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 Office Action is in response to claims filed on 05/10/2023.
Claims 1-20 are pending.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 05/10/2023, 09/23/2024 and 10/24/2025 are being considered by the examiner.
Specification
Applicant is reminded of the proper content of an abstract of the disclosure.
A patent abstract is a concise statement of the technical disclosure of the patent and should include that which is new in the art to which the invention pertains. The abstract should not refer to purported merits or speculative applications of the invention and should not compare the invention with the prior art.
If the patent is of a basic nature, the entire technical disclosure may be new in the art, and the abstract should be directed to the entire disclosure. If the patent is in the nature of an improvement in an old apparatus, process, product, or composition, the abstract should include the technical disclosure of the improvement. The abstract should also mention by way of example any preferred modifications or alternatives.
Where applicable, the abstract should include the following: (1) if a machine or apparatus, its organization and operation; (2) if an article, its method of making; (3) if a chemical compound, its identity and use; (4) if a mixture, its ingredients; (5) if a process, the steps.
Extensive mechanical and design details of an apparatus should not be included in the abstract. The abstract should be in narrative form and generally limited to a single paragraph within the range of 50 to 150 words in length.
See MPEP § 608.01(b) for guidelines for the preparation of patent abstracts.
The abstract of the disclosure is objected to because the abstract should be on a separate paper. A corrected abstract of the disclosure is required and must be presented on a separate sheet, apart from any other text. See MPEP § 608.01(b).
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
To determine if a claim is directed to patent ineligible subject matter, the Court has guided the Office to apply the Alice/Mayo test, which requires:
1. Determining if the claim falls within a statutory category;
2A. Determining if the claim is directed to a patent ineligible judicial exception consisting of a law of nature, a natural phenomenon, or abstract idea; and
Step 2A is a two-prong inquiry. MPEP 2106.04(II)(A). Under the first prong, examiners evaluate whether a law of nature, natural phenomenon, or abstract idea is set forth or described in the claim. Abstract ideas include mathematical concepts, certain methods of organizing human activity, and mental processes. MPEP 2106.04(a)(2). The second prong is an inquiry into whether the claim integrates a judicial exception into a practical application. MPEP 2106.04(d).
2B. If the claim is directed to a judicial exception, determining if the claim recites limitations or elements that amount to significantly more than the judicial exception. (See MPEP 2106).
Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. The claim(s) recite a mental process and a mathematical calculation; see MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III).
Step 1:
Claims 1-15 are directed to the statutory category of processes.
Claim 1 Step 2A prong 1:
For the sake of identifying the abstract ideas, a copy of the claim is provided below. Abstract ideas are bolded.
A method for simulating a quantum circuit using a computer that processes bits, the method comprising:
obtaining a representation of a quantum circuit;
generating a transformed Hamiltonian corresponding to the quantum circuit, the transformed Hamiltonian comprising a transformed local Hamiltonian and a transformed coupling Hamiltonian;
determining a limited eigenbasis including a number of eigenvectors of the transformed local Hamiltonian;
projecting the transformed coupling Hamiltonian, the transformed coupling Hamiltonian expressed in terms of modes of the transformed local Hamiltonian, onto the limited eigenbasis;
projecting the transformed local Hamiltonian onto the limited eigenbasis;
generating an at least partially decoupled Hamiltonian by combining the projection of the transformed coupling Hamiltonian and the projection of the transformed local Hamiltonian; and
simulating, by the computer, a behavior of the quantum circuit using the at least partially decoupled Hamiltonian.
The limitations “generating a transformed Hamiltonian corresponding to the quantum circuit”, “determining a limited eigenbasis”, “projecting the transformed coupling Hamiltonian”, “projecting the transformed local Hamiltonian onto the limited eigenbasis” and “generating an at least partially decoupled Hamiltonian” are an abstract ideas because it is directed to a mathematical model. The limitation, as drafted and under broadest reasonable interpretation, “can be performed using mathematical equations” MPEP 2106.04(a)(2)(I).
