DETAILED ACTION
This action is responsive to the application filed on 01/25/2024. Claims 1-20 are pending in the case. Claims 1, 8, and 16 are independent claims.
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 .
Priority
Acknowledgement is made of applicant’s claim for domestic priority based on a provisional application filed 03/01/2023.
Claim Objections
Claim 19 is objected to because of the following informalities: “maximum number of terms” in line 4 should read “a maximum number of terms” as it appears to be a typographical error. Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
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 1-20 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.
Claim 1 recites the limitation "the expectation value" in lines 23-24. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “an expectation value of the model Hamiltonian measured in a previous iteration”, reciting a new claim element.
Claims 2-4 are rejected as being dependent upon a rejected base claim without curing any of the deficiencies.
Regarding claim 5, the claim recites: “the maximum number of terms in the model Hamiltonian” in lines 1-2. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “a maximum number of terms in the model Hamiltonian”, reciting a new claim element.
Further, the claim recites: “the highest order of polynomials” in line 2. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “a highest order of polynomials”, reciting a new claim element.
Claims 6-7 are rejected as being dependent upon a rejected base claim without curing any of the deficiencies.
Regarding claim 8, the claim recites: "the expectation value" in lines 26. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “an expectation value of the model Hamiltonian measured in a previous iteration”, reciting a new claim element.
Claims 9-12 are rejected as being dependent upon a rejected based claim without curing any of the deficiencies.
Regarding claim 13, the claim recites: “the maximum number of terms in the model Hamiltonian” in lines 4. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “a maximum number of terms in the model Hamiltonian”, reciting a new claim element.
Further, the claim recites: “the highest order of polynomials” in lines 4-5. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “a highest order of polynomials”, reciting a new claim element.
Claims 14-15 are rejected a being dependent upon a rejected base claim without curing any of the deficiencies.
Regarding claim 16, the claim recites: "the expectation value" in lines 26. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “an expectation value of the model Hamiltonian measured in a previous iteration”, reciting a new claim element.
Claims 17-18 are rejected as being dependent upon a rejected base claim without curing any of the deficiencies.
Regarding claim 19, the claim recites: “the highest order of polynomials” in lines 4-5. There is insufficient antecedent basis for this limitation in the claim. It is unclear if applicant is attempting to recite a new claim element or if applicant is attempting to refer to a previously recited claim element. For examination purposes, the limitation is being interpreted as “a highest order of polynomials”, reciting a new claim element.
Claim 20 is rejected as being dependent upon a rejected base claim without curing any of the deficiencies.
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 without significantly more.
Regarding claim 1:
Step 1 Statutory Category: Claim 1 is directed to a method, which falls under one of the four statutory categories.
Step 2A Prong 1 Judicial exception: Claim 1 recites, in part, “computing, …, an approximate cost function of an optimization problem with variables constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function”. This limitation is the abstract idea of a mathematical calculation, as directed to “a claim that recites a mathematical calculation, when the claim is given its broadest reasonable interpretation in light of the specification, will be considered as falling within the "mathematical concepts" grouping. A mathematical calculation is a mathematical operation (such as multiplication) or an act of calculating using mathematical methods to determine a variable or number”. See MPEP §2106.04(a)(2)(I)(C). Further, the claim recites: “mapping, …, the approximate cost function of the optimization problem to a model Hamiltonian to be implemented on a quantum processor comprising a plurality of trapped ions, each of which has two hyperfine states defining a qubit”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical concept, See MPEP §2106.04(a)(2)(I). Further, the claim recites: “selecting, …, a set of variational parameters to construct a parametrized quantum circuit comprising an entangling circuit based on the model Hamiltonian and a mixing circuit”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mental process that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper (including an observation, evaluation, judgment, opinion), in this case a judgment. See MPEP § 2106.04(a)(2)(III). Further, the claim recites: “measuring, …, an expectation value of the model Hamiltonian”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical concept, See MPEP §2106.04(a)(2)(I). Further, the claim recites: “replacing, …, the set of the variational parameters with another set of variational parameters, if a difference between the measured expectation value of the model Hamiltonian and the expectation value of the model Hamiltonian measured in a previous iteration is more than a predetermined value”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mental process that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper (including an observation, evaluation, judgment, opinion), in this case a judgment. See MPEP § 2106.04(a)(2)(III).
Step 2A Prong 2 Integration into a practical application: This judicial exception is not integrated into a practical application. In particular the claim recites: “a hybrid quantum-classical computing system comprising a classical computer and a quantum processor”. This limitation is an additional element that amounts to generally linking the use of the judicial exception to a particular technological environment or field of use. See MPEP §2106.05(h). Further, the claim recites: “by a classical computer”, “by the classical computer”, “by a system controller”, and “by the system controller”. These limitations are additional elements that amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “setting, by a system controller, the quantum processor in an initial state; executing one or more iterations, each iteration comprising: applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state”. This limitation is an additional element that amounts to to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “outputting, …, the set of the variational parameters after executing the one or more iterations”. This limitation is an additional element that amounts to adding insignificant extra-solution activity to the judicial exception. See MPEP §2106.05(g).
Step 2B Significantly more: The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional element: “a hybrid quantum-classical computing system comprising a classical computer and a quantum processor” amounts to generally linking the use of the judicial exception to a particular technological environment or field of use. Elements that merely amount to generally linking the use of the judicial exception to a particular technological environment or field of use cannot provide an inventive concept. Further, the additional elements: “by a classical computer”, “by the classical computer”, “by a system controller”, “by the system controller”, and “setting, by a system controller, the quantum processor in an initial state; executing one or more iterations, each iteration comprising: applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state” amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. Elements that merely amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process cannot provide an inventive concept. Further, the additional element: “outputting, …, the set of the variational parameters after executing the one or more iterations” amounts to adding insignificant extra-solution activity to the judicial exception, and further, is directed to receiving or transmitting data over a network which courts have recognized as well-understood, routine, and conventional when they are claimed in a generic manner, see MPEP §2106.05(d)(II). The claim is not patent eligible.
