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 .
Claims 1-20 are pending.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 10-10-2023, 11-20-2023, 1-8-2025, 1-23-2026 is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea of a mathematical algorithm without significantly more.
Analysis of subject matter eligibility for method claims 1-13 is presented below.
Step 1: claim 1 recites a method in the preamble thus is one of the statutory of invention.
Step 2A Prong 1: claim 1 recites “measuring…to obtain a respective bit strings” this limitation is a process that under its broadest reasonable interpretation covers performance of the limitation by a human user. If a claim limitation, under its broadest reasonable interpretation cover performance of the limitation in the mind, then it falls within the "Mental Processes' grouping of abstract idea (concept performed in the human mind including an observation, evaluation, judgment and opinion). The mere nominal recitation of a classical computer does not take the claim limitation out of the mental processes grouping. Thus, the limitation merely represents a mental process.
Step 2A Prong 2: The judicial exception is not integrated into a practical application because although the claim recites the additional element of "repeatedly sampling... for each sampled unitary operator", these limitations are at best mere data gathering process which is considered to be insignificant extra solution activity (see MPEP 2106.05(g)). The recitation of "applying a quantum circuit…wherein the quantum circuit implements the sample unitary operator” recited at a high level of generality does not integrate the mental process into a practical application, is merely a tool to implement the abstract idea.
Step 2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. The additional elements "storing a record… “providing the records…” do not seem to impose any meaningful limits on practicing the abstract idea, do not add specific limitation other than what is well-understood, routine, conventional activities in the field when they are claimed in a merely generic manner. (See MPEP 2106.05(d)(II) (iv).
Thus claim 1 is rejected under 35 USC 101 as being an abstract idea without significantly more.
Claim 2 merely further describes the quantum computer, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 3 merely further describes the generators of the generalized matchgate group, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 4 merely further describes the sampling, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 5 merely further adds an algorithm to calculate the classical shadow, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 6 merely further describes one or more operations using the classical shadow, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claims 7-13 merely recite limitations similar to claims 1-6 in form of systems thus are not eligible for the same reasons discussed in claims 1-6 above.
Analysis of subject matter eligibility for method claims 14-20 is presented below.
Step 1: claim 14 recites a method in the preamble thus is one of the statutory of invention.
Step 2A Prong 1: claim 14 recites “obtaining a classical shadow…ensemble of random unitaries and measured bit strings” this limitation is a process that under its broadest reasonable interpretation covers performance of the limitation by a human user. If a claim limitation, under its broadest reasonable interpretation cover performance of the limitation in the mind, then it falls within the "Mental Processes' grouping of abstract idea (concept performed in the human mind including an observation, evaluation, judgment and opinion). The mere nominal recitation of a computer does not take the claim limitation out of the mental processes grouping. Thus, the limitation merely represents a mental process.
Step 2A Prong 2: The judicial exception is not integrated into a practical application because although the claim recites the additional element of ”generating updated unitary operators…, these limitations are at best data gathering process which is considered to be insignificant extra solution activity (see MPEP 2106.05(g)). The recitation of "generating updated unitary operators” merely includes a mathematical operation thus is merely a tool to implement the abstract idea.
Step 2B: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. The additional element “computing the expected value... for each sampled unitary operator", merely adds more computations to solve a mathematical algorithm thus does not improve any technology or technical field, does not apply the judicial exception with or by use of a particular machine, does not add unconventional steps that confine the claim to a particular useful application, does not include other meaningful limitations beyond linking the use of the judicial exception to a particular technological environment.
Thus claim 14 is rejected under 35 USC 101 as being an abstract idea of a mathematical concept without significantly more.
Claim 15 merely further describes the projection operator, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 16 merely further describes the ensemble of random unitaries, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 17 merely further includes an algorithm to calculate the classical shadow, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 18 merely further describes the generating the updated unitary operators, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 19 merely further describes the matrix that comprises the updated unitary operators, considered insignificant extra solution activity (see MPEP 2106.05(g)).
Claim 20 merely adds evaluating derivatives of the polynomial, considered insignificant extra solution activity (see MPEP 2106.05(g)).
No claim is patent eligible.
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.
Claim(s) 1-20 is/are rejected under 35 U.S.C. 103 as being unpatentable over ZHAO ET AL: "Fermionic partial tomography via classical shadows", ARXIV.ORG, CORNELL UNIVERSITY LIBRARY, 201 OLIN LIBRARY CORNELL UNIVERSITY ITHACA, NY 14853, 9 September 2021 (2021-09-09), XP091045033, DOI, in view of Jozsa et al “Miyake, Matchgates and classical simulation of quantum circuits”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, 3089 (2008).' [p.31]; both provided by the applicant.