Claim 1 Step 2A prong 2:
Under step 2A prong two, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present general field of use or insignificant extra-solution activity. In particular, the claim recites the additional limitations:
“A method for simulating a quantum circuit using a computer that processes bits” (general field of use – see MPEP 2106.04(d) referencing MPEP 2106.05(h))
“obtaining a representation of a quantum circuit” (general field of use and data gathering – see MPEP 2106.04(d) referencing MPEP 2106.05(h))
“the transformed Hamiltonian comprising a transformed local Hamiltonian and a transformed coupling Hamiltonian” (Field of Use, MPEP 2106.05(h))(Mere Instructions to Apply an Exception, MPEP § 2106.05(f))
“a number of eigenvectors of the transformed local Hamiltonian” (Field of Use, MPEP 2106.05(h))
“the transformed coupling Hamiltonian expressed in terms of modes of the transformed local Hamiltonian, onto the limited eigenbasis” (Field of Use, MPEP 2106.05(h))
“combining the projection of the transformed coupling Hamiltonian and the projection of the transformed local Hamiltonian” (Field of Use, MPEP 2106.05(h))
“simulating, by the computer, a behavior of the quantum circuit using the at least partially decoupled Hamiltonian” (“apply it”, Field of Use, MPEP 2106.05(h))(Mere Instructions to Apply an Exception (math), MPEP § 2106.05(f))
Claim 1 Step 2B:
The Examiner must consider whether each claim limitation individually or as an ordered combination amount to significantly more than the abstract idea. This analysis includes determining whether an inventive concept is furnished by an element or a combination of elements that are beyond the judicial exception. For limitations that were categorized as “apply it” or generally linking the use of the abstract idea to a particular technological environment or field of use, the analysis is the same. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception because the additional limitations considered directed towards field of use or insignificant extra-solution activity. See MPEP 2106.04(d) referencing MPEP 2106.05(h) and MPEP2106.05(g).
Considering the claim limitations as an ordered combination, claim 1 does not include significantly more than the abstract idea.
Claim 2 further recites: “wherein generating the transformed Hamiltonian comprises: repeatedly generating at least partially decoupled Hamiltonians and corresponding coupling values, a repeat comprising: selecting a spanning tree for the quantum circuit; determining an original Hamiltonian for the quantum circuit using the spanning tree, the original Hamiltonian including a charge coupling matrix and a flux coupling matrix; determining a linear transformation of the modes of the original Hamiltonian; generating an at least partially decoupled Hamiltonian using the linear transformation; and determining a corresponding coupling value for the at least partially decoupled Hamiltonian; and selecting as the transformed Hamiltonian the at least partially decoupled Hamiltonian based on the corresponding coupling value.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 3 recites “wherein: the linear transformation depends on a block-diagonal symplectic matrix, the block- diagonal symplectic matrix including a first submatrix and a second submatrix, the second submatrix being a function of the first submatrix.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 4 recites “wherein: generating the at least partially decoupled Hamiltonian using the linear transformation comprises diagonalizing the charge coupling matrix and the flux coupling matrix using the block-diagonal symplectic matrix; and the corresponding coupling value depends on rows of the first submatrix corresponding to junction modes of the original Hamiltonian.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 5 recites “wherein: generating an at least partially decoupled Hamiltonian using the linear transformation comprises: generating a first transformation matrix using the block-diagonal symplectic matrix; transforming the charge coupling matrix by diagonalizing a submatrix of the charge coupling matrix using the first transformation matrix, the submatrix of the charge coupling matrix corresponding to inductor modes of the original Hamiltonian; generating a second transformation matrix using the block-diagonal symplectic matrix; and transforming the flux coupling matrix by diagonalizing a submatrix of the flux coupling matrix, the submatrix of the flux coupling matrix corresponding to the inductor modes; and the corresponding coupling value depends on off-diagonal elements of the transformed charge coupling matrix and transformed flux coupling matrix.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 6 recites “wherein: determining the linear transformation comprises: generating a rotation matrix by iteratively determining rotations around axes of the rotation matrix, the axes corresponding to inductor modes in the original Hamiltonian.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 7 recites “wherein: the method further comprises generating the block-diagonal symplectic matrix, generation including: determining an initial block-diagonal matrix including the flux coupling matrix and the charge coupling matrix; determining a Hermitian matrix based on the initial block-diagonal matrix; determining an eigenbasis for the Hermitian matrix and a matrix of eigenvalues corresponding to the eigenbasis; and determining the block-diagonal symplectic matrix using the initial block-diagonal matrix, the eigenbasis for the Hermitian matrix, and the matrix of corresponding eigenvalues.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 8 recites “wherein generating the transformed Hamiltonian comprises at least partially decoupling an original Hamiltonian corresponding to the quantum circuit.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 9 recites “wherein at least partially decoupling the original Hamiltonian comprises diagonalizing at least one inductor mode of a quadratic portion of the original Hamiltonian.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the dependency (math) under step 2A prong 1 of the abstract idea analysis, the limitation is considered to further define the mathematical formula. MPEP 2106.04(a)(2)(I) and MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Regarding claims 10-19: claims 10-19 are rejected under 35 U.S.C. 101
Step 1:
Claims 10-19 are directed to the statutory category of apparatus/system.