Regarding claim 2, the rejection of claim 1 is incorporated, and further, the claim recites: “wherein the optimization problem is a knapsack problem”. This limitation is an additional element that amounts to generally linking the use of the judicial exception to a particular technological environment or field of use. See MPEP §2106.05(h). Elements that merely amount to generally linking the use of the judicial exception to a particular technological environment or field of use cannot provide an inventive concept. The claim is not patent eligible.
Regarding claim 3, the rejection of claim 1 is incorporated, and further, the claim recites: “wherein a number of the variables equals a number of the plurality of trapped ions”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical relationship, as directed to “a mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols”. See MPEP § 2106.04(a)(2)(I)(A).
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding claim 4, the rejection of claim 1 is incorporated, and further, the claim recites: “wherein the polynomial approximation of the Heaviside step function includes odd order polynomials”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Thus, the claim recites a judicial exception.
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding claim 5, the rejection of claim 4 is incorporated, and further, the claim recites: “wherein the maximum number of terms in the model Hamiltonian is the highest order of polynomials in the polynomial approximation of the Heaviside step function”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Thus, the claim recites a judicial exception.
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding claim 6, the rejection of claim 1 is incorporated, and further, the claim recites: “wherein the optimization problem is further constrained by one or more equalities”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Thus, the claim recites a judicial exception.
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding claim 7, the rejection of claim 1 is incorporated, and further, the claim recites: “wherein the optimization problem is further constrained by one or more additional inequalities”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Thus, the claim recites a judicial exception.
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding claim 8:
Step 1 Statutory Category: Claim 8 is directed to a system, which falls under one of the four statutory categories.
Step 2A Prong 1 Judicial exception: Claim 8 recites, in part, “compute an approximate cost function of an optimization problem with variables constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function”. This limitation is the abstract idea of a mathematical calculation, as directed to “a claim that recites a mathematical calculation, when the claim is given its broadest reasonable interpretation in light of the specification, will be considered as falling within the "mathematical concepts" grouping. A mathematical calculation is a mathematical operation (such as multiplication) or an act of calculating using mathematical methods to determine a variable or number”. See MPEP §2106.04(a)(2)(I)(C). Further, the claim recites: “map the approximate cost function of the optimization problem to a model Hamiltonian to be implemented on the quantum processor”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical concept, See MPEP §2106.04(a)(2)(I). Further, the claim recites: “select a set of variational parameters to construct a parametrized quantum circuit comprising an entangling circuit based on the model Hamiltonian and a mixing circuit”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mental process that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper (including an observation, evaluation, judgment, opinion), in this case a judgment. See MPEP § 2106.04(a)(2)(III). Further, the claim recites: “…measure an expectation value of the model Hamiltonian”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical concept, See MPEP §2106.04(a)(2)(I). Further, the claim recites: “replace the set of the variational parameters with another set of variational parameters, if a difference between the measured expectation value of the model Hamiltonian and the expectation value of the model Hamiltonian measured in a previous iteration is more than a predetermined value”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mental process that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper (including an observation, evaluation, judgment, opinion), in this case a judgment. See MPEP § 2106.04(a)(2)(III).
Step 2A Prong 2 Integration into a practical application: This judicial exception is not integrated into a practical application. In particular, the claim recites: “A hybrid quantum-classical computing system, comprising: a quantum processor comprising a plurality of trapped ions, each of the trapped ions having two hyperfine states defining a qubit; one or more lasers configured to emit a laser beam, which is provided to trapped ions in the quantum processor; and a classical computer”. This limitation is an additional element that amounts to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “control a system controller to” and “control the system controller to”. These limitations are additional elements that amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “…set the quantum processor in an initial state; executing one or more iterations, each iteration comprising: … apply the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state”. This limitation is an additional element that amounts to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “output the set of the variational parameters after executing the one or more iterations”. This limitation is an additional element that amounts to adding insignificant extra-solution activity to the judicial exception. See MPEP §2106.05(g).
Step 2B Significantly more: The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements: “A hybrid quantum-classical computing system, comprising: a quantum processor comprising a plurality of trapped ions, each of the trapped ions having two hyperfine states defining a qubit; one or more lasers configured to emit a laser beam, which is provided to trapped ions in the quantum processor; and a classical computer”, “control a system controller to”, “control the system controller to”, and “…set the quantum processor in an initial state; executing one or more iterations, each iteration comprising: … apply the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state” amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. Elements that merely amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process cannot provide an inventive concept. Further, the additional element: “output the set of the variational parameters after executing the one or more iterations” amounts to adding insignificant extra-solution activity to the judicial exception, and further, is directed to receiving or transmitting data over a network which courts have recognized as well-understood, routine, and conventional when they are claimed in a generic manner, see MPEP §2106.05(d)(II). The claim is not patent eligible.
Regarding claim 9, the rejection of claim 8 is incorporated, and further, the claim recites: “wherein each of the trapped ions is
Y
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+
171
having
S
1
/
2
2
hyperfine states”. This limitation is an additional element that amounts to generally linking the use of the judicial exception to a particular technological environment or field of use. See MPEP §2106.05(h). Elements that merely amount to generally linking the use of the judicial exception to a particular technological environment or field of use cannot provide an inventive concept. The claim is not patent eligible.
Regarding claim 10, the rejection of claim 8 is incorporated, and further, the claim recites: “wherein each of the trapped ions is one selected from Be+, Ca+, Sr+, Mg+, Ba+, Zn+, Hg+, Cd+”. This limitation is an additional element that amounts to generally linking the use of the judicial exception to a particular technological environment or field of use. See MPEP §2106.05(h). Elements that merely amount to generally linking the use of the judicial exception to a particular technological environment or field of use cannot provide an inventive concept. The claim is not patent eligible.
Regarding claim 11, the rejection of claim 8 is incorporated, and further, claim 11 is substantially similar to claim 2 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 12, the rejection of claim 8 is incorporated, and further, claim 12 is substantially similar to claim 3 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 13, the rejection of claim 8 is incorporated, and further, the claim recites: “the polynomial approximation of the Heaviside step function includes odd order polynomials”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Further, the claim recites: “the maximum number of terms in the model Hamiltonian is the highest order of polynomials in the polynomial approximation of the Heaviside step function”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Thus, the claim recites a judicial exception.
