DETAILED ACTION
This Office Action is in response to the claims filed on 10/12/2022.
Claims 1-22 are pending.
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 .
Examiner Notes
Examiner cites particular columns, paragraphs, figures and line numbers in the
references as applied to the claims below for the convenience of the applicant. Although
the specified citations are representative of the teachings in the art and are applied to
the specific limitations within the individual claim, other passages and figures may apply
as well. It is respectfully requested that, in preparing responses, the applicant fully
consider the references in their entirety as potentially teaching all or part of the claimed
invention, as well as the context of the passage as taught by the prior art or disclosed
by the examiner. The entire reference is considered to provide disclosure relating to the
claimed invention. The claims & only the claims form the metes & bounds of the
invention. Office personnel are to give the claims their broadest reasonable
interpretation in light of the supporting disclosure. Unclaimed limitations appearing in the
specification are not read into the claim. Prior art was referenced using terminology
familiar to one of ordinary skill in the art. Such an approach is broad in concept and can
be either explicit or implicit in meaning. Examiner's Notes are provided with the cited
references to assist the applicant to better understand how the examiner interprets the
applied prior art. Such comments are entirely consistent with the intent & spirit of
compact prosecution.
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 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.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 10/12/2022 is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Claim Rejections - 35 USC § 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 4-5,13-15, and 17-21 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.
Regarding claims 4 and 5. The claims recite “with a quantum computer”. It is unclear if the claim limitations are to be performed using a quantum computer or if the claim limitations are to be performed for a quantum computer. For purposes of compact prosecution, the Examiner interprets the claims to mean the latter, i.e. the claim limitations are to be performed for a quantum computer.
Clarification is required.
Regarding claims 13 (Ln.3) and 22 (Ln.6). The claims recite “establishing the representation of”. There is insufficient antecedent basis for this limitation in the claims. For purposes of compact prosecution, the Examiner interprets “establishing the representation of” to mean “establishing a representation of”.
Clarification is required.
Regarding claims 13 (Ln.3) and 22 (Ln.7). The claims recite “the initial wavefunction”. There is insufficient antecedent basis for this limitation in the claims. For purposes of compact prosecution, the Examiner interprets “the initial wavefunction” to mean “an initial wavefunction”.
Clarification is required.
Regarding claims 13 (Ln.3) and 22 (Ln.7). The claims recite “the time evolved wavefunction”. There is insufficient antecedent basis for this limitation in the claims. For purposes of compact prosecution, the Examiner interprets “the time evolved wavefunction” to mean “a time evolved wavefunction”.
Clarification is required.
Regarding claim 16 (Ln.1-2), recites “wherein the kinetic energy” and “wherein the potential energy”. There is insufficient antecedent basis for these limitations in the claims. For purposes of compact prosecution, the Examiner interprets “wherein the kinetic energy” and “wherein the potential energy” to mean “wherein kinetic energy” and “wherein potential energy”, respectively.
Clarification is required.
The dependent claims 14-15 and 18-20, included in the statement of rejection but not specifically addressed in the body of the rejection have inherited the deficiencies of their parent claim and have not resolved the deficiencies. Therefore, they are rejected based on the same rationale as applied to their parent claims above.
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 1-22 are rejected under 35 U.S.C. 101 because the claimed invention recites a judicial exception, is directed to that judicial exception (an abstract idea), as it has not been integrated into a practical application and the claim(s) further do/does not recite significantly more than the judicial exception. Examiner has evaluated the claim(s) under the framework provided in MPEP 2106 and has provided such analysis below.
To determine if a claim is directed to patent ineligible subject matter, the Court
has guided the Office to apply the Alice/Mayo test, which requires:
Step 1. Determining if the claim falls within a statutory category of a Process, Machine, Manufacture, or a Composition of Matter (see MPEP 2106.03);
Step 2A. Determining if the claim is directed to a patent ineligible judicial exception consisting of a law of nature, a natural phenomenon, or abstract idea (MPEP 2106.04);
Step 2A is a two-prong inquiry. MPEP 2106.04(II)(A).
Under the first prong, examiners evaluate whether a law of nature, natural phenomenon, or abstract idea is set forth or described in the claim. Abstract ideas include mathematical concepts, certain methods of organizing human activity, and mental processes. MPEP 2106.04(a)(2).
The second prong is an inquiry into whether the claim integrates a judicial exception into a practical application. MPEP 2106.04(d).
Step 2B. If the claim is directed to a judicial exception, determining if the claim recites limitations or elements that amount to significantly more than the judicial exception. (See MPEP 2106).
Step 1:
Claims 1-21 are directed to a method, as such these claims fall within the statutory category of a process.
Claim 22 is directed to a system, as such these claims fall within the statutory category of machine.
Step 2A, Prong 1:
The examiner submits that the foregoing claim limitations constitute abstract ideas, as the claims cover mental processes performed on a computer and/or mathematical concepts, given the broadest reasonable interpretation.