Claim 10 Step 2A prong 1:
The claim language is substantially similar as claim 1, except for the following claim elements/limitations: A system for simulating a quantum circuit using a computer that processes bits, comprising: at least one processor; and at least one computer-readable medium containing instructions that, when executed by the at least one processor, cause the system to perform operations comprising:
The claim does not include any additional abstract ideas from claim 1
Claim 10 Step 2A prong 2:
Under step 2A prong two, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present general field of use or insignificant extra-solution activity. In particular, the claim recites the additional limitations:
“A system for simulating a quantum circuit using a computer that processes bits, comprising: at least one processor; and at least one computer-readable medium containing instructions that, when executed by the at least one processor, cause the system to perform operations comprising:” (general field of use – see MPEP 2106.04(d) referencing MPEP 2106.05(h)) (Mere Instructions to Apply an Exception, MPEP § 2106.05(f)) (particular machine, MPEP 2106.05(b))
Claim 10 Step 2B:
The additional limitations found in claim 10, these additional elements are recited at a high level of generality (system) and would function in its ordinary capacity for executing code, this additional element does not integrate the judicial exception into a practical application and does not amount to significantly more. These additional elements do not integrate the judicial exception into a practical application and do not amount to significantly more. Step 2A Prong I and Step 2B.
Considering the claim limitations as an ordered combination, claim 10 does not include significantly more than the abstract idea.
Claim 11 further recites: “wherein: the at least partially diagonalizing the charge coupling matrix and the flux coupling matrix comprises: generating a rotation matrix by iterating through axes of the rotation matrix, the axes corresponding to inductor modes of the original Hamiltonian, an iteration around one of the axes comprising: updating the rotation matrix to implement a rotation around the one of the axes.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 12 further recites: “wherein: the axes of the rotation matrix are iterated through until a value of a function of off- diagonal terms of the charge coupling matrix and the flux coupling matrix satisfies a termination condition.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 13 further recites: “wherein: the at least partially diagonalizing the charge coupling matrix and the flux coupling matrix comprises: generating a block-diagonal matrix using the charge coupling matrix and the flux coupling matrix; generating a block-diagonal symplectic matrix that diagonalizes the block- diagonal matrix; generating a transformation matrix using the block-diagonal symplectic matrix; and transforming the charge coupling matrix and the flux coupling matrix using the transformation matrix.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 14 further recites: “wherein: generating the block-diagonal symplectic matrix comprises: determining a Hermitian matrix based on the block-diagonal matrix; determining an eigenbasis for the Hermitian matrix and a matrix of eigenvalues corresponding to the eigenbasis; and determining the block-diagonal symplectic matrix using the block-diagonal matrix, the eigenbasis for the Hermitian matrix, and the matrix of corresponding eigenvalues.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 15 further recites: “wherein: each Josephson junction in the quantum circuit is shunted by an inductor.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 16 further recites: “wherein: the transformation matrix is generated in response to a determination that the flux coupling matrix is positive-definite.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 17 further recites: “wherein: the transformation matrix comprises a block-diagonal matrix including two submatrices: an identity submatrix; and an inverse of a submatrix of the block-diagonal symplectic matrix.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 18 further recites: “wherein: the block-diagonal matrix includes only submatrices of the charge coupling matrix and the flux coupling matrix corresponding to inductor modes of the original Hamiltonian.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Claim 19 further recites: “wherein: the transformed local Hamiltonian includes transformed Josephson junction terms; or the flux coupling matrix and charge coupling matrix of the transformed Hamiltonian are identical.” These feature(s) have been considered in combination with the feature required by the claim(s) from which it depends. The additional feature(s) are considered to further clarify the outcomes that are being determined (math) under step 2A prong 1 of the abstract idea analysis. MPEP 2106.04(a)(2)(III). Therefore, the claim is considered to be ineligible under 35 USC 101.