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding claim 14, the rejection of claim 8 is incorporated, and further, claim 14 is substantially similar to claim 6 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 15, the rejection of claim 8 is incorporated, and further, claim 15 is substantially similar to claim 7 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 16:
Step 1 Statutory Category: Claim 16 is directed to a system, which falls under one of the four statutory categories.
Step 2A Prong 1 Judicial exception: Claim 16 recites, in part, “computing, …, an approximate cost function of an optimization problem with variables constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function”. This limitation is the abstract idea of a mathematical calculation, as directed to “a claim that recites a mathematical calculation, when the claim is given its broadest reasonable interpretation in light of the specification, will be considered as falling within the "mathematical concepts" grouping. A mathematical calculation is a mathematical operation (such as multiplication) or an act of calculating using mathematical methods to determine a variable or number”. See MPEP §2106.04(a)(2)(I)(C). Further, the claim recites: “mapping, …, the approximate cost function of the optimization problem to a model Hamiltonian to be implemented on a quantum processor comprising a plurality of trapped ions, each of which has two hyperfine states defining a qubit”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical concept, See MPEP §2106.04(a)(2)(I). Further, the claim recites: “selecting, …, a set of variational parameters to construct a parametrized quantum circuit comprising an entangling circuit based on the model Hamiltonian and a mixing circuit”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mental process that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper (including an observation, evaluation, judgment, opinion), in this case a judgment. See MPEP § 2106.04(a)(2)(III). Further, the claim recites: “measuring, …, an expectation value of the model Hamiltonian”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mathematical concept, See MPEP §2106.04(a)(2)(I). Further, the claim recites: “replacing, …, the set of the variational parameters with another set of variational parameters, if a difference between the measured expectation value of the model Hamiltonian and the expectation value of the model Hamiltonian measured in a previous iteration is more than a predetermined value”. This limitation, under the broadest reasonable interpretation, covers the recitation of a mental process that can practically be performed in the human mind, with or without the use of a physical aid such as pen and paper (including an observation, evaluation, judgment, opinion), in this case a judgment. See MPEP § 2106.04(a)(2)(III).
Step 2A Prong 2 Integration into a practical application: This judicial exception is not integrated into a practical application. In particular, the claim recites: “A hybrid quantum-classical computing system comprising non-volatile memory having a number of instructions stored therein which, when executed by one or more processors, causes the hybrid quantum-classical computing system to perform operations”. This limitation is an additional element that amounts to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “by a classical computer”, “by the classical computer”, “by a system controller”, and “by the system controller”. These limitations are additional elements that amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “setting, by a system controller, the quantum processor in an initial state; executing one or more iterations, each iteration comprising: applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state”. This limitation is an additional element that amounts to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. See MPEP §2106.05(f). Further, the claim recites: “outputting, …, the set of the variational parameters after executing the one or more iterations”. This limitation is an additional element that amounts to adding insignificant extra-solution activity to the judicial exception. See MPEP §2106.05(g).
Step 2B Significantly more: The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements: “A hybrid quantum-classical computing system comprising non-volatile memory having a number of instructions stored therein which, when executed by one or more processors, causes the hybrid quantum-classical computing system to perform operations”, “by a classical computer”, “by the classical computer”, “by a system controller”, “by the system controller”, and “setting, by a system controller, the quantum processor in an initial state; executing one or more iterations, each iteration comprising: applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state” amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process. Elements that merely amount to adding the words “apply it” (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer, or merely uses a computer in its ordinary capacity as a tool to perform an existing process cannot provide an inventive concept. Further, the additional element: “outputting, …, the set of the variational parameters after executing the one or more iterations” amounts to adding insignificant extra-solution activity to the judicial exception, and further, is directed to receiving or transmitting data over a network which courts have recognized as well-understood, routine, and conventional when they are claimed in a generic manner, see MPEP §2106.05(d)(II). The claim is not patent eligible.
Regarding claim 17, the rejection of claim 16 is incorporated, and further, claim 17 is substantially similar to claim 2 and claim 11 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 18, the rejection of claim 16 is incorporated, and further, claim 18 is substantially similar to claim 3 and claim 12 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 19, the rejection of claim 16 is incorporated, and further, claim 19 is substantially similar to claim 13 respectively, and is rejected in the same manner and reasoning applying.
Regarding claim 20, the rejection of claim 16 is incorporated, and further, the claim recites: “the optimization problem is further constrained by one or more equalities, and the optimization problem is further constrained by one or more additional inequalities”. This limitation recites mathematical concepts in addition to those identified in the rejection of the parent claim. Thus, the claim recites a judicial exception.
The claim does not include any additional elements that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Claim Rejections - 35 USC § 103
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.
Claims 1-5, 8-13, 16-19 are rejected under 35 U.S.C. 103 as being unpatentable over Shehab et al., U.S. Patent Application Publication No. 20210056455, hereinafter referred to as “Shehab” in view of Orus et al., Forecasting financial crashes with quantum computing, 06/27/2019, https://journals.aps.org/pra/pdf/10.1103/PhysRevA.99.060301, hereinafter referred to as “Orus”.
