DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
This action is in response to the application and preliminary amendment field 5/01/2023. In the preliminary amendment, claims 4-7, 11-14 and 18-21 were amended, and no claims were added or cancelled. As such, claim 1-21 are pending and have been examined. Claims 1-21 are rejected.
Priority
Applicant’s claim for the benefit of a prior-filed application under 35 U.S.C. 119(e) or under 35 U.S.C. 120, 121, 365(c), or 386(c) is acknowledged. The present application is a national stage application under 35 U.S.C. 371 of International Application No. PCT/CN2020/130301, filed on November 20, 2020.
Information Disclosure Statement
Acknowledgment is made of the information disclosure statements filed 5/12/2023 and 9/23/2024, which comply with 37 CFR 1.97. As such, the information disclosure statements have been placed in the application file and the information referred to therein has been considered by the examiner
Drawings
The drawings are also objected to as failing to comply with 37 CFR 1.84(p)(5) because they include the following reference characters not mentioned in the description:
Reference character 410 shown in Figure 4A is not found in the detailed description (see, e.g., paragraph 74 describing FIG. 4A);
Reference character 420 shown in Figure 4B is not found in the detailed description (see, e.g., paragraph 80 describing FIG. 4B); and
Reference character 500 shown in Figure 5 is not found in the detailed description (see, e.g., paragraphs 82-88 describing FIG. 5).
The drawings are further objected to as failing to comply with 37 CFR 1.84(p)(3) because Figure 4A includes letters which do not measure at least .32 cm. (1/8 inch) in height (i.e., most of the characters FIG. 4A).
Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Specification
The disclosure is objected to because of the following informalities:
Reference characters 410 and 420 shown in Figures 4A and 4B are not found in the detailed description (see, e.g., paragraphs 74 and 80 describing FIGs. 4A and 4B), and reference character 500 shown in Figure 5 is not found in the detailed description (see, e.g., paragraphs 82-88 describing FIG. 5). Appropriate correction is required.
Claim Objections
Claim 5 is objected to because of the following informalities:
The preamble of claim 5 recites “The method of claim 1, further comprises”. This recitation is grammatically incorrect and appears to be missing one or more words. If supported by the original specification, examiner suggests that two possible ways to address this objection would be to amend “The method of claim 1, further comprises” to read “The method of claim 1, wherein the method further comprises” or “The method of claim 1, further comprising”. Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
Claims 1-21 are rejected under 35 U.S.C. 112(b) as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention.
Independent claims 1, 8 and 15 each recite “optimizing a quantum circuit” (see line 1 of claims 1 and 18, and line 3 of claim 15). The term “optimizing a quantum circuit” is a relative term which renders the claims indefinite. This term is not defined by the claims, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. The specification repeats the claim language in stating “a method for optimizing a quantum circuit” and “an apparatus for optimizing a quantum circuit” and provides general examples in stating “when the simulation result shows that quantum circuit 201 behaves as planned or designed, quantum circuit adjuster 230 may confirm that no adjustment is needed or that the quantum circuit 201 is optimum. … quantum circuit adjuster 230 can adjust quantum circuit 201 such that the quantum circuit 201 can adequately behave as it is planned or designed or such that the quantum circuit 201 can behave to provide optimal performance in view of its purpose.” (see, e.g., paragraphs 4-6, 27-28, 66, 88, 90, 97 and 104). Thus, the specification fails to describe or define what is meant by this term. In particular, it is unclear what metrics or standards are used for ascertaining the requisite degree of quantum circuit optimality for the claimed “optimizing a quantum circuit.” As such, the specification does not provide a standard for determining the requisite degree of circuit optimality for the claimed “optimizing a quantum circuit” in claims 1, 8 and 15. For the purposes of determining patent eligibility and comparison with the prior art, the Examiner is interpreting “optimizing a quantum circuit” as any adjustment, modification, calibration or alteration of the behavior or operation of quantum circuit or circuitry based on any purpose, plan or design of the circuit or circuitry. Appropriate correction is required.