In order to apply Step 2A, a recitation of claims is copied below. The limitations of those claims which describe an abstract idea are bolded.
As per claim 1, the claim recites the limitations of:
computing resultant energy eigenvalues and eigenstate wavefunctions
of the Hamiltonian for one or more quantum states, with a classical computer. (As drafted and under its broadest reasonable interpretation, this limitation amounts to Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Mental Processes are defined as concepts that can practically be performed in the human mind (e.g. observations, evaluations, judgments, opinions), or by a human using pen and paper as a physical aid. For instance, a person can reasonably compute/calculate energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states. 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. Note that the complexity of a mathematical concept or the difficulty of a mental step does not, by itself, render the claim patent-eligible. The Courts do not distinguish between mental processes performed entirely in the mind and those requiring the assistance of a physical aid, such as a pen and paper. Implementing an abstract idea on a generic computer is not enough to make the claim patent-eligible.)
Step 2A, Prong 2:
As per claim 1, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present mere instructions to apply an exception. In particular, the claim recites the additional limitations:
representing wavefunctions using a Cartesian component-separated
tensor-product; (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process.)
representing the Hamiltonian using a Cartesian component-separated
tensor-product; (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process.)
Accordingly, these additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea when considered as an ordered combination and as a whole.
Step 2B:
For step 2B of the analysis, the Examiner must consider whether each claim limitation individually or as an ordered combination amounts to significantly more than the abstract idea. This analysis includes determining whether an inventive concept is furnished by an element or a combination of elements that are beyond the judicial exception. For limitations that were categorized as “apply it” or generally linking the use of the abstract idea to a particular technological environment or field of use, the analysis is the same.
The additional elements as described in Step 2A Prong 2 are not sufficient to amount to significantly more than the judicial exception because the additional limitations are considered directed towards mere instructions to apply an exception. Per MPEP 2106.05(f), “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more.” What’s more, the claim as a whole simply recites only the idea of a solution or outcome, i.e. the claim fails to recite details how a solution to a problem is accomplished.
Per MPEP 2106.05(d), the courts have recognized the following computer functions as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. i. Receiving or transmitting data over a network, ii. Performing repetitive calculations, iii. Electronic recordkeeping, iv. Storing and retrieving information in memory.
For the foregoing reasons, claim 1 is directed to an abstract idea without significantly more and is rejected as not patent eligible under 35 U.S.C. 101.
Step 2A, Prong 1 (Claim 13):
The examiner submits that the foregoing claim limitations constitute abstract ideas, as the claims cover mental processes performed on a computer and/or mathematical concepts, given the broadest reasonable interpretation.
In order to apply Step 2A, a recitation of claims is copied below. The limitations of those claims which describe an abstract idea are bolded.
As per independent claim 13, the claim recites the limitations of:
computing the time evolved wavefunction
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(As drafted and under its broadest reasonable interpretation, this limitation amounts to Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). For instance, a person can reasonably compute / calculate the time evolved wavefunction with the aid of pen/paper. 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. Note that the complexity of a mathematical concept or the difficulty of a mental step does not, by itself, render the claim patent-eligible. The Courts do not distinguish between mental processes performed entirely in the mind and those requiring the assistance of a physical aid. Implementing an abstract idea on a computer is not enough to make the claim patent-eligible.)
Step 2A, Prong 2 (Claim 13):
As per claim 13, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present mere instructions to apply an exception. In particular, the claim recites the additional limitations:
establishing the representation of a physical system; (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process. Also, the claim recites only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished. The recitation of claim limitations that attempt to cover any solution to an identified problem with no restriction on how the result is accomplished and no description of the mechanism for accomplishing the result, does not integrate a judicial exception into a practical application or provide significantly more because this type of recitation is equivalent to the words "apply it".)
representing the initial wavefunction
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(The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process. Also, the claim recites only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished. The recitation of claim limitations that attempt to cover any solution to an identified problem with no restriction on how the result is accomplished and no description of the mechanism for accomplishing the result, does not integrate a judicial exception into a practical application or provide significantly more because this type of recitation is equivalent to the words "apply it".)
representing the Hamiltonian using a Cartesian component-separated tensor- product; (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process.)
Step 2B (Claim 13):
For step 2B of the analysis, the Examiner must consider whether each claim limitation individually or as an ordered combination amounts to significantly more than the abstract idea. This analysis includes determining whether an inventive concept is furnished by an element or a combination of elements that are beyond the judicial exception. For limitations that were categorized as “apply it” or generally linking the use of the abstract idea to a particular technological environment or field of use, the analysis is the same.
The additional elements as described in Step 2A Prong 2 are not sufficient to amount to significantly more than the judicial exception because the additional limitations are considered directed towards mere instructions to apply an exception. Per MPEP 2106.05(f), “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more.” What’s more, the claim as a whole simply recites only the idea of a solution or outcome, i.e. the claim fails to recite details how a solution to a problem is accomplished.