Regarding claim 20, claim 20 is rejected under 35 U.S.C. 101
Step 1:
Claim 20 Step 2A prong 1:
The claim language is substantially similar as claim 1, except for the following claim elements/limitations: A non-transitory computer-readable medium containing instructions that are executable by at least one processor of a system to cause the system to perform operations comprising:
The claim does not include any additional abstract ideas from claim 1
Claim 20 Step 2A prong 2:
Under step 2A prong two, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present general field of use or insignificant extra-solution activity. In particular, the claim recites the additional limitations:
“A non-transitory computer-readable medium containing instructions that are executable by at least one processor of a system to cause the system to perform operations comprising:” (general field of use – see MPEP 2106.04(d) referencing MPEP 2106.05(h)) (Mere Instructions to Apply an Exception, MPEP § 2106.05(f)) (particular machine, MPEP 2106.05(b))
Claim 20 Step 2B:
The additional limitations found in claim 20, these additional elements are recited at a high level of generality (medium, processor, executable) and would function in its ordinary capacity for executing code, this additional element does not integrate the judicial exception into a practical application and does not amount to significantly more. These additional elements do not integrate the judicial exception into a practical application and do not amount to significantly more. Step 2A Prong I and Step 2B.
Considering the claim limitations as an ordered combination, claim 20 does not include significantly more than the abstract idea.
Claim Rejections - 35 USC § 102
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 the appropriate paragraphs of 35 U.S.C. 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
Claims 1, 2, 6, 8-12 and 20 are rejected under 35 U.S.C. 102(a)(1) as being anticipated by Andrew J. Kerman, NPL “Efficient numerical simulation of complex Josephson quantum circuits”, Published: 28 Oct 2020, (hereafter Kerman).
Regarding claim 1. Kerman teaches a method for simulating a quantum circuit using a computer that processes bits (Page 1, abstract, simulation quantum circuits), the method comprising:
obtaining a representation of a quantum circuit (Page 9, Fig 1, RF-SQUID style circuit) (Page 2, Col 2, par 1, superconducting spanning tree S is any subgraph of GL with the property, circuit);
generating a transformed Hamiltonian corresponding to the quantum circuit, the transformed Hamiltonian comprising a transformed local Hamiltonian and a transformed coupling Hamiltonian (Page 8, Col 2, Par 2, Quantum Hamiltonian, joseph potential) (Page 9, col 2, Par 1, equation 51, EJBL, EJBR);
determining a limited eigenbasis including a number of eigenvectors of the transformed local Hamiltonian (Page 11, Col 1, Par 1, diagonalize the subsystem Hamiltonians to obtain their eigenvalues and eigenvectors);
projecting the transformed coupling Hamiltonian, the transformed coupling Hamiltonian expressed in terms of modes of the transformed local Hamiltonian, onto the limited eigenbasis (Page 13, sec VI, divide the Hilbert space, using projection operator, rewrite the Schrodinger equation projected onto the |g> subspace);
projecting the transformed local Hamiltonian onto the limited eigenbasis (Page 13, sec VI, subsystem beta and alpha, the effective interaction in the subspace);
generating an at least partially decoupled Hamiltonian by combining the projection of the transformed coupling Hamiltonian and the projection of the transformed local Hamiltonian (Page 14, Col 1, Par 2, static dipole of beta, coupling between subsystem beta and alpha, polarizability, dispersion interaction between beta and alpha) (Page 14, Col 2, Par 1, resulting Hamiltonian is then diagonalized); and
simulating, by the computer, a behavior of the quantum circuit using the at least partially decoupled Hamiltonian (Page 1, abstract, theoretical framework to approximate numerical simulation of quantum circuit) (Page 9, Col 2, Par 3, quantum circuit facilitate accurate simulation of more complex circuits).