Claims 5, 12 and 19 each recite “an effective capacitance matrix of the first Hamiltonian” (see lines 2-3 of claims 5 and 12, and line 3 of claim 19). The term “an effective capacitance matrix” is a relative term which renders the claims indefinite. This term is not defined by the claims, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. The specification repeats the claim language in stating “the linear transformation matrix is configured to perform Gaussian elimination on an effective capacitance matrix of the first Hamiltonian.” and provides general examples in stating “Matrix C0 can be defined as the effective capacitance matrix C of quantum circuit 201.” and “Based on Equation 3, transformed effective capacitance matrix C' for quantum circuit 300 can be expressed.” (see, e.g., paragraphs 101, 108, 40 and 75). Thus, the specification fails to describe or define what is meant by this term. In particular, it is unclear what metrics or standards are used for ascertaining the requisite degree of effectiveness for the claimed “effective capacitance matrix”. As such, the specification does not provide a standard for determining the requisite degree of effectiveness for the claimed “effective capacitance matrix” in claims 5, 12 and 19. Applicant’s specification also does not provide a standard for ascertaining the requisite degree of effect, effectiveness or range of effective capacitance values in the term “effective capacitance matrix”.
The plain meaning of “effective” is adequate to accomplish a purpose; producing the intended or expected result. See https://www.dictionary.com/browse/effective. Thus, an “effective capacitance matrix” could include a matrix of any capacitance values that are adequate or capable of producing an intended or expected result. It appears as though applicant is intending to use a special definition of “effective capacitance matrix”, but the specification fails to redefine the term. See MPEP § 2173.05(a).
Therefore, one of ordinary skill in the art would not be able to ascertain what “an effective capacitance matrix” would encompass. See MPEP § 2173.05(b).
For the purposes of determining patent eligibility and comparison with the prior art, the Examiner is interpreting “an effective capacitance matrix of the first Hamiltonian” as any matrix or vector of capacitance values that are adequate for the first Hamiltonian. Appropriate correction is required.
Also, claims 2-7, 9-14 and 16-21, which each depend directly or indirectly from claims 1, 8 and 15, respectively, are rejected under 35 U.S.C. 112(b) as being indefinite under the same rationale as claims 1, 8 and 15.
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.
Claims 1-21 are rejected under 35 U.S.C. 103 as being unpatentable over Bravyi et al (U.S. Patent Application Pub. No. 2018/0053112 A1, part of the prior art made of record cited in applicant’s IDS filed 9/23/2024, hereinafter “Bravyi”) in view of non-patent literature Kerman (“Efficient numerical simulation of complex Josephson quantum circuits," Lincoln Laboratory, Massachusetts Institute of Technology, arXiv preprint arXiv:2010.14929 v1 (October 2020), part of the prior art made of record cited in applicant’s IDS filed 9/23/2024, hereinafter “Kerman”).
Regarding claim 1, Bravyi discloses the invention as claimed including a method for optimizing a quantum circuit1 (see, e.g., paragraphs 5, “a computer-implemented method of reducing a number of qubits required on a quantum computer is provided.”, 29, “embodiments provide a compression scheme to reduce the number of qubits relying on particle number preservation, and the compression scheme is both efficient to perform as well as asymptotically optimal.” and 86, “a variational approach where the quantum computer 900 is used to measure the energy <ψ|H|ψ> of some fixed Q-qubit state ψ that can be prepared on the available quantum hardware (i.e., quantum computer). … The energy <ψ|H|ψ> is then minimized over some class of variational states using a suitable classical optimization algorithm.” [i.e., approach/method for optimizing a quantum circuit/hardware]), comprising:
acquiring a representation of a quantum circuit comprising one or more qubits (see, e.g., paragraphs 109, “the circuit 600 is considered as a quantum computer with qubits”, 109, “circuit 600 for the quadratic hopping term … for a single qubit in eight modes with bit representation given by W(8,1) and compressed to Q(8,1)=3 qubits.” and 132, “the computer 800 is configured to transform the Hamiltonian utilizing a Fermion to qubit mapping that transforms from M Fermionic modes to M qubits, where the M qubits are represented by M-bit strings in a computational basis.” [i.e., obtain a representation of a quantum circuit/computer including qubits]);