Per MPEP 2106.05(d), the courts have recognized the following computer functions as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. i. Receiving or transmitting data over a network, ii. Performing repetitive calculations, iii. Electronic recordkeeping, iv. Storing and retrieving information in memory.
For the foregoing reasons, claim 13 is directed to an abstract idea without significantly more and is rejected as not patent eligible under 35 U.S.C. 101.
Step 2A, Prong 1 (Claim 22):
The examiner submits that the foregoing claim limitations constitute abstract ideas, as the claims cover mental processes performed on a computer and/or mathematical concepts, given the broadest reasonable interpretation.
In order to apply Step 2A, a recitation of claims is copied below. The limitations of those claims which describe an abstract idea are bolded.
As per independent claim 22, the claim recites the limitations of:
computing the time evolved wavefunction
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(As drafted and under its broadest reasonable interpretation, this limitation amounts to Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). For instance, a person can reasonably compute/calculate the time evolved wavefunction with the aid of pen/paper. 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. Note that the complexity of a mathematical concept or the difficulty of a mental step does not, by itself, render the claim patent-eligible. The Courts do not distinguish between mental processes performed entirely in the mind and those requiring the assistance of a physical aid, such as a pen and paper. Implementing an abstract idea on a computer is not enough to make the claim patent-eligible.)
Step 2A, Prong 2 (Claim 22):
As per claim 22, this judicial exception is not integrated into a practical application because the additional claim limitations outside the abstract idea only present field of use and technological environment and/or mere instructions to apply an exception.
In particular, the claim recites the additional limitations:
quantum hardware, the quantum hardware further comprising a quantum system comprising one or more qubits, and one or more control devices configured to operate the quantum system wherein the apparatus is configured to perform operations comprising: (The additional element amounts to Field of Use and Technological Environment per MPEP 2106.05(h) and/or Mere Instructions to Apply an Exception per MPEP 2106.05(f). The additional elements amount to generally linking the use of a judicial exception (i.e. Mental Processes/Mathematical Concepts) to a particular technological environment or field of use (i.e. quantum system). The claim also recites only the idea of a solution or outcome i.e., the claim fails to recite details of how the control devices operate the quantum system.)
establishing the representation of a physical system; (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). The claim recites only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished. The recitation of claim limitations that attempt to cover any solution to an identified problem with no restriction on how the result is accomplished and no description of the mechanism for accomplishing the result, does not integrate a judicial exception into a practical application or provide significantly more because this type of recitation is equivalent to the words "apply it".)
representing the initial wavefunction
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(The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process. Also, the claim recites only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished. The recitation of claim limitations that attempt to cover any solution to an identified problem with no restriction on how the result is accomplished and no description of the mechanism for accomplishing the result, does not integrate a judicial exception into a practical application or provide significantly more because this type of recitation is equivalent to the words "apply it".)
representing the Hamiltonian using a Cartesian component-separated tensor- product; (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f), i.e. mere instructions to implement an abstract idea on a computer. Specifically, this limitation invokes computers or other machinery merely as a tool to perform an existing process.)
Step 2B (Claim 22):
For step 2B of the analysis, the Examiner must consider whether each claim limitation individually or as an ordered combination amounts to significantly more than the abstract idea. This analysis includes determining whether an inventive concept is furnished by an element or a combination of elements that are beyond the judicial exception. For limitations that were categorized as “apply it” or generally linking the use of the abstract idea to a particular technological environment or field of use, the analysis is the same.
The additional elements as described in Step 2A Prong 2 are not sufficient to amount to significantly more than the judicial exception because the additional limitations are considered directed towards field of use and technological environment and/or mere instructions to apply an exception. Per MPEP 2106.05(h), “As explained by the Supreme Court, a claim directed to a judicial exception cannot be made eligible "simply by having the applicant acquiesce to limiting the reach of the patent for the formula to a particular technological use." Diamond v. Diehr, 450 U.S. 175, 192 n.14, 209 USPQ 1, 10 n. 14 (1981). Thus, limitations that amount to merely indicating a field of use or technological environment (i.e. quantum system) in which to apply a judicial exception do not amount to significantly more than the exception itself, and cannot integrate a judicial exception into a practical application.
Per MPEP 2106.05(f), “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more.” What’s more, the claim as a whole simply recites only the idea of a solution or outcome, i.e. the claim fails to recite details how a solution to a problem is accomplished.
Per MPEP 2106.05(d), the courts have recognized the following computer functions as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. i. Receiving or transmitting data over a network, ii. Performing repetitive calculations, iii. Electronic recordkeeping, iv. Storing and retrieving information in memory.