Regarding claim 2. Kerman teaches the method of claim 1, wherein generating the transformed Hamiltonian comprises:
repeatedly generating at least partially decoupled Hamiltonians and corresponding coupling values, a repeat comprising: selecting a spanning tree for the quantum circuit (Page 15, col 2, par 3, repeated iteratively, re-expressing the interactions between these subsystems int eh resulting eigenbasis) (Page 2, col 2, par 2, define the spanning tree, superconducting spanning tree S is any subgraph of GL with the property that from each node in the circuit);
determining an original Hamiltonian for the quantum circuit using the spanning tree, the original Hamiltonian including a charge coupling matrix and a flux coupling matrix (Page 2, col 2, par 3, perform the procedure, spanning tree, union of the resulting set of spanning trees then constitutes S, having the generalized spanning property that from any node in the circuit);
determining a linear transformation of the modes of the original Hamiltonian (Page 4, Col 1, Par 4, corresponding to the principal curvature of the linear inductive potential) (Page 13, Col 2, Par 3, make the structure, linear electromagnetic interaction between subsystem);
generating an at least partially decoupled Hamiltonian using the linear transformation (Page 13, equations 64 and 65); and
determining a corresponding coupling value for the at least partially decoupled Hamiltonian (Page 15, Fig 5, qubit circuit values are plotted); and
selecting as the transformed Hamiltonian the at least partially decoupled Hamiltonian based on the corresponding coupling value (Page 14, equation 66, rewrite eq 65, appears static interactions between subspace dipoles).
Regarding claim 6. Kerman teaches the method of claim 2, wherein: determining the linear transformation comprises:
generating a rotation matrix by iteratively determining rotations around axes of the rotation matrix, the axes corresponding to inductor modes in the original Hamiltonian (Page 4, Col 1, Par 3, No, NI, NJ) (Page 15, Col 2, par 3, repeated iteratively, then re-expressing the interactions ) (Page 15, Col 2, Par 2, mode polarized by the island offset charge delta QI).
Regarding claim 8. Kerman teaches the method of claim 1, wherein generating the transformed Hamiltonian comprises at least partially decoupling an original Hamiltonian corresponding to the quantum circuit (Page 4, col 1, par 1, canonical representation, expressed in terms of matrix R).
Regarding claim 9. Kerman teaches the method of claim 8, wherein at least partially decoupling the original Hamiltonian comprises diagonalizing at least one inductor mode of a quadratic portion of the original Hamiltonian (Page 4, Col 1, Par 2, inverse inductance and capacitance matrices are transformed).
Regarding claim 10. Kerman teaches a system for simulating a quantum circuit using a computer that processes bits (Page 1, abstract, simulation quantum circuits), comprising:
at least one processor; and at least one computer-readable medium containing instructions that, when executed by the at least one processor (Page 10, Sec V, simulation of two coupled JPSQs, by a desktop computer), cause the system to perform operations comprising:
generating a transformed Hamiltonian corresponding to a quantum circuit, the transformed Hamiltonian including a transformed local Hamiltonian and a transformed coupling Hamiltonian (Page 8, Col 2, Par 2, Quantum Hamiltonian, joseph potential) (Page 9, col 2, Par 1, equation 51, EJBL, EJBR),
generation comprising:
obtaining a charge coupling matrix and a flux coupling matrix of an original Hamiltonian corresponding to the quantum circuit (Page 9, Fig 1, RF-SQUID style circuit) (Page 2, Col 2, par 1, superconducting spanning tree S is any subgraph of GL with the property, circuit) (Page 4, equation 14);
at least partially diagonalizing the charge coupling matrix and the flux coupling matrix (Page 6, col 1, par 2, diagonalizing the matrix Hamiltonian);
determining a limited eigenbasis including a number of eigenvectors of the transformed local Hamiltonian (Page 11, Col 1, Par 1, diagonalize the subsystem Hamiltonians to obtain their eigenvalues and eigenvectors);
projecting the transformed coupling Hamiltonian, expressed in terms of modes of the transformed local Hamiltonian, onto the limited eigenbasis (Page 13, sec VI, divide the Hilbert space, using projection operator, rewrite the Schrodinger equation projected onto the |g> subspace);
projecting the transformed local Hamiltonian onto the limited eigenbasis (Page 13, sec VI, subsystem beta and alpha, the effective interaction in the subspace);
generating an at least partially decoupled Hamiltonian by combining the projection of the transformed coupling Hamiltonian and the projection of the transformed local Hamiltonian (Page 14, Col 1, Par 2, static dipole of beta, coupling between subsystem beta and alpha, polarizability, dispersion interaction between beta and alpha) (Page 14, Col 2, Par 1, resulting Hamiltonian is then diagonalized); and
simulating a behavior of the quantum circuit using the at least partially decoupled Hamiltonian (Page 1, abstract, theoretical framework to approximate numerical simulation of quantum circuit) (Page 9, Col 2, Par 3, quantum circuit facilitate accurate simulation of more complex circuits).