transforming, using a linear transformation matrix, a first Hamiltonian corresponding to the quantum circuit to generate a second Hamiltonian in which free modes are decoupled from non-free modes (see, e.g., paragraphs 68, “Hamiltonian, with the underlying anti commutation rules for the Fermionic modes … The transformation maps the fermionic operators … to a low-order linear combination of Pauli matrices … where Xi, Zi, acts as a single qubit Pauli -X and Pauli -Z matrix on the i-th qubit, for a total of 2M qubits … this transformation requires that the total number of modes 2M is a power of two … The Bravyi-Kitaev transformation for quantum computation … maps the Hamiltonian H to a sum of Hermitian Pauli vectors, so that the experimenters can write H in terms of qubit degrees of freedom as Hq … can be computed as a linear combination from the Hamiltonian coefficients” [i.e., transforming a 1st Hamiltonian H using a linear matrix corresponding to the quantum circuit to generate a 2nd Hamiltonian Hq] and 79, “Let M and N be the number of fermionic modes and the number of particles (occupied modes)” [i.e., in which fermionic/free and occupied/non-free modes are decoupled, separate]);
generating a third Hamiltonian by removing the free modes from the second Hamiltonian (see, e.g., paragraphs 40, “transform Hamiltonian Hq to Hq,- 2 (Hq 4 Hq,- 2 ) by removing a qubit with label M and removing a qubit with label 2M in every term of the Hamiltonian Hq”, and 68-70, “maps the Hamiltonian H to a sum of Hermitian Pauli vectors, so that the experimenters can write H in terms of qubit degrees of freedom”, “reduce the 2M qubit Hamiltonian to Hq,-2 on 2M-2 qubits
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Eq. (6)” , “Here бA\{M,2M} means the qubits M, 2M are removed” [i.e., generate a 3rd Hamiltonian Hq,-2 by removing the free modes M from 2nd Hamiltonian Hq]);
simulating a behavior of the quantum circuit using the third Hamiltonian (see, e.g., paragraphs 36, “transform the Hamiltonian into a qubit Hamiltonian for quantum simulation on 2M-2 qubits … is executed on the quantum hardware of the quantum computer”, 40, “a 2M-2 qubit Hamiltonian Hq,-2 , (See Eq. (6) below), which is applied to the quantum computer” and 54, “use the transformed Hamiltonian in quantum simulations algorithms based on the variational approach where a quantum computer (e.g., quantum computer 900) is used to measure the energy of a given Q-qubit variational state.” [i.e., simulate quantum circuit using 3rd Hamiltonian Hq,-2]).
Although Bravyi substantially discloses the claimed invention, Bravyi is not relied on for explicitly disclosing adjusting a design of the quantum circuit based on the simulated behavior of the quantum circuit.
In the same field, analogous art Kerman teaches adjusting a design of the quantum circuit based on the simulated behavior of the quantum circuit (see, e.g., page 1, Sect. I, “quantum circuits … present an extraordinarily large design space ... Because of the complexity of this design space, … we present a new physical and numerical framework for treating such circuits. Its purpose is both to enable and to encourage the exploration of a much broader range of quantum circuit designs … complex quantum circuit Hamiltonians are diagonalized in multiple stages, to find approximate eigenstates … The methods we describe here have allowed us to simulate larger and more complex Josephson quantum circuits” and 16, Sect. VII, “We have described a new theoretical and numerical framework for simulating the static properties of quantum superconducting circuits, whose purpose is to substantially broaden the reach of possible new circuit designs ... allows for detailed, predictive simulation of larger and more complex combinations of existing qubits, but also for the design of entirely new kinds of quantum circuits which could not previously be considered due to the difficulty of the required design simulations.” [i.e., adjusting the design of the quantum circuit based on the simulated behavior of the quantum circuit]).
Bravyi and Kerman are analogous art because they are both directed to techniques, methods and systems for implementing and designing quantum computing architectures, circuits and devices including quantum operators such as Hamiltonians (see, e.g., Bravyi, Abstract and paragraphs 2, 31-32 and 108-109, and Kerman, Abstract and pages 1 and 4-5, Sects I and III).
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 Bravyi to incorporate the teachings of Kerman to provide “a new theoretical framework for approximate numerical simulation of Josephson quantum circuits.” and “an iterative method in which subsystems are diagonalized separately and then coupled together, at increasing size scales with each iteration, allowing diagonalization of Hamiltonians in extremely large Hilbert spaces to be approximated” where “complex quantum circuit Hamiltonians are diagonalized in multiple stages, to find approximate eigenstates” (See, e.g., Kerman, Abstract and page 1, Sect. I). Doing so would have allowed Bravyi to use Kerman’s quantum circuit simulation framework and method “to enable and to encourage the exploration of a much broader range of quantum circuit designs” and “to simulate larger and more complex Josephson quantum circuits”, as suggested by Kerman (See, e.g., Kerman, page 1, Sect. I).
With respect to independent claim 8, claim 8 is substantially similar to claim 1 and therefore is rejected on the same ground as claim 1, discussed above. In particular, claim 8 is an apparatus claim with operations that correspond to the method steps of claim 1.