For the foregoing reasons, claim 22 is directed to an abstract idea without significantly more and is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 2, wherein representing wavefunctions using a Cartesian component-separated tensor-product further comprises: representing wavefunctions using a Cartesian component-separated tensor- product on a plane-wave-dual grid. The additional element simply elaborates on the wavefunction, thus further amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 3, wherein representing the Hamiltonian using a Cartesian component-separated tensor-product further comprises: representing the Hamiltonian using a Cartesian component-separated tensor- product on a plane-wave-dual grid. The additional element simply elaborates on the Hamiltonian, thus further amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 4, determining the number of qubits required for a commensurate calculation with a quantum computer; and determining the number of quantum gates required for a commensurate calculation with a quantum computer. The additional elements amount to Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). As noted in claim 1 above, 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. Note that the complexity of a mathematical concept or the difficulty of a mental step does not, by itself, render the claim patent-eligible. The Courts do not distinguish between mental processes performed entirely in the mind and those requiring the assistance of a physical aid, such as a pen and paper. Implementing an abstract idea on a computer is not enough to make the claim patent-eligible. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 5, using the resultant energy eigenvalues to predict an expected output from a commensurate calculation with a quantum computer;
using the resultant eigenstate wavefunctions to predict an expected output from a commensurate calculation with a quantum computer; and using correlation functions obtained from the eigenstate wavefunctions, to predict an expected output from a commensurate calculation with a quantum computer. The additional elements are directed towards Mere Instructions to Apply an Exception per MPEP 2106.05(f). The claim recites only the idea of a solution or outcome, i.e. fails to recite details as to how to predict an expected outcome. The claim also invoked computers or other machinery merely as a tool to perform an existing process. Note that the recitation of claim limitations that attempt to cover any solution to an identified problem with no restriction on how the result is accomplished and no description of the mechanism for accomplishing the result, does not integrate a judicial exception into a practical application or provide significantly more because this type of recitation is equivalent to the words "apply it". Also, use of a computer or other machinery in its ordinary capacity or simply adding a general purpose computer or computer components after the fact to an abstract idea does not integrate a judicial exception into a practical application or provide significantly more. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 6, wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: establishing optimal component-separated basis sets. The additional element elaborates on the computation of resultant energy eigenvalues and eigenstate wavefunctions, thus is further directed towards Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 7, wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: determining tensor-product Hamiltonian-wavefunction matrix-vector products. The additional element elaborates on the computation of resultant energy eigenvalues and eigenstate wavefunctions, thus is further directed towards Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 8, wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: applying (block) Krylov iteration to generate new Krylov vectors. The additional element elaborates on the computation of resultant energy eigenvalues and eigenstate wavefunctions, thus is further directed towards Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 9, wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: projecting the Hamiltonian onto the Krylov vectors. The additional element elaborates on the computation of resultant energy eigenvalues and eigenstate wavefunctions, thus is further directed towards Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 10, wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: band-pass staging. The additional element elaborates on the computation of resultant energy eigenvalues and eigenstate wavefunctions, thus is further directed towards Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 11, wherein the wavefunctions comprise a Cartesian component-separated tensor product of the form
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. The additional element elaborates on the wavefunctions, thus is further directed towards Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 12, wherein the one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
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respectively. The additional element elaborates on the Hamilton, thus further amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 14, wherein computing the time evolved wavefunction
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further comprises: computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states (The additional element elaborates on the wavefunction computation, thus further amounts to Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I)), with a quantum computer. (The additional element amounts to Mere Instructions to Apply an Exception per MPEP 2106.05(f) and/or Field of Use and Technological Environment per MPEP 2106.05(h))
Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 15, the representation of the physical system is a plane-wave-dual grid-based representation comprising: coordinate grid spacing; minimum and maximum coordinate values; and a number of grid points. The additional elements elaborate on the physical system, thus further amount to Mere Instructions to Apply an Exception per MPEP 2106.05(f). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 16, wherein the kinetic energy is represented in a plane-wave basis representation, the potential energy is represented in component-separated tensor-product form in a plane-wave-dual grid-based representation, and the initial wavefunction
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is represented in a plane-wave-dual grid-based representation. The additional elements amount to Mathematical Concepts per MPEP 2106.04(a)(2)(I). This limitation is directed towards a mathematical relationships and/or mathematical formulas/equations. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols. A claim that recites a numerical formula or equation will be considered as falling within the "mathematical concepts" grouping. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 17, wherein the one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
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respectively. The additional element elaborates on the Hamilton, thus further amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding claim 18, wherein applying the Quantum Phase Estimation algorithm provides a ground state energy level and eigenstate wavefunction. The additional element amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I) and/or Mere Instructions to Apply an Exception per MPEP 2106.05(f). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. Also, the additional element amounts to no more than a recitation of the words "apply it" (or an equivalent) or mere instructions to implement an abstract idea or other exception on a computer. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding claim 19, wherein applying the Quantum Phase Estimation algorithm provides excited state energy levels and eigenstate wavefunctions. The additional element amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I) and/or Mere Instructions to Apply an Exception per MPEP 2106.05(f). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. Also, the additional element amounts to no more than a recitation of the words "apply it" (or an equivalent) or mere instructions to implement an abstract idea or other exception on a computer. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding claim 20, wherein computing the time evolved wavefunction further comprises:
applying a sequence of
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operations with a small time step ε, using the Trotter approximation. The additional element elaborates on the wavefunction computation, thus further amounts to Mental Processes performed on a computer per MPEP 2106.04(a)(2)(III) and/or Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding claim 21, wherein the one-particle and two-particle potential energy contributions to the Trotter approximation,
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31
117
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and
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35
125
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respectively, are implemented using a Cartesian component-separated tensor-product quantum circuit. The additional element elaborates on the Trotter approximation, thus further amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
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 1-17 and 20-21 are rejected under 35 U.S.C. 103 as being unpatentable over Jones, N. Cody, et al. "Faster quantum chemistry simulation on fault-tolerant quantum computers." New Journal of Physics 14.11 (2012): 115023 (hereinafter referred to as “Jones”), in view of Jerke, Jonathan, and Bill Poirier. "Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions." The Journal of Chemical Physics 148, no. 10 (2018) (hereinafter referred to as “Jerke”).