Regarding claim 11. Kerman teaches the system of claim 10, wherein: the at least partially diagonalizing the charge coupling matrix and the flux coupling matrix comprises:
generating a rotation matrix by iterating through axes of the rotation matrix, the axes corresponding to inductor modes of the original Hamiltonian (Page 4, Col 1, Par 3, No, NI, NJ) (Page 15, Col 2, par 3, repeated iteratively, then re-expressing the interactions ) (Page 15, Col 2, Par 2, mode polarized by the island offset charge delta QI),
an iteration around one of the axes comprising: updating the rotation matrix to implement a rotation around the one of the axes (Page 15, col 2, par 3, repeated iteratively, re-expressing the interactions between these subsystems int eh resulting eigenbasis).
Regarding claim 12. Kerman teaches the system of claim 11, wherein: the axes of the rotation matrix are iterated through until a value of a function of off- diagonal terms of the charge coupling matrix and the flux coupling matrix satisfies a termination condition (Page 1, abstract, iteration method, allowing diagonalization of Hamiltonians) (Page 2, Col 2, Par 2, loop must satisfy the fluxoid quantization condition).
Regarding claim 20. Kerman teaches a non-transitory computer-readable medium containing instructions that are executable by at least one processor of a system to cause the system to perform operations (Page 10, Sec V, simulation of two coupled JPSQs, by a desktop computer) comprising:
generating a transformed Hamiltonian corresponding to a quantum circuit, the transformed Hamiltonian including a transformed local Hamiltonian and a transformed coupling Hamiltonian (Page 8, Col 2, Par 2, Quantum Hamiltonian, joseph potential)(Page 9, col 2, Par 1, equation 51, EJBL, EJBR),
generation comprising:
obtaining a charge coupling matrix and a flux coupling matrix of an original Hamiltonian corresponding to the quantum circuit (Page 9, Fig 1, RF-SQUID style circuit) (Page 2, Col 2, par 1, superconducting spanning tree S is any subgraph of GL with the property, circuit) (Page 4, equation 14);
at least partially diagonalizing the charge coupling matrix and the flux coupling matrix (Page 6, col 1, par 2, diagonalizing the matrix Hamiltonian);
determining a limited eigenbasis including a number of eigenvectors of the transformed local Hamiltonian (Page 11, Col 1, Par 1, diagonalize the subsystem Hamiltonians to obtain their eigenvalues and eigenvectors);
projecting the transformed coupling Hamiltonian, expressed in terms of modes of the transformed local Hamiltonian, onto the limited eigenbasis (Page 13, sec VI, divide the Hilbert space, using projection operator, rewrite the Schrodinger equation projected onto the |g> subspace);
projecting the transformed local Hamiltonian onto the limited eigenbasis (Page 13, sec VI, subsystem beta and alpha, the effective interaction in the subspace);
generating an at least partially decoupled Hamiltonian by combining the projection of the transformed coupling Hamiltonian and the projection of the transformed local Hamiltonian (Page 14, Col 1, Par 2, static dipole of beta, coupling between subsystem beta and alpha, polarizability, dispersion interaction between beta and alpha) (Page 14, Col 2, Par 1, resulting Hamiltonian is then diagonalized); and
simulating, by a computer that processes bits, a behavior of the quantum circuit using the at least partially decoupled Hamiltonian (Page 1, abstract, theoretical framework to approximate numerical simulation of quantum circuit) (Page 9, Col 2, Par 3, quantum circuit facilitate accurate simulation of more complex circuits).