Bravyi further discloses an apparatus for optimizing a quantum circuit2, comprising: a memory for storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform operations (see, e.g., paragraphs 29, “embodiments provide a compression scheme to reduce the number of qubits relying on particle number preservation, and the compression scheme is both efficient to perform as well as asymptotically optimal.”, 86, “a variational approach where the quantum computer 900 is used to measure the energy <ψ|H|ψ> of some fixed Q-qubit state ψ that can be prepared on the available quantum hardware (i.e., quantum computer). … The energy <ψ|H|ψ> is then minimized over some class of variational states using a suitable classical optimization algorithm.” and 153, “computer readable program instructions may be provided to a processor of a … programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified … These computer readable program instructions may also be stored in a computer readable storage medium” [i.e., apparatus for optimizing a quantum circuit/hardware including a memory/storage medium storing executable instructions and a processor to execute the instructions to cause the apparatus to perform operations/acts]).
With respect to independent claim 15, claim 15 is substantially similar to claim 1 and therefore is rejected on the same ground as claim 1, discussed above. In particular, claim 15 is a non-transitory computer-readable medium claim with steps that correspond to the method steps of claim 1.
Bravyi further discloses a non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to perform a method for optimizing a quantum circuit3 (see, e.g., paragraphs 29, “embodiments provide a compression scheme to reduce the number of qubits relying on particle number preservation, and the compression scheme is both efficient to perform as well as asymptotically optimal.”, 86, “a variational approach where the quantum computer 900 is used to measure the energy <ψ|H|ψ> of some fixed Q-qubit state ψ that can be prepared on the available quantum hardware (i.e., quantum computer). … The energy <ψ|H|ψ> is then minimized over some class of variational states using a suitable classical optimization algorithm.” and 153, “computer readable program instructions may be provided to a processor of a general purpose computer … to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified … These computer readable program instructions may also be stored in a computer readable storage medium” [i.e., computer readable medium storing instructions executable by a computer processor to perform method for optimizing a quantum circuit/hardware]).
Regarding claims 2, 9 and 16, as discussed above, Bravyi in view of Kerman teaches the method of claim 1, the apparatus of claim 8 and the computer-readable medium of claim 15.
Bravyi further discloses wherein transforming the first Hamiltonian to generate the second Hamiltonian (see, e.g., paragraphs 68, “Hamiltonian … where Xi, Zi, acts as a single qubit Pauli -X and Pauli -Z matrix on the i-th qubit, for a total of 2M qubits … this transformation requires that the total number of modes 2M is a power of two … The Bravyi-Kitaev transformation … maps the Hamiltonian H to a sum of Hermitian Pauli vectors, so that the experimenters can write H in terms of qubit degrees of freedom as Hq … can be computed as a linear combination from the Hamiltonian coefficients” [i.e., transforming 1st Hamiltonian H to generate 2nd Hamiltonian Hq]) comprises:
transforming … a … matrix of the first Hamiltonian to an inverse of a transformed … matrix such that the transformed … matrix in the second Hamiltonian is block diagonalized into a free mode sector and a non-free mode sector (see, e.g., paragraphs 54, “Reduction 3 maps a local fermionic operator preserving the number of particles to a non-local qubit operator that can be represented as a product of a local Pauli and a non-local diagonal operator. The Reduction 3 is applied separately to each term in the Hamiltonian. Assuming that the fermionic system to be simulated consists of M orbitals occupied by N electrons, the transformed Hamiltonian describes a system of Q qubits, where Q<M is a certain function of M and N. … computing the inverse of the compression map. The transformed Hamiltonian”, 79, “Let M and N be the number of fermionic modes and the number of particles (occupied modes)” and 96, “Dj is a diagonal operator such that … applies Pauli X to each qubit … Dj is a diagonal operator with matrix elements” [i.e., transform matrix of 1st Hamiltonian H into an inverse transformed matrix that is diagonalized into a fermionic/free mode sector and an occupied/non-free mode sector]).
Although Bravyi substantially discloses the claimed invention, Bravyi is not relied on for explicitly disclosing transforming an inverse of a charge coupling matrix of the first Hamiltonian to an inverse of a transformed charge coupling matrix such that the transformed charge coupling matrix in the second Hamiltonian is block diagonalized.