Regarding claim 1, Jones discloses A method for simulating performance of quantum computational chemistry (“We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault tolerant quantum computers” Jones [Abstract]), comprising:
with a classical computer (“All of the terms hpq’s and hpqrs’s are pre-computed numerically with classical computers, and the values are then used in the quantum computer to simulate the Hamiltonian evolution” Jones [Pg.10 last paragraph]).
Jones fails to specifically disclose representing wavefunctions using a Cartesian component-separated tensor- product, representing the Hamiltonian using a Cartesian component-separated tensor- product, and computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states.
However, Jerke discloses representing wavefunctions using a Cartesian component-separated tensor- product; (“in our approach, we are able to represent the numerical wave function essentially exactly, using only around one hundred gigabytes (100 GB) of RAM [...] the success of our approach is the recent development of the so-called “Gaussian-Sinc” technology” Jerke [Pg.1 Col.2 P.2-3]. The utilization of Gaussian-sinc is interpreted as “a cartesian component-separated tensor-product” due to Applicant’s disclosure “This "Gaussian-Sinc" methodology exploits a tensor product expansion of y that factors by Cartesian component [...] This Cartesian component-separated tensor-product approach constitutes a machine learning methodology that can be applied to first-quantized quantum chemistry.” Spec. [P.0074])
representing the Hamiltonian using a Cartesian component-separated tensor- product (“Having obtained the Gaussian-Sinc SOP (sum of products) FBR (full basis representations) of the electronic structure Hamiltonian as per Sec. II C, we can now proceed to the eigensolve phase of the calculation.” Jerke [Pg.5 Sec.III.A]);
and computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, . (“The strategy, then, is to start with a very small basis representation of H (i.e. Hamiltonian), for which block Krylov convergence of the desired eigenvectors (i.e. energy eigenstate wavefunction) is numerically stable. Once this initial calculation is completed—and numerically computed eigenvalues for the given basis duly recorded—a new “stage” is commenced.” Jerke [Pg.7 Col.2 P.4]. Eigenvectors are interpreted as eigenstate wavefunctions due to Applicant’s disclosure “eigenvectors represent the corresponding energy eigenstate wavefunctions” Spec. [P.0075])
Jones and Jerke are analogous art as they both relate to quantum chemistry calculations/simulation. Jones discloses “We aim to demonstrate constructively how quantum computers can simulate chemistry with an efficient use of resources by representing the molecular system with a first-principles Hamiltonian consisting of kinetic energy and Coulomb potential operators between electrons and nuclei.” [Pg.3 P.1], and Jerke discloses “Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy [...] The method also allows for exact wave functions to be computed, as well as energy levels” [Abstract].
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have modified the performance optimization methods of Jones to include the calculation methods of Jerke in order to “greatly reduce computer memory (RAM) storage requirements” Jerke [Pg.1 Col.1 P.1].