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.
Claims 3-5, 7 and 13-19 are rejected under 35 U.S.C. 103 as being unpatentable over Andrew J. Kerman, NPL “Efficient numerical simulation of complex Josephson quantum circuits”, Published: 28 Oct 2020, (hereafter Kerman), in views of Francesco Arzani, NPL, “Measurement based quantum information with optical frequency combs”, Published: 18 Sep 2018 (hereafter Arzani).
Regarding claim 3. Kerman teaches the method of claim 2, wherein: the linear transformation depends on a block-diagonal matrix, the block- diagonal matrix including a first submatrix and a second submatrix, the second submatrix being a function of the first submatrix (Page 4, equation 14, partition into block submatrices corresponding to the three mode types, {O,I,J}).
Kerman does not teach symplectic matrix.
Arzani teaches symplectic matrix ((Arzani, Page 67, S is a symplectic matrix, equation 3.28, R1, R2 are symplectic and orthogonal matrices, K is a symplectic diagonal matrix)).
It would have been obvious to a person having ordinary skill in the art prior to the effective filing date of the claimed invention to have modified Kerman to incorporate the teachings of Arzani to have a symplectic matrix because any transformation can be generated by Hamiltonian at most quadratic (Arzani, Page 23, sec 1.4.2 and 64, sec 3.3).
Regarding claim 4. Kerman and Arzani teach the method of claim 3, wherein: generating the at least partially decoupled Hamiltonian using the linear transformation comprises diagonalizing the charge coupling matrix and the flux coupling matrix using the block-diagonal symplectic matrix (Arzani, Page 68, par 1, squeezing matrix, a symplectic diagonal matrix, K); and
the corresponding coupling value depends on rows of the first submatrix corresponding to junction modes of the original Hamiltonian (Arzani, Page 68, Par 1, R1=CR1C).
Regarding claim 5. Kerman and Arzani teach the method of claim 3, wherein: generating an at least partially decoupled Hamiltonian using the linear transformation comprises:
generating a first transformation matrix using the block-diagonal symplectic matrix (Arzani, Page 68, Par 3, covariance matrix of the output state, computed from S);
transforming the charge coupling matrix by diagonalizing a submatrix of the charge coupling matrix using the first transformation matrix, the submatrix of the charge coupling matrix corresponding to inductor modes of the original Hamiltonian (Arzani, Page 64, sec 3.3, ) (Arzani, Page 68, sec 3.3.3, permutations of the diagonal elements);
generating a second transformation matrix using the block-diagonal symplectic matrix (Arzani, Page 68, sec 3.3.3, K is the same as equation 3.28, diagonal elements); and
transforming the flux coupling matrix by diagonalizing a submatrix of the flux coupling matrix, the submatrix of the flux coupling matrix corresponding to the inductor modes (Arzani, Page 69, Par 2, diagonalization, leads to alternating signs in the gains, and rotates the squeezing direction); and
the corresponding coupling value depends on off-diagonal elements of the transformed charge coupling matrix and transformed flux coupling matrix (Arzani, Page 68, equation 3.36).
Regarding claim 7. Kerman and Arzani teach the method of claim 3, wherein: the method further comprises generating the block-diagonal symplectic matrix (Arzani, Page 67, S is a symplectic matrix, equation 3.28, R1, R2 are symplectic and orthogonal matrices, K is a symplectic diagonal matrix), generation including:
determining an initial block-diagonal matrix including the flux coupling matrix and the charge coupling matrix (Arzani, Page 23, sec 1.4.3, K, diagonal matrix with positive entries);
determining a Hermitian matrix based on the initial block-diagonal matrix (Arzani, Page 23, M, Hermitian matrix and l an arbitrary real vector);
determining an eigenbasis for the Hermitian matrix and a matrix of eigenvalues corresponding to the eigenbasis (Kerman, Page 4, No, Ln-1, nonzero eigenvalues, equation 14); and
determining the block-diagonal symplectic matrix using the initial block-diagonal matrix, the eigenbasis for the Hermitian matrix, and the matrix of corresponding eigenvalues (Arzani, Page 23, equation 3.28, S is symplectic matrix).