In the same field, analogous art Kerman teaches transforming an inverse of a charge coupling matrix of the first Hamiltonian to an inverse of a transformed charge coupling matrix such that the transformed charge coupling matrix in the second Hamiltonian is block diagonalized (see, e.g., Abstract “subsystems are diagonalized separately and then coupled together, at increasing size scales with each iteration, allowing diagonalization of Hamiltonians” and pages 1, Sect. I, “Hamiltonian matrices to be diagonalized. Second, we use a hierarchical diagonalization technique … in which complex quantum circuit Hamiltonians are diagonalized in multiple stages”, 2-3, Sect. II, “matrix Lb is the (Nb x Nb) diagonal branch inductance matrix, whose diagonal elements are the self-inductances of each branch … The relationships between node voltages and charges, and branch currents and fluxoids are given by the constitutive relations”, “quantize the circuit by interpreting the canonically conjugate node fluxoid/charge (coordinate/momentum) pairs … where Φ→ and Q→ are the circuit's fluxoid and charge vectors in the new coordinate representation, and the inverse inductance and capacitance matrices are transformed” and 6, Sect. III, “diagonalizing the matrix Hamiltonian” [i.e., transform an inverse of a fluxoid/charge coupling matrix of the 1st Hamiltonian to an inverse of a transformed fluxoid/charge coupling matrix where transformed fluxoid/charge coupling matrix in the 2nd Hamiltonian is diagonalized]).
Bravyi and Kerman are analogous art because they are both directed to techniques, methods and systems for implementing and designing quantum computing architectures, circuits and devices including quantum operators such as Hamiltonians (see, e.g., Bravyi, Abstract and paragraphs 2, 31-32 and 108-109, and Kerman, Abstract and pages 1 and 5, Sects I and III).
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 Bravyi to incorporate the teachings of Kerman to provide “a new theoretical framework for approximate numerical simulation of Josephson quantum circuits.” and “an iterative method in which subsystems are diagonalized separately and then coupled together, at increasing size scales with each iteration, allowing diagonalization of Hamiltonians in extremely large Hilbert spaces to be approximated” where “complex quantum circuit Hamiltonians are diagonalized in multiple stages, to find approximate eigenstates” (See, e.g., Kerman, Abstract and page 1, Sect. I). Doing so would have allowed Bravyi to use Kerman’s quantum circuit simulation framework and method “to enable and to encourage the exploration of a much broader range of quantum circuit designs” and “to simulate larger and more complex Josephson quantum circuits”, as suggested by Kerman (See, e.g., Kerman, page 1, Sect. I).
Regarding claims 3, 10 and 17, as discussed above, Bravyi in view of Kerman teaches the method of claim 2, the apparatus of claim 9 and the computer-readable medium of claim 16.
Bravyi further discloses wherein transforming the first Hamiltonian to generate the second Hamiltonian further comprises: … using the linear transformation matrix (see, e.g., paragraph 68, “Hamiltonian, with the underlying anti commutation rules for the Fermionic modes … The transformation maps the fermionic operators … to a low-order linear combination of Pauli matrices … where Xi, Zi, acts as a single qubit Pauli -X and Pauli -Z matrix on the i-th qubit, for a total of 2M qubits … this transformation requires that the total number of modes 2M is a power of two … The Bravyi-Kitaev transformation for quantum computation … maps the Hamiltonian H to a sum of Hermitian Pauli vectors, so that the experimenters can write H in terms of qubit degrees of freedom as Hq … can be computed as a linear combination from the Hamiltonian coefficients” [i.e., transforming the 1st Hamiltonian H using the linear transformation matrix corresponding to the quantum circuit to generate the 2nd Hamiltonian Hq]).
Although Bravyi substantially discloses the claimed invention, Bravyi is not relied on for explicitly disclosing transforming a charge operator of the first Hamiltonian using the … transformation matrix.
In the same field, analogous art Kerman teaches transforming a charge operator of the first Hamiltonian using the … transformation matrix (see, e.g., pages 6-7, Sect. III A-B, “we can re-express the circuit Hamiltonian formally in a displaced oscillator basis using a unitary transformation” [i.e., transforming an operator of the 1st Hamiltonian using a transformation matrix], “We truncate the charge state basis … In this basis, the charge operator [Q→J,I ]i for mode i can be written as the matrix
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… By our definition above, the classical Hamiltonian must be Φ0-periodic” [i.e., transforming a charge operator of the 1st Hamiltonian using a transformation matrix]).
The motivation to combine Bravyi and Kerman is the same as discussed above with respect to claims 2, 9 and 16.