Regarding claim 1, Shehab teaches A method of performing computation in a hybrid quantum-classical computing system comprising a classical computer and a quantum processor (Shehab, Abstract, Lines 1-10, “Embodiments described herein are generally related to a method and a system for performing a computation using a hybrid quantum-classical computing system … A hybrid quantum-classical computing system that is able to provide a solution to a combinatorial optimization problem may include a classical computer, a system controller, and a quantum processor”), comprising:
computing, by a classical computer, an … cost function of an optimization problem (Shehab, Paragraph 0042, Lines 1-5, “A combinatorial optimization problem is modeled by an objective function (also referred to as a cost function) that maps events or values of one or more variables onto real numbers representing “cost” associated with the events or values and seeks to minimize the cost function”) with variables constrained (Shehab, Paragraph 0047, Lines 1-2 – Paragraph 0048, Line 1, “a combinatorial optimization problem on a set of N binary variables with t constraints)
…
mapping, by the classical computer, the … cost function of the optimization problem to a model Hamiltonian to be implemented on a quantum processor comprising a plurality of trapped ions, each of which has two hyperfine states defining a qubit (Shehab, Paragraph 0042, Lines 7-12, “The combinatorial optimization problem is further mapped onto a simple physical system described by a model Hamiltonian (corresponding to the sum of kinetic energy and potential energy of all particles in the system) and the problem seeks the low-lying energy state of the physical system”; Shehab, Paragraph 0044, Lines 6-8, “the quantum processor is the group 106 of N trapped ions, in which the two hyperfine states of each of the N trapped ions form a qubit”);
selecting, by the classical computer, a set of variational parameters to construct a parametrized quantum circuit comprising an entangling circuit based on the model Hamiltonian and a mixing circuit (Shehab, Paragraph 0049, Lines 1-6, “In block 804, following the mapping of the selected combinatorial optimization problem onto a model Hamiltonian
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a set of variational parameters (
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is selected, by the classical computer 102, to construct a sequence of gates (also referred to a “trial preparation circuit”)”; Shehab, Paragraph 0049, Lines 11-14, “The trail state preparation circuit
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(
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) includes p layers (i.e., p-time repetitions) of a model-Hamiltonian circuit … and a mixing circuit”);
setting, by a system controller, the quantum processor in an initial state (Shehab, Paragraph 0050, Lines 1-3, “In block 806, following the selection of a set of variational parameters
y
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, the quantum processor 106 is set in an initial state
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by the system controller 104”);
executing one or more iterations (Shehab, Paragraph 0045, Lines 3-4, “The variational method consists of iterations”), each iteration comprising:
applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state (Shehab, Paragraph 0051, Lines 1-5, “In block 808, following the preparation of the quantum processor 106 in the initial state
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, the trial state preparation circuit
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β
→
) is applied to the quantum processor 106, by the system controller 104, to construct the trail state
|
ψ
(
y
→
,
β
→
)
”);
measuring, by the system controller, an expectation value of the model Hamiltonian (Shehab, Paragraph 0052, Lines 1-5, “In block 810, following the construction of the trial state
|
ψ
(
y
→
,
β
→
)
on the quantum processor 106, the expectation value … of the Pauli term … is measured by the system controller 104”); and
replacing, by the classical computer, the set of the variational parameters with another set of variational parameters, if a difference between the measured expectation value of the model Hamiltonian and the expectation value of the model Hamiltonian measured in a previous iteration is more than a predetermined value (Shehab, Paragraph 0055 – Paragraph 0056, Line 3, In block 816, following the computation of the measured expectation value of the model Hamiltonian
H
C
, the measured expectation value
F
(
y
→
,
β
→
) of the model Hamiltonian
H
C
is compared to the measured expectation value of the model Hamiltonian
H
C
in the previous iteration, by the classical computer 102 … If the difference between the two values is more than the predetermined value, the method proceeds to block 818. In block 818, another set of variational parameters
y
→
,
β
→
for a next iteration of blocks 806-816 is computed by the classical computer 102”); and
outputting, by the classical computer, the set of the variational parameters after executing the one or more iterations (Shehab, Paragraph 0062, Lines 1-5, “In block 820, the classical computer 102 will typically output the results of the variational search to a user interface of the classical computer 102 and/or save the results of the variational search in the memory of the classical computer 102. The results of the variational search will include … the measurement of the trial state
|
ψ
(
y
→
,
β
→
)
in the final iteration”).
Shehab does not explicitly teach the cost function being approximate nor the variables being constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function.
Orus teaches the cost function being approximate and the variables being constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function (Orus, Page 060301-2, Section 3, Subsection A, Lines 3-9, “This equilibrium may not be unique. In general, though, one would have
F
v
→
=
v
→
-
C
~
I
-
C
-
1
D
p
→
-
b
→
v
→
,
p
→
2
≥
0
. The above expression is strictly larger than zero away from equilibrium, and equal to zero and therefore minimum at equilibrium. The vector v at equilibrium will be the one that minimizes the classical cost function F(v) for a given network configuration”; Orus, Page 060301-3, Lines 6-7, “the most viable option is to approximate the Heaviside function by a polynomial expansion”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention, to have modified the hybrid computing method of Shehab to include an approximate cost function with variables constrained by an inequality, where the inequality is included using a polynomial approximation of a Heaviside step function as taught by Orus. The motivation to do so would have been that the Heaviside step function is discontinuous and in order to obtain a Hamiltonian, a continuous function is needed, further, the polynomial approximation will function to make the Hamiltonian easily described. Further, it keeps the cost function easier to handle while remaining nonlinear (Orus, Page 060301-3, Lines 1-5; Orus, Page 060301-3, Paragraph 2).
Regarding claim 2, the rejection of claim 1 is incorporated, and further, the proposed combination teaches wherein the optimization problem is a knapsack problem (Shehab, Paragraph 0041, Final 7 lines, “Another combinatorial optimization problem is the knapsack problem to find a way to pack a knapsack to get the maximum total value, given some items. The knapsack problem is applied to resource allocation given financial constraints in home energy management, network selection for mobile nodes, cognitive radio networks, sensor selection in distributed multiple radar, or the like”).
Regarding claim 3, the rejection of claim 1 is incorporated, and further, the proposed combination teaches wherein a number of the variables equals a number of the plurality of trapped ions (Shehab, Paragraph 0047, Lines 1-2 – Paragraph 0048, Line 1, “In a combinatorial optimization problem on a set of N binary variables with t constraints … The quantum processor 106 has N qubits”; Shehab, Paragraph 0044, Lines 6-8, “the quantum processor is the group 106 of N trapped ions, in which the two hyperfine states of each of the N trapped ions form a qubit”).
Regarding claim 4, the rejection of claim 1 is incorporated, and further, the proposed combination teaches wherein the polynomial approximation of the Heaviside step function includes odd order polynomials (Orus, Page 060301-3, Lines 5-12, “we have found that the most viable option is to approximate the Heaviside function by a polynomial expansion. Of course, such an expansion is not unique. While it would be possible to find the optimal polynomial of a given degree approximating the function in a given interval and for a given error norm[23], standard approximations exist in terms of, e.g., shifted Legendre polynomials [24], which are sufficient to show the validity of our approach. In particular, one can make use of the Fourier-Legendre expansion” A person of ordinary skill in the art would recognize the Fourier-Legendre expansion includes odd order polynomials).