Regarding claim 13. Kerman teaches the system of claim 10, wherein: the at least partially diagonalizing the charge coupling matrix and the flux coupling matrix comprises:
generating a block-diagonal matrix using the charge coupling matrix and the flux coupling matrix (Page 11, equation 62) (Page 11, col 1, diagonalize the subsystem Hamiltonians);
generating a block-diagonal matrix that diagonalizes the block- diagonal matrix (Page 11, equations 62 and 63);
generating a transformation matrix using the block-diagonal matrix (Page 8, Col 2, Par 2, Quantum Hamiltonian, joseph potential) (Page 9, col 2, Par 1, equation 51, EJBL, EJBR); and
transforming the charge coupling matrix and the flux coupling matrix using the transformation matrix (Page 3, col 1, circuit, using the transformation, branch matrix Rbn).
Kerman does not teach symplectic matrix.
Arzani teaches symplectic matrix, (Arzani, Page 67, S is a symplectic matrix, equation 3.28, R1, R2 are symplectic and orthogonal matrices, K is a symplectic diagonal matrix).
It would have been obvious to a person having ordinary skill in the art prior to the effective filing date of the claimed invention to have modified Kerman to incorporate the teachings of Arzani to have a symplectic matrix because any transformation can be generated by Hamiltonian at most quadratic (Arzani, Page 23, sec 1.4.2 and 64, sec 3.3).
Regarding claim 14. Kerman and Arzani teach the system of claim 13, wherein: generating the block-diagonal symplectic matrix comprises:
determining a Hermitian matrix based on the block-diagonal matrix (Arzani, Page 23, M, Hermitian matrix and l an arbitrary real vector);
determining an eigenbasis for the Hermitian matrix and a matrix of eigenvalues corresponding to the eigenbasis (Kerman, Page 4, No, Ln-1, nonzero eigenvalues, equation 14); and
determining the block-diagonal symplectic matrix using the block-diagonal matrix, the eigenbasis for the Hermitian matrix, and the matrix of corresponding eigenvalues (Arzani, Page 23, equation 3.28, S is symplectic matrix).
Regarding claim 15. Kerman and Arzani teach the system of claim 13, wherein: each Josephson junction in the quantum circuit is shunted by an inductor (Kerman, Page 9, Fig 1, L).
Regarding claim 16. Kerman and Arzani teach the system of claim 13, wherein: the transformation matrix is generated in response to a determination that the flux coupling matrix is positive-definite (Arzani, Page 22, sec 1.4, a positive semi-definite symmetric matrix) (Arzani, Page 80, fig 3.5, positive squeezing values).
Regarding claim 17. Kerman and Arzani teach the system of claim 13, wherein: the transformation matrix comprises a block-diagonal matrix including two submatrices:
an identity submatrix (Arzani, Page 54, equation 2.65, I denotes the identity map); and an inverse of a submatrix of the block-diagonal symplectic matrix (Arzani, Page 24, par 1, inverse of the transformation).
Regarding claim 18. Kerman and Arzani teach the system of claim 13, wherein: the block-diagonal matrix includes only submatrices of the charge coupling matrix and the flux coupling matrix corresponding to inductor modes of the original Hamiltonian (Arzani, Page 4, Col 1, Par 2, inverse inductance and capacitance matrices are transformed).
Regarding claim 19. Kerman and Arzani teach the system of claim 13, wherein: the transformed local Hamiltonian includes transformed Josephson junction terms (Arzani, Page 9, Col 2, Josephson terms do not depend on the l oscillator mode); or the flux coupling matrix and charge coupling matrix of the transformed Hamiltonian are identical (Kerman, Page 9, fig 1, JBL, JBR).
Conclusion
The prior art made of record, listed on PTO-892, and not relied upon is considered pertinent to applicant's disclosure.
Glen Evenbly, NPL, “Foundations and Applications of Entanglement Renormalization”, discloses simulations of many body systems, provide new insight to quantum collective phenomena.
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/A.C./Examiner, Art Unit 2189
/REHANA PERVEEN/Supervisory Patent Examiner, Art Unit 2189
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