Regarding claims 4, 11 and 18, as discussed above, Bravyi in view of Kerman teaches the method of claim 2, the apparatus of claim 9 and the computer-readable medium of claim 16.
Bravyi further discloses wherein transforming the first Hamiltonian to generate the second Hamiltonian further comprises: transforming a … operator of the first Hamiltonian such that a … commutation relation of the first Hamiltonian is preserved in the second Hamiltonian (see, e.g., paragraphs 35, “spin parity preservation in every term of the Hamiltonian both P1 and P2 commute with every term in the transformed Hamiltonian.” and 68-69, “Hamiltonian, with the underlying anti commutation rules for the Fermionic modes … The transformation maps the fermionic operators … to a low-order linear combination of Pauli matrices … where Xi, Zi, acts as a single qubit Pauli -X and Pauli -Z matrix on the i-th qubit, for a total of 2M qubits … this transformation requires that the total number of modes 2M is a power of two … The Bravyi-Kitaev transformation for quantum computation … maps the Hamiltonian H to a sum of Hermitian Pauli vectors, so that the experimenters can write H in terms of qubit degrees of freedom as Hq … the symmetry operators F, will transform, accordingly to Eq. (3)”, “[p↓↑, H]=0 and p↑=ZM as well as p↓p↑=Z2M are single qubit operators, they commute with every term in the Hamiltonian” [i.e., transforming an operator of the 1st Hamiltonian H so that a commutation relation of H is preserved in the 2nd Hamiltonian Hq]).
Although Bravyi substantially discloses the claimed invention, Bravyi is not relied on for explicitly disclosing transforming a flux operator of the first Hamiltonian such that a canonical commutation relation of the first Hamiltonian is preserved in the second Hamiltonian.
In the same field, analogous art Kerman teaches transforming a flux operator of the first Hamiltonian such that a canonical commutation relation of the first Hamiltonian is preserved in the second Hamiltonian (see, e.g., FIG. 5 – depicting “Truncation corrections for the .. qubit circuit” including “corrections for the flux … at the flux symmetry point Φz= Φ0/2).” and pages 2-3, Sect. II, “external bias sources are treated by writing charge and/or fluxoid offsets directly into the Hamiltonian”, “we need to express the magnetic part of eq. 2 in terms of the canonical node fluxoid coordinates Φ→n using the transformation … an apparent charge offset appears in the Hamiltonian … the flux offset for an inductive branch arises from the additional term in the constitutive relation of eq. 4 … The last step in expressing the Hamiltonian in terms of a set of canonical coordinates is to express eq. 5 in the node representation. … We are now in a position to quantize the circuit by interpreting the canonically conjugate node fluxoid/charge (coordinate/momentum) pairs as quantum-mechanical operators obeying the canonical commutation relations.”, 4, Sect. III, “We can now quantize in the usual manner, treating each classical coordinate/momentum (fluxoid/charge) pair as quantum operators obeying the canonical commutation relations” and 15, Sect. VI, “The solid lines in panel (b) [of FIG. 5] show the expectation value of the loop flux operator Φ^б, which corresponds to the qubit persistent current.” [i.e., transforming a flux operator Φ of the 1st Hamiltonian so that its canonical commutation relation persists and is obeyed/expressed/preserved in the 2nd Hamiltonian]).
The motivation to combine Bravyi and Kerman is the same as discussed above with respect to claims 2, 9 and 16.
Regarding claims 5, 12 and 19, as discussed above, Bravyi in view of Kerman teaches the method of claim 1, the apparatus of claim 8 and the computer-readable medium of claim 15.
Bravyi further discloses performing Gaussian elimination on an effective capacitance matrix4 of the first Hamiltonian using the linear transformation matrix (see, e.g., paragraphs 43, “The kernel of this parity check matrix … corresponds to bit strings which encode Pauli matrices that commute with every term in the Hamiltonian … The kernel can be determined by simple Gaussian elimination, which is an efficient reduction and scales polynomially in the number of modes and terms in the Hamiltonian.” and 68, “Hamiltonian, with the underlying anti commutation rules for the Fermionic modes … The transformation maps the fermionic operators … to a low-order linear combination of Pauli matrices … where Xi, Zi, acts as a single qubit Pauli -X and Pauli -Z matrix … The Bravyi-Kitaev transformation for quantum computation … maps the Hamiltonian H to a sum of Hermitian Pauli vectors … can be computed as a linear combination from the Hamiltonian coefficients” [i.e., performing Gaussian elimination on a capacitance matrix of the 1st Hamiltonian H using the linear transformation matrix]).