Regarding claim 5, the rejection of claim 4 is incorporated, and further, the proposed combination teaches wherein the maximum number of terms in the model Hamiltonian is the highest order of polynomials in the polynomial approximation of the Heaviside step function (Orus, Page 060301-2, Equation 3, “
F
v
→
=
v
→
-
C
~
I
-
C
-
1
D
p
→
-
b
→
v
→
,
p
→
2
≥
0
”; Orus, Page 060301-3, Equation 6, “
b
→
v
→
,
p
→
≈
β
i
p
→
P
o
l
y
r
(
v
i
-
v
i
c
)
”; Orus, Page 060301-3, Lines 6-9, and Equation 7, “Consider Eqs. (3), (4), and (6) together, one can see after some inspection that
G
x
i
,
a
=
P
o
l
y
r
x
i
,
a
”).
Regarding claim 8, Shehab teaches A hybrid quantum-classical computing system (Shehab, Abstract, Lines 1-10, “Embodiments described herein are generally related to a method and a system for performing a computation using a hybrid quantum-classical computing system … A hybrid quantum-classical computing system that is able to provide a solution to a combinatorial optimization problem may include a classical computer, a system controller, and a quantum processor”), comprising:
a quantum processor comprising a plurality of trapped ions, each of the trapped ions having two hyperfine states defining a qubit (Shehab, Paragraph 0044, Lines 6-8, “the quantum processor is the group 106 of N trapped ions, in which the two hyperfine states of each of the N trapped ions form a qubit”);
one or more lasers configured to emit a laser beam, which is provided to trapped ions in the quantum processor (Shehab, Paragraph 0004, Lines 7-22, “These hyperfine states can be controlled using radiation provided from a laser, or sometimes referred to herein as the interaction with laser beams. The ions can be cooled to near their motional ground states using such laser interactions. The ions can also be optically pumped to one of the two hyperfine states with high accuracy (preparation of qubits), manipulated between the two hyperfine states (single-qubit gate operations) by laser beams, and their internal hyperfine states detected by fluorescence upon application of a resonant laser beam (read-out of qubits). A pair of ions can be controllably entangled (two-qubit gate operations) by qubit-state dependent force using laser pulses that couple the ions to the collective motional modes of a group of trapped ions, which arise from their Coulombic interaction between the ions”); and
a classical computer (Shehab, Abstract, Lines 7-10, “A hybrid quantum-classical computing system that is able to provide a solution to a combinatorial optimization problem may include a classical computer, a system controller, and a quantum processor”) configured to:
compute an … cost function of an optimization problem (Shehab, Paragraph 0042, Lines 1-5, “A combinatorial optimization problem is modeled by an objective function (also referred to as a cost function) that maps events or values of one or more variables onto real numbers representing “cost” associated with the events or values and seeks to minimize the cost function”) with variables constrained (Shehab, Paragraph 0047, Lines 1-2 – Paragraph 0048, Line 1, “a combinatorial optimization problem on a set of N binary variables with t constraints)
…
map the … cost function of the optimization problem to a model Hamiltonian to be implemented on the quantum processor (Shehab, Paragraph 0042, Lines 7-12, “The combinatorial optimization problem is further mapped onto a simple physical system described by a model Hamiltonian (corresponding to the sum of kinetic energy and potential energy of all particles in the system) and the problem seeks the low-lying energy state of the physical system”);
select a set of variational parameters to construct a parametrized quantum circuit comprising an entangling circuit based on the model Hamiltonian and a mixing circuit (Shehab, Paragraph 0049, Lines 1-6, “In block 804, following the mapping of the selected combinatorial optimization problem onto a model Hamiltonian
H
C
=
∑
a
=
1
h
a
p
w
t
a set of variational parameters (
y
→
=
y
1
,
y
2
,
…
,
y
p
,
β
→
=
β
1
,
β
2
,
…
,
β
p
)
is selected, by the classical computer 102, to construct a sequence of gates (also referred to a “trial preparation circuit”)”; Shehab, Paragraph 0049, Lines 11-14, “The trail state preparation circuit
A
(
y
→
,
β
→
) includes p layers (i.e., p-time repetitions) of a model-Hamiltonian circuit … and a mixing circuit”);
control the system controller to set the quantum processor in an initial state (Shehab, Paragraph 0050, Lines 1-3, “In block 806, following the selection of a set of variational parameters
y
→
,
β
→
, the quantum processor 106 is set in an initial state
|
ψ
0
by the system controller 104”);
execute one or more iterations (Shehab, Paragraph 0045, Lines 3-4, “The variational method consists of iterations”), each iteration comprising:
control the system controller to apply the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state (Shehab, Paragraph 0051, Lines 1-5, “In block 808, following the preparation of the quantum processor 106 in the initial state
|
ψ
0
, the trial state preparation circuit
A
(
y
→
,
β
→
) is applied to the quantum processor 106, by the system controller 104, to construct the trail state
|
ψ
(
y
→
,
β
→
)
”);
control the system controller to measure an expectation value of the model Hamiltonian (Shehab, Paragraph 0052, Lines 1-5, “In block 810, following the construction of the trial state
|
ψ
(
y
→
,
β
→
)
on the quantum processor 106, the expectation value … of the Pauli term … is measured by the system controller 104”); and
replace the set of the variational parameters with another set of variational parameters, if a difference between the measured expectation value of the model Hamiltonian and the expectation value of the model Hamiltonian measured in a previous iteration is more than a predetermined value (Shehab, Paragraph 0055 – Paragraph 0056, Line 3, In block 816, following the computation of the measured expectation value of the model Hamiltonian
H
C
, the measured expectation value
F
(
y
→
,
β
→
) of the model Hamiltonian
H
C
is compared to the measured expectation value of the model Hamiltonian
H
C
in the previous iteration, by the classical computer 102 … If the difference between the two values is more than the predetermined value, the method proceeds to block 818. In block 818, another set of variational parameters
y
→
,
β
→
for a next iteration of blocks 806-816 is computed by the classical computer 102”); and
output the set of the variational parameters after executing the one or more iterations (Shehab, Paragraph 0062, Lines 1-5, “In block 820, the classical computer 102 will typically output the results of the variational search to a user interface of the classical computer 102 and/or save the results of the variational search in the memory of the classical computer 102. The results of the variational search will include … the measurement of the trial state
|
ψ
(
y
→
,
β
→
)
in the final iteration”).