Regarding claim 1, Zhao substantially discloses a method for computing a classical shadow of an n-qubit quantum state, the method comprising:
repeatedly sampling, by a classical computer, a unitary operator from an ensemble of random unitaries (see at least the abstract …Our approach extents the framework of classical shadows, a randomized approach to learning a collection of quantum state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, page 2 right column last paragraph to page 3 left column 1st paragraph Randomized measurement with fermionic Gaussian unitaries);
the difference is Zhao does not specifically show wherein the ensemble of random unitaries comprises a generalized matchgate group. However it is customary in the art to do so as shown by Jozsa (see at least pages 3094-3095 section 3. Perfect matchings and matchgates);
it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to include such features while implementing the method of Zhao in order to form quantum circuits that can be classically efficiently simulated as taught by Jozsa.
Zhao/Jozsa further teaches for each sampled unitary operator:
applying, by a quantum computer, a quantum circuit to the n-qubit quantum state to obtain an evolved quantum state, wherein the quantum circuit implements the sampled unitary operator (See Zhao page 2 left column section “Classical shadows and randomized measurements” to right column),
measuring, by the quantum computer, the evolved quantum state to obtain a respective bit string , (See Zhao page 2 left column section “Classical shadows and randomized measurements” to right column), and
storing, by the classical computer, a record of the respective bit string and the sampled unitary operator; and providing, by the classical computer, the records as a classical shadow of the quantum state (See Zhao page 2 left column section “Classical shadows and randomized measurements” to right column),
Regarding claim 2, Zhao/Jozsa further teaches or suggests the method of claim 1, wherein generators of the generalized matchgate group comprise unitary operators generated as claimed (see at least Jozsa page 3100 section 6. Gaussian quantum circuits intertwined by Clifford operations).
Regarding claim 3, Zhao/Jozsa further teaches or suggests the method of claim 1, wherein
the generalized matchgate group has a one-to-one correspondence with a group of 2n x 2n orthogonal matrices 0(2n); and
for every element R in the group 0 (2n) there exists a unique unitary operator in the generalized matchgate group that satisfies the claimed conditions (see at least Jozsa page 3096 last paragraph, page 3098 section 5. The Jordan-Wigner representation and theorem 1.1).
Regarding claim 4, Zhao/Jozsa further teaches or suggests the method of claim 3, wherein sampling the unitary operator from the ensemble of random unitaries comprises sampling from the group 0 (2n) according to a Haar measure and constructing a corresponding generalized matchgate unitary operator using the one-to-one correspondence (see at least Zhao page 2 Classical shadows and randomized measurements).
Regarding claim 5, Zhao/Jozsa further teaches or suggests the method of claim 1, wherein the classical shadow is given by the claimed equation (see at least Zhao page 2 Classical shadows and randomized measurements).
Regarding claim 6, Zhao/Jozsa further teaches the method of claim 1, further comprising performing one or more operations using the classical shadow of the quantum state, the operations comprising one or more of: predicting an expectation value of an observable with respect to the quantum state, performing direct fidelity estimation, performing entanglement verification, estimating correlation functions, or predicting entanglement entropy (see Zhao, at least the Introduction at page 1 left column first paragraph),.
Claims 7-13 essentially recite limitations similar to claims 1-6 in form of systems thus are rejected for the same reasons discussed in claims 1-6 above.
Regarding claim 14, Zhao substantially discloses a computer implemented method for computing an expectation value of a projector operator (see at least page 1 Introduction), the method comprising:
obtaining a classical shadow of an n-qubit quantum state, wherein the classical shadow comprises a quantum channel of unitary operators sampled from an ensemble of random unitaries and measured bit strings (see at least the abstract …Our approach extents the framework of classical shadows, a randomized approach to learning a collection of quantum state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, page 2 right column last paragraph to page 3 left column 1st paragraph Randomized measurement with fermionic Gaussian unitaries);
generating updated unitary operators, comprising multiplying a unitary operator that defines the projector operator with i) the unitary operators sampled from the ensemble of random unitaries and ii) operators that prepare the measured bit strings from a vacuum state (Zhao page 2 left column section “Classical shadows and randomized measurements” to right column), and
computing the expectation value of the quantum channel with respect to the vacuum state (Zhao page 1 right column last paragraph),
the difference is Zhao does not specifically show the computing comprising evaluating derivatives of a polynomial, the polynomial comprising a Pfaffian of a matrix comprising the updated unitary operators.
However it is customary in the art to do so as shown by Jozsa (page 3095 Pfaffian).
it would have been obvious to one of ordinary skill in the art to include such features while implementing the method of Zhao in order to benefit from a standardized expected value computing technique.