Regarding claims 6, 13 and 20, as discussed above, Bravyi in view of Kerman teaches the method of claim 1, the apparatus of claim 8 and the computer-readable medium of claim 15.
Bravyi further discloses wherein simulating the behavior of the quantum circuit using the third Hamiltonian comprises:
obtaining discrete energy eigenvalues of the quantum circuit by diagonalizing the third Hamiltonian (see, e.g., paragraphs 36, “transform the Hamiltonian into a qubit Hamiltonian for quantum simulation on 2M-2 qubits … is executed on the quantum hardware of the quantum computer”, 40, “transform Hamiltonian Hq to Hq,-2 … then multiplying the term with the appropriate eigenvalue … a 2M-2 qubit Hamiltonian Hq,-2 , (See Eq. (6) below), which is applied to the quantum computer”, 54, “use the transformed Hamiltonian in quantum simulations algorithms based on the variational approach where a quantum computer (e.g., quantum computer 900) is used to measure the energy of a given Q-qubit variational state.” and 69, “The eigenvalue for p↑, p↓ is ±1, and can be therefore evaluated and stated in each Pauli operator … so that one can reduce the 2M qubit Hamiltonian to Hq,-2 on 2M-2 qubits” and 96, “Dj is a diagonal operator such that … applies Pauli X to each qubit … Dj is a diagonal operator with matrix elements 0, ±1” [i.e., simulating quantum circuit using 3rd Hamiltonian Hq,-2 by obtaining discrete eigenvalues of the quantum circuit by diagonalizing the 3rd Hamiltonian]).
Alternatively, or additionally, in the same field, analogous art Kerman also teaches obtaining discrete energy eigenvalues of the quantum circuit by diagonalizing the third Hamiltonian (see, e.g., Abstract “subsystems are diagonalized separately and then coupled together, at increasing size scales with each iteration, allowing diagonalization of Hamiltonians” and pages 1, Sect. I, “Hamiltonian matrices to be diagonalized. Second, we use a hierarchical diagonalization technique … in which complex quantum circuit Hamiltonians are diagonalized in multiple stages”, 6, Sect. III, “diagonalizing the matrix Hamiltonian” , 11, Sect. V, “diagonalize the subsystem Hamiltonians to obtain their eigenvalues and eigenvectors in the absence of H^1” and 15-16, Sect. VI, “diagonalization process described by eqs. 56-61 can be repeated iteratively, at each step diagonalizing a new set of (fewer, and larger) subsystems, and then re-expressing the interactions between these subsystems in the resulting eigen-basis, before diagonalizing again.”).
Bravyi and Kerman are analogous art because they are both directed to techniques, methods and systems for implementing and designing quantum computing architectures, circuits and devices including quantum operators such as Hamiltonians (see, e.g., Bravyi, Abstract and paragraphs 2, 31-32 and 108-109, and Kerman, Abstract and pages 1 and 4-5, Sects I and III).
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 Bravyi to incorporate the teachings of Kerman to provide “a new theoretical framework for approximate numerical simulation of Josephson quantum circuits.” and “an iterative method in which subsystems are diagonalized separately and then coupled together, at increasing size scales with each iteration, allowing diagonalization of Hamiltonians in extremely large Hilbert spaces to be approximated” where “complex quantum circuit Hamiltonians are diagonalized in multiple stages, to find approximate eigenstates” (See, e.g., Kerman, Abstract and page 1, Sect. I). Doing so would have allowed Bravyi to use Kerman’s quantum circuit simulation framework and method “to enable and to encourage the exploration of a much broader range of quantum circuit designs” and “to simulate larger and more complex Josephson quantum circuits”, as suggested by Kerman (See, e.g., Kerman, page 1, Sect. I).
Regarding claims 7, 14 and 21, as discussed above, Bravyi in view of Kerman teaches the method of claim 1, the apparatus of claim 8 and the computer-readable medium of claim 15.
Although Bravyi substantially discloses the claimed invention, Bravyi is not relied on for explicitly disclosing wherein the behavior of the quantum circuit comprises a frequency of a qubit among the one or more qubits.
