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 1-3, 5-10, 12-22 are pending.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 17 March 2026 was filed after the mailing date of the non-final Office action on 4 February 2026. The submission is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Response to Amendment
Applicant’s amendment filed 2 June 2026 is not sufficient to overcome the rejections of claims 14-20 under 35 U.S.C. 101, the rejection of claims 1-3, 5-10, 12, 13, 21, 22 under 35 U.S.C, 103 and further introduces new issues of 35 U.S.C. 112 discussed below.
Response to Arguments
Applicant’s arguments filed 2 June 2026 regarding the art rejection of claims 1, 7 have been fully considered but they are moot in view of the new grounds of rejection presented in this Office action. Note applicant argues the claims as amended.
Regarding the rejection under 35 U.S.C. 101 of claim 14, applicant argues at page 15 of the response filed 2 June 2026:
“In contrast, the presently claimed method absorbs the projector-defining unitary and the state-preparation operators into updated unitary operators and reformulates the expectation value as a vacuum expectation of a quantum channel. This reformulation enables the expectation value to be expressed as a derivative of a polynomial whose value is given by a Pfaffian of a matrix constructed from the updated unitary operators. Because Pfaffians of antisymmetric matrices can be computed using standard cubic-time algorithms, the overall classical post-processing cost scales at most cubically with the number of qubits. This represents a technical improvement in the field of quantum computation. As a result, the method remains scalable for larger quantum systems and can be practically implemented on near-term hardware’.
In response the examiner points out applicant argues limitations not reflected in the claim language. Nothing in claim 14 set forth how post-processing cost scales at most cubically with the number of qubits and represent a technical improvement in the field of quantum computation for larger quantum systems and can be implemented on near-term hardware as argued.
Applicant presents no further argument regarding the dependent claims. For all the reasons discussed above, the rejection of claims 14 and its dependent claims under 35 U.S.C. 101 is maintained.
Claim Rejections - 35 USC § 112
The following is a quotation of the first paragraph of 35 U.S.C. 112(a):
(a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention.
The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112:
The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention.
Claims 1-3, 5-10, 12, 13, 21, 22 are rejected under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the inventor(s), at the time the application was filed, had possession of the claimed invention.
The specification as originally filed does not support the now claimed
“applying an inverse measurement channel to measurement-outcome operators defined by the stored records, the inverse measurement channel performing Majorana-degree-dependent rescaling of components of the measurement-outcome operators, and averaging the rescaled measurement-outcome operators to obtain the classical shadow of the n-qubit quantum state” in amended claims 1, 7
“conjugating a computational-basis projector corresponding to the stored bit string with the corresponding sampled unitary operator to form a measurement-outcome operator corresponding to the stored bit string under the sampled unitary operator”; in claims 21-22
“decomposing the measurement-outcome operator into one or more components, wherein each component comprises a product of Majorana operators having a respective degree corresponding to a number of Majorana operators in the product”; in claims 21-22
“weighting the one or more components using coefficients that depend on the number of qubits n in the n-qubit state and the respective degree to obtain a rescaled measurement-outcome operator, wherein the weighting defines an invertible fermionic measurement channel”. In claims 21-22.
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.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-3, 5-10, 12, 13, 21, 22 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
The specification as originally filed does not support the now claimed
“applying an inverse measurement channel to measurement-outcome operators defined by the stored records, the inverse measurement channel performing Majorana-degree-dependent rescaling of components of the measurement-outcome operators, and averaging the rescaled measurement-outcome operators to obtain the classical shadow of the n-qubit quantum state” in amended claims 1, 7
“conjugating a computational-basis projector corresponding to the stored bit string with the corresponding sampled unitary operator to form a measurement-outcome operator corresponding to the stored bit string under the sampled unitary operator”; in claims 21-22
“decomposing the measurement-outcome operator into one or more components, wherein each component comprises a product of Majorana operators having a respective degree corresponding to a number of Majorana operators in the product”; in claims 21-22
“weighting the one or more components using coefficients that depend on the number of qubits n in the n-qubit state and the respective degree to obtain a rescaled measurement-outcome operator, wherein the weighting defines an invertible fermionic measurement channel”. In claims 21-22.
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 14-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
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)).
For all the reasons discussed above claims 14-20 are not 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) 1-3, 5-10, 12, 13, 21, 22 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]; of record both provided by the applicant, in view of Radin et al (US 20200226487 A1), in view of Bravyi et al (US 20210256410 A1), in view of SMELYANSKIY et al (WO 2020263302 A1).
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 the 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 unitaries;
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 “unitaries parameterized by orthogonal matrices sampled from a continuous orthogonal group O(2n) according to a Haar distribution, and wherein sampling the unitary operator comprises sampling a random orthogonal matrix from the continuous orthogonal group O(2n) and constructing the unitary operator corresponding to the sampled orthogonal matrix (see at least Zhao page 2 Classical shadows and randomized measurements),
Although Zhao/Jozsa does not specifically show the unitary operator being parameterized by a plurality of continuous rotation parameters derived from the sampled orthogonal matrix; it is customary in the art to do so as shown by Radin (see at least [0067] In one embodiment, the invention implements an improvement to the variational quantum eigensolver (VQE), in which the number of shots to be performed in order to apply the VQE method is reduced by applying a quantum circuit corresponding to an orbital rotation of the quantum state during each shot instead of applying single-qubit context-selection gates or, more generally, context-selection gates from any Pauli-based grouping method. A shot in the invention comprises qubit initialization, application of the ansatz circuit, application of an orbital rotation, and measurement).