Regarding claim 2, Jones in view of Jerke disclose the method of claim 1, Jerke further discloses wherein representing wavefunctions using a Cartesian component-separated tensor-product further comprises: representing wavefunctions using a Cartesian component-separated tensor- product on a plane-wave-dual grid. (“in our approach, we are able to represent the numerical wave function essentially exactly, using only around one hundred gigabytes (100 GB) of RAM [...] the success of our approach is the recent development of the so-called “Gaussian-Sinc” technology (i.e. cartesian component-separated tensor-product)” Jerke [Pg.1 Col.2 P.2-3]. The utilization of Gaussian-sinc is interpreted as “a cartesian component-separated tensor-product” due to reasons previously disclosed in claim 1. The use is also interpreted as plane-wave dual grid due to Applicant’s disclosure “what is also referred to here as the "plane wave dual" or "Sinc" representation” Spec. [P.0070])
Jerke discloses the limitations of claim 2 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 3, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein representing the Hamiltonian using a Cartesian component-separated tensor-product further comprises: representing the Hamiltonian using a Cartesian component-separated tensor- product on a plane-wave-dual grid. (“Having obtained the Gaussian-Sinc (i.e. cartesian component-separated tensor-product) SOP (sum of products) FBR (full basis representations) of the electronic structure Hamiltonian as per Sec. II C, we can now proceed to the eigensolve phase of the calculation.” Jerke [Pg.5 Sec.III.A]. The utilization of Gaussian-sinc is interpreted as “a cartesian component-separated tensor-product” due to reasons previously disclosed in claim 1. The use is also interpreted as plane-wave dual grid due to Applicant’s disclosure “what is also referred to here as the "plane wave dual" or "Sinc" representation” Spec. [P.0070])
Jerke discloses the limitations of claim 3 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 4, Jones-Jerke disclose the method of claim 1, Jones further discloses determining the number of qubits required for a commensurate calculation with a quantum computer; (“Using the hypothetical quantum computer from section 2.4, we examine the resources required to perform simulation in second-quantized form. Estimates of the number of qubits required for various instances of second-quantized chemical simulation have been reported” Jones [Pg.17 Sec.3.4]) and determining the number of quantum gates required for a commensurate calculation with a quantum computer. (“we focus instead on the execution time and effort to prepare fault-tolerant gates (here we consider the number of T gates). Figure 12 shows both the circuit depth and the number of T gates required to simulate LiH in the STO-3G basis” Jones [Pg.17 Sec.3.4])
Jones discloses the limitations of claim 4 and maintains the same rationale for combination with Jerke as claim 1.
Regarding claim 5, Jones-Jerke disclose the method of claim 1, Jerke further discloses using the resultant energy eigenvalues to predict an expected output from a commensurate calculation with a quantum computer; using the resultant eigenstate wavefunctions to predict an expected output from a commensurate calculation with a quantum computer; (“The primary goal of the calculations performed here is to compute the ground and several excited electronic states (K
≈
10) of the helium atom, to chemical accuracy—i.e., to within 1–2 mhartree or better. In addition, a test calculation of the ground state energy of the hydrogen atom, and of the three lowest-lying energies of the hydrogen molecule at several nuclear separations, was also performed as a proof of concept.” Jerke [Pg.8 IV.Results]. Given the information disclosed by Jerke, the Examiner interprets the calculated results were derived from the use of resultant eigenvalues and eigenstate wavefunctions. Also note Examiners interpretation of “with a quantum computer” in Claim Interpretation section above.) and
using correlation functions obtained from the eigenstate wavefunctions, to predict an expected output from a commensurate calculation with a quantum computer. (“In Fig. 6, we present radial correlation functions. The ground state distribution is again singly peaked; it agrees very well with an extremely accurate, many-point Hylleraas-basis calculation, performed previously by Coulson and Neilson. In particular, both calculations predict a peak of 0.6 at r = 1.1 bohrs. The excited state radial correlation functions presented in Fig. 6—as obtained from accurately converged,
full 6D wave functions” Jerke [Pg.12 Col.1 P.1])
Jerke discloses the limitations of claim 5 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 6, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, (See Jones, claim 1), further comprises: establishing optimal component-separated basis sets. (“starting from a small basis and working up through larger basis sets, each time using the output of the preceding stage as input for the next stage, until basis set convergence of all K desired eigenvectors is achieved to the desired level of accuracy.” Jerke [Pg.7 Col.2 P.5])
Jerke discloses the limitations of claim 6 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 7, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: determining tensor-product Hamiltonian-wavefunction matrix-vector products. (“Once the foundation vectors are computed, successive matrix–vector products with Hk1k2,l1l2 are applied separately to each, in order to generate the set of all block Krylov vectors,
Φ
Λ
n
n
,
b
. [...] The resultant block Krylov vectors are then used to generate the MB X MB Hamiltonian matrix HBK (and overlap matrix SBK), which is diagonalized using a generalized eigensolver.” Jerke [Pg.6 Col.1 P.6 – Col.2 P.1])
Jerke discloses the limitations of claim 7 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 8, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, (see Jones, claim 1), further comprises: applying (block) Krylov iteration to generate new Krylov vectors. (“a “staging” algorithm is introduced, as a modification to the block Krylov procedure. After a certain number of iterations M, the set of MB Krylov vectors is replaced with a smaller set of B’ new vectors, each with rank Λ’0 = 1.” Jerke [Pg.7 Col.1 P.4])
Jerke discloses the limitations of claim 8 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 9, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, (see Jones, claim 1), further comprises: projecting the Hamiltonian onto the Krylov vectors. (“After a certain number of iterations M, the set of MB Krylov vectors is replaced with a smaller set of B’ new vectors, each with rank Λ’0 = 1. The new vectors then serve as the foundation for a new block Krylov cycle—which can again be restarted after M’ new iterations, etc.” Jerke [Pg.7 Sec.D P.2]. The resulting B’ new vectors are interpreted as the result of projecting the Hamiltonian onto the Krylov vectors due to Applicant’s disclosure “After every few iterations, the matrix H (i.e. Hamiltonian) is projected onto the set of all Krylov vectors defined up to that point. The result is a much smaller matrix, h, with eigenvalues close to those of H itself, at the bottom of the spectrum.” Spec. [P.0103])
Jerke discloses the limitations of claim 9 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 10, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, with a classical computer, further comprises: band-pass staging. (See Jerke Pg.7 Sec. D. Bandpass staging)
Jerke discloses the limitations of claim 10 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 11, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein the wavefunctions comprise a Cartesian component-separated tensor product of the form
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56
363
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.