Regarding claim 15, Zhao/Jozsa further teaches or suggests the method of claim 14, wherein the projection operator comprises an operator that projects a quantum state onto a pure fermionic Gaussian state, wherein the pure fermionic Gaussian state comprises a unitary operator in the ensemble of random unitaries applied to a vacuum state, wherein the projector operator is obtained as claimed (see Zhao page 2 left column Classical shadows and randomized measurements, page 2 right column last paragraph Randomized measurements with fermionic Gaussian unitaries)
Regarding claim 16, Zhao/Jozsa further teaches the method of claim 14, wherein the ensemble of random unitaries comprises a generalized matchgate group (Jozsa pages 3094-3095 section 3. Perfect matchings and matchgates);
Regarding claim 17, Zhao/Jozsa further teaches or suggests the method of claim 16, wherein the classical shadow is given as claimed (Zhao page 2 left column Classical shadows and randomized measurements)
Regarding claim 18, Zhao/Jozsa further teaches or suggests the method of claim 17, wherein generating the updated unitary operators comprises redefining the unitary operators as claimed (Zhao page 2 right column, expectation value estimation).
Regarding claim 19, Zhao/Jozsa further teaches or suggests the method of claim 14, wherein the matrix that comprises the updated unitary operators is obtained as claimed (Zhao page 2 left column Fermionic RDMs).
Regarding claim 20, Zhao/Jozsa further teaches or suggests the method of claim 14, wherein evaluating the derivatives of the polynomial comprises performing numerical differentiation or polynomial interpolation techniques (Jozsa pages 3089-3090 Introduction).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Bravyi et al (US 20220114468 A1) teach Systems and techniques that facilitate efficient synthesis of optimal multi-qubit Clifford circuits are provided. In various embodiments, a system can receive as input a number n representing a quantity of qubits. In various instances, the system can generate, via a cost-invariant reduction function, as output a library of different n-qubit canonical representatives that respectively correspond to different cost-invariant equivalence classes of n-qubit Clifford group elements. In various embodiments, a system can receive as input a first Clifford group element. In various aspects, the system can search a database of canonical representatives, wherein different canonical representatives in the database respectively correspond to different cost-invariant equivalence classes of Clifford group elements. In various cases, the system can identify based on the search a second Clifford group element that implements the first Clifford group element and that has a lower entangling-gate cost than the first Clifford group element.
Wang et al (CN 114021728 A) teach Measuring quantum data comprises obtaining N quantum states, where N is a positive integer; measuring each qubit of the quantum state to obtain first measurement result; obtaining the classical shadow of the quantum state based on the first measurement result; measuring each qubit of the quantum state separately to obtain second measurement result; obtaining a classical shadow of the quantum state based on the second measurement result; and determining distance between the quantum states based on the classical shadows corresponding to the quantum states and the classical shadows corresponding to the quantum states.
Grabsch, Aurélien, Yevheniia Cheipesh, and Carlo WJ Beenakker. "Pfaffian formula for fermion parity fluctuations in a superconductor and application to Majorana fusion detection." Annalen der Physik 531.10 (2019): 1900129.
Abstract- Kitaev's Pfaffian formula equates the ground-state fermion parity of a closed system to the sign of the Pfaffian of the Hamiltonian in the Majorana basis. Using Klich's theory of counting statistics for paired fermions, the Pfaffian formula is generalized to account for quantum fluctuations in the fermion parity of an open subsystem. A statistical description in the framework of random-matrix theory is used to answer the question when a vanishing fermion parity in a superconductor fusion experiment becomes a distinctive signature of an isolated Majorana zero-mode.
Zhang, Ting, et al. "Experimental quantum state measurement with classical shadows." Physical Review Letters 127.20 (2021): 200501.
Abstract- A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], a thrifty scheme showed how to project the quantum state into classical shadows and simultaneously predict 𝑀 different functions of a state with only O(log2𝑀) measurements, independent of the system size and saturating the information-theoretical limit. Here, we experimentally explore the feasibility of the scheme in the realistic scenario with a finite number of measurements and noisy operations. We prepare a four-qubit GHZ state and show how to estimate expectation values of multiple observables and Hamiltonians. We compare the measurement strategies with uniform, biased, and derandomized classical shadows to conventional ones that sequentially measure each state function exploiting either importance sampling or observable grouping. We next demonstrate the estimation of nonlinear functions using classical shadows and analyze the entanglement of the prepared quantum state. Our experiment verifies the efficacy of exploiting (derandomized) classical shadows and sheds light on efficient quantum computing with noisy intermediate-scale quantum hardware.
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/UYEN T LE/Primary Examiner, Art Unit 2156 2 February 2026