiltonian (specification, paragraph 23).Lee et al. teaches generalized single excitation operators placed after double operators. Barkoutsos et al. taught quantum state synthesis constrained to symmetry of Fock space. Romero et al. teaches the UCCSD double excitation operators. Whitfield et al. teaches the Jorddan Winger transformation from spatial orbitals to spin orbitals. A person of ordinary skill in the art would be motivated to combine the references as all reference deal with the same problem of reducing circuit depth in hybrid classical-quantum simulation by structured use of excitation operators. Additionally, Anand et al. provides expressed motivation to combine the others. As a comprehensive field review, it explicitly surveys and synthesizes the techniques of Whitfield et al, Barkoutsos et al, Elfving et al. As the known toolkit for reducing to quibit gate count, a person of ordinary skill in the arc, reading Anand et al. would recognize that applying these references in the sequence is the natural, obvious implementation of the pipeline. A person of ordinary skill in the art would understand that the sequence is the natural obvious order. Anand et al. symmetry filtering produces a set of allowed excitation, which Barkoutsos et al. symmetry sector state preparation uses to constrain the trial state, which Elfving et al.'s bosonic spatial excitation synthesis then builds on, which Whitfield et al. Jordan-Wigner transformation then maps to spin orbitals, which Elfving et al. introduces onto the circuit, which Anand et al.'s commuting set compilation then compiles into an executable circuit. Each output is required input for the next step. The stages are sequential and not redundant by design. Elfving et al. also provides express suggestion. It states the method can readily be extended to include higher order excitations, directly inviting combination with the full pipeline. No reference teaches away from any other, and none at all explicitly presents all approaches as complementary and references addresses a stage the others do not. A person of ordinary skill in the art when attempting to construct a quantum circuit for UCCSD or related simulations on a quantum computer with reduced gate count and depth would combine all methods described above. The instant application just puts together multiple steps from the prior art without modifying how they work. There is an additional reasonable expectation of success as each method works individually and the function, inputs and outputs of the methods are not changed when they are combined therefore the methods are expected to work as the methods did individually. Additionally, there is only a limited number of ways to put these methods together a person of ordinary skill in the art would be motivated to try them all until they find the optimum method.
Response to Arguments 103
Examiner asserts that Anand states the exact mathematical and physical rules of symmetry filtering (using group theory and irreducible representations). While applicant high-level, systems-engineering overview of how a hybrid quantum-classical algorithm automates that exact process. Single excitations only occur between orbitals of the same irreducible representation. Double excitations must satisfy specific tensor product symmetry rules, and the overall excitation must contain the fully symmetric irrep. "Symmetry filtering" is simply the algorithmic name for discarding any excitation operator that violates the exact rules laid out in your first statement which is exactly what Anand et al does.
Anand et al. the comprehensive review explicitly synthesizes the techniques of Whitfield et al, Barkoutsos et al, Elfving et al. as the known field toolkit. The discussion of operator compilation, symmetry filtering, and bosonic representations. There is a strong motivation to reduce gate count and make simulations more efficient therefore a person of ordinary skill in the art would be motivated to combine the prior art. Anand et al. provides expressed motivation to combine the others. As a comprehensive field review, it explicitly surveys and synthesizes the techniques of Whitfield et al, Barkoutsos et al, Elfving et al. As the known toolkit for reducing to quibit gate count, a person of ordinary skill in the arc, reading Anand et al. would recognize that applying these references in the sequence is the natural, obvious implementation of the pipeline. A person of ordinary skill in the art would understand that the sequence is the natural obvious order. Anand et al. symmetry filtering produces a set of allowed excitation, which Barkoutsos et al. symmetry sector state preparation uses to constrain the trial state, which Elfving et al.'s bosonic spatial excitation synthesis then builds on, which Whitfield et al. Jordan-Wigner transformation then maps to spin orbitals, which Elfving et al. introduces onto the circuit, which Anand et al.'s commuting set compilation then compiles into an executable circuit. Each output is required input for the next step. The stages are sequential and not redundant by design. Elfving et al. also provides express suggestion. It states the method can readily be extended to include higher order excitations, directly inviting combination with the full pipeline. No reference teaches away from any other, and none at all explicitly presents all approaches as complementary and references addresses a stage the others do not. Additionally, there is only a limited number of ways to put these methods together a person of ordinary skill in the art would be motivated to try them all until they find the optimum method.
Conclusion
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Connor Beveridge whose telephone number is 571-272-2099. The examiner can normally be reached Monday - Thursday 9 am - 5 pm.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Karlheinz Skowronek can be reached at 571-272-9047. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/C.H.B./Examiner, Art Unit 1687
/Karlheinz R. Skowronek/Supervisory Patent Examiner, Art Unit 1687