Shehab does not explicitly teach the cost function being approximate nor the variables being constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function.
Orus teaches the cost function being approximate and the variables being constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function (Orus, Page 060301-2, Section 3, Subsection A, Lines 3-9, “This equilibrium may not be unique. In general, though, one would have
F
v
→
=
v
→
-
C
~
I
-
C
-
1
D
p
→
-
b
→
v
→
,
p
→
2
≥
0
. The above expression is strictly larger than zero away from equilibrium, and equal to zero and therefore minimum at equilibrium. The vector v at equilibrium will be the one that minimizes the classical cost function F(v) for a given network configuration”; Orus, Page 060301-3, Lines 6-7, “the most viable option is to approximate the Heaviside function by a polynomial expansion”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention, to have modified the hybrid computing method of Shehab to include an approximate cost function with variables constrained by an inequality, where the inequality is included using a polynomial approximation of a Heaviside step function as taught by Orus. The motivation to do so would have been that the Heaviside step function is discontinuous and in order to obtain a Hamiltonian, a continuous function is needed, further, the polynomial approximation will function to make the Hamiltonian easily described. Further, it keeps the cost function easier to handle while remaining nonlinear (Orus, Page 060301-3, Lines 1-5; Orus, Page 060301-3, Paragraph 2).
Regarding claim 9, the rejection of claim 8 is incorporated, and further, the proposed combination teaches wherein each of the trapped ions is
Y
b
+
171
having
S
1
/
2
2
hyperfine states (Shehab, Paragraph 0029, Lines 3-4, “In one example, each ion may be a positive Ytterbium ion,
Y
b
+
171
, which has the
S
1
/
2
2
hyperfine states”).
Regarding claim 10, the rejection of claim 8 is incorporated, and further, the proposed combination teaches wherein each of the trapped ions is one selected from Be+, Ca+, Sr+, Mg+, Ba+, Zn+, Hg+, Cd+ (Shehab, Paragraph 0031, “It should be noted that the particular atomic species used in the discussion provided herein is just one example of atomic species which has stable and well-defined two-level energy structures when ionized and an excited state that is optically accessible, and thus is not intended to limit the possible configurations … For example, other ion species include alkaline earth metal ions (Be+, Ca+, Sr+, Mg+, and Ba+) or transition metal ions (Zn+, Hg+, Cd+)”).
Regarding claim 11, the rejection of claim 8 is incorporated, and further, the proposed combination teaches wherein the optimization problem is a knapsack problem (Shehab, Paragraph 0041, Final 7 lines, “Another combinatorial optimization problem is the knapsack problem to find a way to pack a knapsack to get the maximum total value, given some items. The knapsack problem is applied to resource allocation given financial constraints in home energy management, network selection for mobile nodes, cognitive radio networks, sensor selection in distributed multiple radar, or the like”).
Regarding claim 12, the rejection of claim 8 is incorporated, and further, the proposed combination teaches wherein a number of the variables equals a number of the plurality of trapped ions (Shehab, Paragraph 0047, Lines 1-2 – Paragraph 0048, Line 1, “In a combinatorial optimization problem on a set of N binary variables with t constraints … The quantum processor 106 has N qubits”; Shehab, Paragraph 0044, Lines 6-8, “the quantum processor is the group 106 of N trapped ions, in which the two hyperfine states of each of the N trapped ions form a qubit”).
Regarding claim 13, the rejection of claim 8 is incorporated, and further, the proposed combination teaches wherein the polynomial approximation of the Heaviside step function includes odd order polynomials (Orus, Page 060301-3, Lines 5-12, “we have found that the most viable option is to approximate the Heaviside function by a polynomial expansion. Of course, such an expansion is not unique. While it would be possible to find the optimal polynomial of a given degree approximating the function in a given interval and for a given error norm[23], standard approximations exist in terms of, e.g., shifted Legendre polynomials [24], which are sufficient to show the validity of our approach. In particular, one can make use of the Fourier-Legendre expansion” A person of ordinary skill in the art would recognize the Fourier-Legendre expansion includes odd order polynomials), and
the maximum number of terms in the model Hamiltonian is the highest order of polynomials in the polynomial approximation of the Heaviside step function (Orus, Page 060301-2, Equation 3, “
F
v
→
=
v
→
-
C
~
I
-
C
-
1
D
p
→
-
b
→
v
→
,
p
→
2
≥
0
”; Orus, Page 060301-3, Equation 6, “
b
→
v
→
,
p
→
≈
β
i
p
→
P
o
l
y
r
(
v
i
-
v
i
c
)
”; Orus, Page 060301-3, Lines 6-9, and Equation 7, “Consider Eqs. (3), (4), and (6) together, one can see after some inspection that
G
x
i
,
a
=
P
o
l
y
r
x
i
,
a
”).