It would have been obvious to one or ordinary skill in the art before the effective filing date of the claimed invention to include such features while implementing the method of Zhao/Jozsa in order to improve expected value estimation as taught by Radin (see at least the abstract);
Zhao/Jozsa/Radin further teaches
for each sampled unitary operator:
applying, by the 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 using rotation operations having continuously variable rotation angles correspo9nding to the continuous rotation parameters (See Zhao page 2 left column section "Classical shadows and randomized measurements" to right column, Radin abstract),
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; wherein the record defines a measurement outcome operator corresponding to the respective bit string under the sampled unitary operator (See Zhao page 2 left column section "Classical shadows and randomized measurements" to right column),
Zhao/Jozsa/Radin does not specifically show:
computing, by the classical computer, the classical shadow of the n-qubit quantum state, comprising:
applying an inverse measurement channel to measurement-outcome operators defined by the stored records, the inverse measurement channel performing Majorana-degree-dependent rescaling of components of the measurement-outcome operators, and
however it is customary in the art as shown by Bravyi to use stochastic matrix inversion to mitigate quantum readout errors (see at least the abstract);
it would have been obvious to one or ordinary skill in the art before the effective filing date of the claimed invention to include such features while implementing the method of Zhao/Jozsa/Radin in order to benefit from a standardized technique for reducing readout errors;
Zhao/Jozsa/Radin/Bravyi does not specifically show:
averaging the rescaled measurement-outcome operators to obtain the classical shadow of the n-qubit quantum state;
however averaging measurement outcome operators is well known in the art as shown by SMELYANSKIY (see at least [00014], [00020];
it would have been obvious to one or ordinary skill in the art before the effective filing date of the claimed invention to include such features while implementing the method of Zhao/Jozsa/Radin/Bravyi in order to obtain an overall measurement of the evolved states;
Zhao/Jozsa/Radin/Bravyi/SMELYANSKIY further teaches:
and providing, by the classical computer, the classical shadow of the n-qubit quantum state as output (see Zhao page 2 left column section "Classical shadows and randomized measurements" to right column, SMELYANSKIY [00041], [00047]).
Regarding claim 2, Zhao/Jozsa/Radin/Bravyi/SMELYANSKIY 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/Radin/Bravyi/SMELYANSKIY 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 5, Zhao/Jozsa/Radin/Bravyi/SMELYANSKIY 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/Radin/Bravyi/SMELYANSKIY 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),.
Regarding claim 21, Zhao/Jozsa/Radin/Bravyi/SMELYANSKIY teaches the method of claim 1, wherein applying the inverse measurement channel to the measurement-outcome operators defined by the stored records comprises:
for each stored bit string and corresponding sampled unitary operator:
conjugating a computational-basis projector corresponding to the stored bit string with the corresponding sampled unitary operator to form a measurement-outcome operator corresponding to the stored bit string under the sampled unitary operator (Zhao page 2 both columns);
decomposing the measurement-outcome operator into one or more components, wherein each component comprises a product of Majorana operators having a respective degree corresponding to a number of Majorana operators in the product (Zhao page 2 both columns); and
weighting the one or more components using coefficients that depend on the number of qubits n in the n-qubit state and the respective degree to obtain a rescaled measurement-outcome operator, wherein the weighting defines an invertible fermionic measurement channel (Zhao page 2 both columns).
Claims 7-10, 12, 13, 22 essentially recite limitations similar to claims 1-3, 5, 6, 21 in form of systems thus are rejected for the same reasons discussed in claims 1-3, 5, 6, 21 above.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Reagor (WO 2023064481 A1) teaches performing parametric dissipation operations in a quantum computing system. In some implementations, a method includes executing a computer program in a computer system. Executing the computer program includes applying a quantum logic gate associated with a unitary operation to qubits defined by qubit devices on a quantum processing unit; obtaining an estimated value of a dissipation rate parameter; applying a parametric dissipation operation to one or more of the qubit devices; and measuring a state of one or more of the qubit devices. The parametric dissipation operation has a programmable dissipation rate that is controlled by the estimated value of the dissipation rate parameter; and the parametric dissipation operation is applied separately from the quantum logic gate.
Mezzacapo et al (US 20210049482 A1) teach systems, computer-implemented methods, and computer program products to facilitate state dependent calibration of qubit measurements are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a state prediction component that predicts a readout state of one or more qubits of a quantum circuit. The computer executable components can further comprise a calibration component that calibrates a qubit readout signal based on the readout state to generate a state dependent qubit readout signal to read the one or more qubits.
Bergholm, Ville, et al. "Quantum circuits with uniformly controlled one-qubit gates." Physical Review A—Atomic, Molecular, and Optical Physics 71.5 (2005): 052330.
Abstract
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any 𝑛-qubit gate of this type using at most 2𝑛−1−1 controlled-NOT gates, 2𝑛−1 one-qubit gates, and a single diagonal 𝑛-qubit gate. To illustrate the versatility of these gates we then apply them to the decomposition of a general 𝑛-qubit gate and a state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.
Struchalin, G. I., et al. "Experimental estimation of quantum state properties from classical shadows." PRX quantum 2.1 (2021): 010307.
Abstract
Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas have been proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here, we provide an experimental demonstration of property estimation based on classical shadows proposed in Huang et al. [Nat. Phys. 16, 1050 (2020)] and study its performance in a quantum-optical experiment with high-dimensional spatial states of photons. We show by means of experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to UYEN T LE whose telephone number is (571)272-4021. The examiner can normally be reached M-F 9-5.
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/UYEN T LE/Primary Examiner, Art Unit 2156 8 August 2026
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