(The cited wave expression is interpreted as a product of 3 functions (
X
,
Y
,
Z
), each depending on a set of coordinates (
x
N
,
y
N
,
z
N
). As shown in claim 1, Jerke [Pg.1 Col.2 P.2-3] discloses wavefunctions using a Cartesian component-separated tensor- product (see Gaussian Sinc technology), which “are naturally expressed in a sum-of-products (SOP) form” Jerke [Pg.1 Col.2 P.3]. By definition, wavefunctions comprising Cartesian component-separated tensor products are of the cited wave expression.)
Jerke discloses the limitations of claim 11 and maintains the same rationale for combination with Jones as claim 1.
Regarding claim 12, Jones-Jerke disclose the method of claim 1, Jerke further discloses wherein the one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
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44
484
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respectively. (The cited expressions are interpreted as Cartesian component-separated tensor products. Jerke [Pg.4 Sec.C.2 and C.3] discloses electron-electron (i.e. two-particle) interaction and external (i.e. one-particle) potential energy contributions expressed in the Gaussian-Sinc form. For reasons given in claim 1, the Gaussian-Sinc form is interpreted as Cartesian component-separated tensor products. Therefore, Jerke’s disclosed one/two-particle potential energy contributions are interpreted to be in the form of the cited expressions.)
Jerke discloses the limitations of claim 12 and maintains the same rationale for combination with Jones as claim 1.
Regarding independent claim 13, Jones discloses A method for performing first-quantized quantum computational chemistry (Jones [Pg.19 4. Simulating chemical structure and dynamics in a first-quantized representation]) comprising:
establishing the representation of a physical system; We aim to demonstrate
constructively how quantum computers can simulate chemistry with an efficient use of resources by representing the molecular system with a first-principles Hamiltonian consisting of kinetic energy and Coulomb potential operators between electrons and nuclei.” Jones [Pg.3 P.1])
representing the initial wave function
|
ψ
0
⟩
; (“After preparing an initial state |ψ0
⟩
, the system is evolved” Jones [Pg.4 Figure 1])
and computing the time evolved wavefunction
ψ
t
=
U
^
t
|
ψ
0
⟩
. (“After preparing an initial state |ψ0
⟩
, the system is evolved in simulated time by solving the time-dependent Schrodinger equation.” Jones [Pg.4 Figure 1])
Jones fails to specifically disclose representing the Hamiltonian using a Cartesian component-separated tensor- product.
However, Jerke discloses representing the Hamiltonian using a Cartesian component-separated tensor- product (“Having obtained the Gaussian-Sinc SOP (sum of products) FBR (full basis representations) of the electronic structure Hamiltonian as per Sec. II C, we can now proceed to the eigensolve phase of the calculation.” Jerke [Pg.5 Sec.III.A]. The utilization of Gaussian-sinc is interpreted as “a cartesian component-separated tensor-product” due to Applicant’s disclosure “This "Gaussian-Sinc" methodology exploits a tensor product expansion of y that factors by Cartesian component [...] This Cartesian component-separated tensor-product approach constitutes a machine learning methodology that can be applied to first-quantized quantum chemistry.” Spec. [P.0074]).
Jones and Jerke are analogous art as they both relate to quantum chemistry calculations/simulation. Jones discloses “We aim to demonstrate constructively how quantum computers can simulate chemistry with an efficient use of resources by representing the molecular system with a first-principles Hamiltonian consisting of kinetic energy and Coulomb potential operators between electrons and nuclei.” [Pg.3 P.1], and Jerke discloses “Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy [...] The method also allows for exact wave functions to be computed, as well as energy levels” [Abstract].
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have modified the performance optimization methods of Jones to include representing the Hamiltonian using a Cartesian component-separated tensor- product, as taught by Jerke, since its “naturally expressed in a sum-of-products (SOP) form, which reduces RAM requirements tremendously” Jerke [Pg.1 Col.2 P.3].
Regarding claim 14, Jones in view of Jerke disclose the method of claim 13, Jones further discloses wherein computing the time evolved wavefunction
ψ
t
=
U
^
t
|
ψ
0
⟩
further comprises: computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states (“we narrow our focus to quantum chemistry problems such as calculating the eigenvalues of a molecular Hamiltonian [...] by representing the molecular system with a first-principles Hamiltonian consisting of kinetic energy and Coulomb potential operators between electrons and nuclei” Jones [Pg.2-3 1.Intro.], with a quantum computer (“We propose methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault tolerant quantum computers.) Jones [Abstract])
Jones discloses the limitations of claim 14 and maintains the same rationale for combination with Jerke as claim 13.