Regarding claim 16, Shehab teaches A hybrid quantum-classical computing system comprising non-volatile memory having a number of instructions stored therein which, when executed by one or more processors, causes the hybrid quantum-classical computing system to perform operations (Shehab, Abstract, Lines 1-10, “Embodiments described herein are generally related to a method and a system for performing a computation using a hybrid quantum-classical computing system … A hybrid quantum-classical computing system that is able to provide a solution to a combinatorial optimization problem may include a classical computer, a system controller, and a quantum processor”; Shehab, Paragraph 0008, Lines 30-36, “Embodiments of the disclosure may also provide a hybrid quantum-classical computing system comprising non-volatile memory having a number of instructions stored therein which, when executed by one or more processors, causes the hybrid quantum-classical computing system to perform operations of the method described above”) comprising:
computing, by a classical computer, an … cost function of an optimization problem (Shehab, Paragraph 0042, Lines 1-5, “A combinatorial optimization problem is modeled by an objective function (also referred to as a cost function) that maps events or values of one or more variables onto real numbers representing “cost” associated with the events or values and seeks to minimize the cost function”) with variables constrained (Shehab, Paragraph 0047, Lines 1-2 – Paragraph 0048, Line 1, “a combinatorial optimization problem on a set of N binary variables with t constraints)
…
mapping, by the classical computer, the … cost function of the optimization problem to a model Hamiltonian to be implemented on a quantum processor comprising a plurality of trapped ions, each of which has two hyperfine states defining a qubit (Shehab, Paragraph 0042, Lines 7-12, “The combinatorial optimization problem is further mapped onto a simple physical system described by a model Hamiltonian (corresponding to the sum of kinetic energy and potential energy of all particles in the system) and the problem seeks the low-lying energy state of the physical system”; Shehab, Paragraph 0044, Lines 6-8, “the quantum processor is the group 106 of N trapped ions, in which the two hyperfine states of each of the N trapped ions form a qubit”);
selecting, by the classical computer, a set of variational parameters to construct a parametrized quantum circuit comprising an entangling circuit based on the model Hamiltonian and a mixing circuit (Shehab, Paragraph 0049, Lines 1-6, “In block 804, following the mapping of the selected combinatorial optimization problem onto a model Hamiltonian
H
C
=
∑
a
=
1
h
a
p
w
t
a set of variational parameters (
y
→
=
y
1
,
y
2
,
…
,
y
p
,
β
→
=
β
1
,
β
2
,
…
,
β
p
)
is selected, by the classical computer 102, to construct a sequence of gates (also referred to a “trial preparation circuit”)”; Shehab, Paragraph 0049, Lines 11-14, “The trail state preparation circuit
A
(
y
→
,
β
→
) includes p layers (i.e., p-time repetitions) of a model-Hamiltonian circuit … and a mixing circuit”);
setting, by a system controller, the quantum processor in an initial state (Shehab, Paragraph 0050, Lines 1-3, “In block 806, following the selection of a set of variational parameters
y
→
,
β
→
, the quantum processor 106 is set in an initial state
|
ψ
0
by the system controller 104”);
executing one or more iterations (Shehab, Paragraph 0045, Lines 3-4, “The variational method consists of iterations”), each iteration comprising:
applying, by the system controller, the parametrized quantum circuit to the quantum processor based on the set of the variational parameters and the model Hamiltonian, to transform the quantum processor to a trial state (Shehab, Paragraph 0051, Lines 1-5, “In block 808, following the preparation of the quantum processor 106 in the initial state
|
ψ
0
, the trial state preparation circuit
A
(
y
→
,
β
→
) is applied to the quantum processor 106, by the system controller 104, to construct the trail state
|
ψ
(
y
→
,
β
→
)
”);
measuring, by the system controller, an expectation value of the model Hamiltonian (Shehab, Paragraph 0052, Lines 1-5, “In block 810, following the construction of the trial state
|
ψ
(
y
→
,
β
→
)
on the quantum processor 106, the expectation value … of the Pauli term … is measured by the system controller 104”); and
replacing, by the classical computer, the set of the variational parameters with another set of variational parameters, if a difference between the measured expectation value of the model Hamiltonian and the expectation value of the model Hamiltonian measured in a previous iteration is more than a predetermined value (Shehab, Paragraph 0055 – Paragraph 0056, Line 3, In block 816, following the computation of the measured expectation value of the model Hamiltonian
H
C
, the measured expectation value
F
(
y
→
,
β
→
) of the model Hamiltonian
H
C
is compared to the measured expectation value of the model Hamiltonian
H
C
in the previous iteration, by the classical computer 102 … If the difference between the two values is more than the predetermined value, the method proceeds to block 818. In block 818, another set of variational parameters
y
→
,
β
→
for a next iteration of blocks 806-816 is computed by the classical computer 102”); and
outputting, by the classical computer, the set of the variational parameters after executing the one or more iterations (Shehab, Paragraph 0062, Lines 1-5, “In block 820, the classical computer 102 will typically output the results of the variational search to a user interface of the classical computer 102 and/or save the results of the variational search in the memory of the classical computer 102. The results of the variational search will include … the measurement of the trial state
|
ψ
(
y
→
,
β
→
)
in the final iteration”).
Shehab does not explicitly teach the cost function being approximate nor the variables being constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function.
Orus teaches the cost function being approximate and the variables being constrained by an inequality, wherein the inequality constraint is included using a polynomial approximation of a Heaviside step function (Orus, Page 060301-2, Section 3, Subsection A, Lines 3-9, “This equilibrium may not be unique. In general, though, one would have
F
v
→
=
v
→
-
C
~
I
-
C
-
1
D
p
→
-
b
→
v
→
,
p
→
2
≥
0
. The above expression is strictly larger than zero away from equilibrium, and equal to zero and therefore minimum at equilibrium. The vector v at equilibrium will be the one that minimizes the classical cost function F(v) for a given network configuration”; Orus, Page 060301-3, Lines 6-7, “the most viable option is to approximate the Heaviside function by a polynomial expansion”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention, to have modified the hybrid computing method of Shehab to include an approximate cost function with variables constrained by an inequality, where the inequality is included using a polynomial approximation of a Heaviside step function as taught by Orus. The motivation to do so would have been that the Heaviside step function is discontinuous and in order to obtain a Hamiltonian, a continuous function is needed, further, the polynomial approximation will function to make the Hamiltonian easily described. Further, it keeps the cost function easier to handle while remaining nonlinear (Orus, Page 060301-3, Lines 1-5; Orus, Page 060301-3, Paragraph 2).
Regarding claim 17, the rejection of claim 16 is incorporated, and further, the proposed combination teaches wherein the optimization problem is a knapsack problem (Shehab, Paragraph 0041, Final 7 lines, “Another combinatorial optimization problem is the knapsack problem to find a way to pack a knapsack to get the maximum total value, given some items. The knapsack problem is applied to resource allocation given financial constraints in home energy management, network selection for mobile nodes, cognitive radio networks, sensor selection in distributed multiple radar, or the like”).
Regarding claim 18, the rejection of claim 16 is incorporated, and further, the proposed combination teaches wherein a number of the variables equals a number of the plurality of trapped ions (Shehab, Paragraph 0047, Lines 1-2 – Paragraph 0048, Line 1, “In a combinatorial optimization problem on a set of N binary variables with t constraints … The quantum processor 106 has N qubits”; Shehab, Paragraph 0044, Lines 6-8, “the quantum processor is the group 106 of N trapped ions, in which the two hyperfine states of each of the N trapped ions form a qubit”).