In the same field, analogous art Kerman teaches wherein the behavior of the quantum circuit comprises a frequency of a qubit among the one or more qubits (see, e.g., FIG. 5 – depicting behavior of “the … qubit circuit …for which the qubit splitting is 1.6 GHz” and pages 10, Sect, IV, “all of the information needed to accurately describe the low-energy properties of a circuit is already contained in a few low-energy basis states for each oscillator mode. … because the oscillator frequencies for these modes tend to be much higher than the low-energy range of interest for the whole circuit.” and 12-13, Sects. V-VI, “Figure 4 shows the absolute error in the energy [at different Hz values/frequencies] splitting between the two qubit levels of the total circuit … when constructing and diagonalizing the total Hamiltonian of eq. 59. A relative error at the ~10 kHz level”, “we are talking about calculating with high precision a qubit energy splitting of around 1 GHz magnitude, the oscillator mode frequencies for this circuit [c.f., eq. 20] range from ~100 GHz to above 1 THz.” [i.e., behavior of quantum circuit includes a qubit frequency/energy in Hz in the qubits]).
Bravyi and Kerman are analogous art because they are both directed to techniques, methods and systems for implementing and designing quantum computing architectures, circuits and devices including quantum operators such as Hamiltonians (see, e.g., Bravyi, Abstract and paragraphs 2, 31-32 and 108-109, and Kerman, Abstract and pages 1 and 4-5, Sects I and III).
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 Bravyi to incorporate the teachings of Kerman to provide “a new theoretical framework for approximate numerical simulation of Josephson quantum circuits.” and “an iterative method in which subsystems are diagonalized separately and then coupled together, at increasing size scales with each iteration, allowing diagonalization of Hamiltonians in extremely large Hilbert spaces to be approximated” where “complex quantum circuit Hamiltonians are diagonalized in multiple stages, to find approximate eigenstates” (See, e.g., Kerman, Abstract and page 1, Sect. I). Doing so would have allowed Bravyi to use Kerman’s quantum circuit simulation framework and method “to enable and to encourage the exploration of a much broader range of quantum circuit designs” and “to simulate larger and more complex Josephson quantum circuits”, as suggested by Kerman (See, e.g., Kerman, page 1, Sect. I).
Conclusion
The prior art made of record, listed on form PTO-892, and not relied upon, is considered pertinent to applicant's disclosure.
The references listed on form PTO-892 are all generally related to techniques, methods and systems for implementing and using quantum computing architectures, circuits and devices to execute quantum operators such as Hamiltonians.
For example, Johnson et al. (U.S. Patent Application Pub. No. 2023/0289636), hereinafter “Johnson”)5 discloses “A quantum optimization system and method estimate, on a classical computer and for a quantum state, an expectation value of a Hamiltonian, expressible as a linear combination of observables, based on expectation values of the observables; and transform, on the classical computer, one or both of the Hamiltonian and the quantum state to reduce the expectation value of the Hamiltonian.” and a method that “includes repeating (i) generating the expectation value of each of the observables, (ii) transforming one or both of the Hamiltonian and the quantum state, and (iii) updating the first representation of the quantum state, until the first representation of the quantum state has converged.” (see, Abstract and paragraph 15).
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/RANDALL K. BALDWIN/Primary Examiner, Art Unit 2125
1 As discussed above in the section 112(b) rejection of this claim, “optimizing a quantum circuit” has been interpreted as any adjustment, modification, calibration or alteration of the behavior or operation of quantum circuit or circuitry based on any purpose, plan or design of the circuit or circuitry.
2 As discussed above in the section 112(b) rejection of this claim, “optimizing a quantum circuit” has been interpreted as any adjustment, modification, calibration or alteration of the behavior or operation of quantum circuit or circuitry based on any purpose, plan or design of the circuit or circuitry.
3 As discussed above in the section 112(b) rejection of this claim, “optimizing a quantum circuit” has been interpreted as any adjustment, modification, calibration or alteration of the behavior or operation of quantum circuit or circuitry based on any purpose, plan or design of the circuit or circuitry.
4 As indicated above in the section 112(b) rejections of these claims, “an effective capacitance matrix of the first Hamiltonian” has been interpreted as any matrix or vector of capacitance values that are adequate for the 1st Hamiltonian.
5 Johnson is a Divisional application of U.S. application number 16/543,165, filed on August 16, 2019, which is prior to the earliest effective filing data of the instant application, November 20, 2020. Therefore it constitutes prior art under 35 U.S.C. 102(a)(2). Johnson also claims priority to U.S. Provisional application No. 62/719,330, filed on August 17, 2018, which is also prior to the earliest effective filing data of the instant application.