Regarding claim 19, the rejection of claim 16 is incorporated, and further, the proposed combination teaches wherein the polynomial approximation of the Heaviside step function includes odd order polynomials (Orus, Page 060301-3, Lines 5-12, “we have found that the most viable option is to approximate the Heaviside function by a polynomial expansion. Of course, such an expansion is not unique. While it would be possible to find the optimal polynomial of a given degree approximating the function in a given interval and for a given error norm[23], standard approximations exist in terms of, e.g., shifted Legendre polynomials [24], which are sufficient to show the validity of our approach. In particular, one can make use of the Fourier-Legendre expansion” A person of ordinary skill in the art would recognize the Fourier-Legendre expansion includes odd order polynomials), and
the maximum number of terms in the model Hamiltonian is the highest order of polynomials in the polynomial approximation of the Heaviside step function (Orus, Page 060301-2, Equation 3, “
F
v
→
=
v
→
-
C
~
I
-
C
-
1
D
p
→
-
b
→
v
→
,
p
→
2
≥
0
”; Orus, Page 060301-3, Equation 6, “
b
→
v
→
,
p
→
≈
β
i
p
→
P
o
l
y
r
(
v
i
-
v
i
c
)
”; Orus, Page 060301-3, Lines 6-9, and Equation 7, “Consider Eqs. (3), (4), and (6) together, one can see after some inspection that
G
x
i
,
a
=
P
o
l
y
r
x
i
,
a
”).
Claims 6-7, 14-15, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Shehab in view of Orus in further view of Kuroda et al., Quantum annealing for ICT system design automation, 08/02/2021, doi: 10.1109/CCGrid51090.2021.00025 hereinafter referred to as “Kuroda”.
Regarding claim 6, the rejection of claim 1 is incorporated, and further, the proposed combination thus far does not explicitly teach wherein the optimization problem is further constrained by one or more equalities.
Kuroda teaches wherein the optimization problem is further constrained by one or more equalities (Kuroda, Page 160, Section B, Lines 1-3, “Because the system requirements include the equality and inequality constraints, we need to represent both of them in the QUBO formulation”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention, to have modified the optimization problem of the proposed combination to include the problem being constrained by one or more equalities as taught by Kuroda. The motivation to do so would have been the ability to optimize the system to fit multiple objectives at once (Kuroda, Page 160, Paragraphs 3-4).
Regarding claim 7, the rejection of claim 1 is incorporated, and further, the proposed combination thus far does not explicitly teach wherein the optimization problem is further constrained by one or more additional inequalities.
Kuroda teaches wherein the optimization problem is further constrained by one or more additional inequalities (Kuroda, Page 160, Section B, Lines 1-3, “Because the system requirements include the equality and inequality constraints, we need to represent both of them in the QUBO formulation”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention to have modified the optimization problem of the proposed combination to include the problem being constrained by one or more additional inequalities as taught by Kuroda. The motivation to do so would have been the ability to optimize the system to fit multiple objectives at once (Kuroda, Page 160, Paragraphs 3-4).
Regarding claim 14, the rejection of claim 8 is incorporated, and further, the proposed combination thus far does not explicitly teach wherein the optimization problem is further constrained by one or more equalities.
Kuroda teaches wherein the optimization problem is further constrained by one or more equalities (Kuroda, Page 160, Section B, Lines 1-3, “Because the system requirements include the equality and inequality constraints, we need to represent both of them in the QUBO formulation”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention, to have modified the optimization problem of the proposed combination to include the problem being constrained by one or more equalities as taught by Kuroda. The motivation to do so would have been the ability to optimize the system to fit multiple objectives at once (Kuroda, Page 160, Paragraphs 3-4).
Regarding claim 15, the rejection of claim 8 is incorporated, and further, the proposed combination thus far does not explicitly teach wherein the optimization problem is further constrained by one or more additional inequalities.
Kuroda teaches wherein the optimization problem is further constrained by one or more additional inequalities (Kuroda, Page 160, Section B, Lines 1-3, “Because the system requirements include the equality and inequality constraints, we need to represent both of them in the QUBO formulation”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention to have modified the optimization problem of the proposed combination to include the problem being constrained by one or more additional inequalities as taught by Kuroda. The motivation to do so would have been the ability to optimize the system to fit multiple objectives at once (Kuroda, Page 160, Paragraphs 3-4).
Regarding claim 20, the rejection of claim 16 is incorporated, and further, the proposed combination thus far does not explicitly teach wherein the optimization problem is further constrained by one or more equalities, and the optimization problem is further constrained by one or more additional inequalities.
Kuroda teaches wherein the optimization problem is further constrained by one or more equalities (Kuroda, Page 160, Section B, Lines 1-3, “Because the system requirements include the equality and inequality constraints, we need to represent both of them in the QUBO formulation”), and
the optimization problem is further constrained by one or more additional inequalities (Kuroda, Page 160, Section B, Lines 1-3, “Because the system requirements include the equality and inequality constraints, we need to represent both of them in the QUBO formulation”).
It would have been obvious to a person of ordinary skill in the art, before the effective filing date of the invention to have modified the optimization problem of the proposed combination to include the problem being constrained by one or more equalities and one or more additional inequalities as taught by Kuroda. The motivation to do so would have been the ability to optimize the system to fit multiple objectives at once (Kuroda, Page 160, Paragraphs 3-4).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Endo et al., Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation, 02/1/2021, https://doi.org/10.7566/JPSJ.90.032001 reviews the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques, the references discloses several variational quantum algorithms including variational quantum eigensolvers and variational quantum simulation algorithms.
Fellner et al., Parity Quantum Optimization: Benchmarks, 05/13/2021, https://arxiv.org/pdf/2105.06240v1 analyzes the gate resources required to implement a single QAOA cycle for real-world scenarios, in particular, the method considers random spin models with higher order terms, as well as the problems of predicting financial crashes and finding ground states of electronic structure Hamiltonians.
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/M.C.S./ Examiner, Art Unit 2122
/KAKALI CHAKI/ Supervisory Patent Examiner, Art Unit 2122
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