Regarding claim 15, Jones-Jerke disclose the method of claim 13, Jerke further discloses the representation of the physical system is a plane-wave-dual grid-based representation (“in our approach, we are able to represent the numerical wave function essentially exactly, using only around one hundred gigabytes (100 GB) of RAM [...] the success of our approach is the recent development of the so-called “Gaussian-Sinc” technology (i.e. cartesian component-separated tensor-product)” Jerke [Pg.1 Col.2 P.2-3]. The utilization of Gaussian-sinc is interpreted as “a cartesian component-separated tensor-product” due to reasons previously disclosed in claim 1. The use is also interpreted as plane-wave dual grid due to Applicant’s disclosure “what is also referred to here as the "plane wave dual" or "Sinc" representation” Spec. [P.0070])
comprising: coordinate grid spacing; minimum and maximum coordinate values (“a new Sinc basis representation that is better converged, with respect to both resolution (lattice spacing) and coordinate range” Jerke [Pg.7 Col.2 P.4]. Coordinate range is interpreted to include a min/max coordinate value.); and a number of grid points. (“the new Gaussian-Sinc technology makes it possible to represent singular Coulombic potential interactions robustly, with no special heed taken vis-`a-vis the placement of grid points; it is even possible to place a grid point directly on a singularity” Jerke [Pg.13 Col.1 P.3])
Jerke discloses the limitations of claim 15 and maintains the same rationale for combination with Jones as claim 13.
Regarding claim 16, Jones-Jerke disclose the method of claim 13, Jones further discloses wherein the kinetic energy is represented in a plane-wave basis representation (“The kinetic energy is the sum of individual kinetic energy operators on each particle [...] By performing a QFT along each spatial dimension of the wavefunction, the system representation is transformed from position basis to momentum basis (i.e. plane-wave basis)” Jones [Pg.32 P.4]. Momentum basis is interpreted to be plane-wave due to Applicant’s disclosure “Elements of the first-quantized Hamiltonian may be written in the following basis representations: plane wave (i.e., Fourier, or momentum- space)” Spec. [P.0060]),
Jerke further discloses the potential energy is represented in component-separated tensor-product form in a plane-wave-dual grid-based representation (“Potential energy curves for the lowest three hydrogen molecule electronic states, as computed using Cartesian Sinc (i.e. Gaussian sinc) SOP FBR (i.e. sum of products full basis representation) calculation.” Jerke [Pg.9 FIG.1]. Cartesian Sinc SOP is interpreted as component-separated tensor-product form because “in our approach, we are able to represent the numerical wave function essentially exactly [...] the success of our approach is the recent development of the so-called “Gaussian-Sinc” technology” Jerke [Pg.1 Col.2 P.2-3]. The utilization of Gaussian-sinc is interpreted as “a cartesian component-separated tensor-product” due to Applicant’s disclosure “This "Gaussian-Sinc" methodology exploits a tensor product expansion of y that factors by Cartesian component [...] This Cartesian component-separated tensor-product approach constitutes a machine learning methodology that can be applied to first-quantized quantum chemistry.” Spec. [P.0074]. The use is also interpreted as plane-wave dual grid due to Applicant’s disclosure “what is also referred to here as the "plane wave dual" or "Sinc" representation” Spec. [P.0070]),
Jones further discloses and the initial wavefunction |
ψ
0
⟩
is represented in a plane-wave-dual grid-based representation. (“After preparing an initial state |ψ0
⟩
, the system is evolved” Jones [Pg.4 Figure 1]. See claim 15 Jerke [Pg.1 Col.2 P.2-3] for plane-wave-dual-grid-based representation.)
Jones-Jerke disclose the limitations of claim 16 and maintain the same rationale for combination as claim 13.
Regarding claim 17, Jones-Jerke disclose the method of claim 13, Jerke further discloses wherein the one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
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48
478
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respectively. (The cited expressions are interpreted as Cartesian component-separated tensor products. Jerke [Pg.4 Sec.C.2 and C.3] discloses electron-electron (i.e. two-particle) interaction and external (i.e. one-particle) potential energy contributions expressed in the Gaussian-Sinc form. For reasons given in claim 1, the Gaussian-Sinc form is interpreted as Cartesian component-separated tensor products. Therefore, Jerke’s disclosed one/two-particle potential energy contributions are interpreted to be in the form of the cited expressions.)
Jerke discloses the limitations of claim 17 and maintains the same rationale for combination with Jones as claim 13.
Regarding claim 20, Jones-Jerke disclose the method of claim 13, Jones further discloses wherein computing the time evolved wavefunction
ψ
t
=
U
^
t
|
ψ
0
⟩
further comprises: applying a sequence
U
^
ε
|
ψ
⟩
of operations with a small time step ε, using the Trotter approximation. (“Let us outline how first-quantized simulation works before delving into details. The core of the algorithm is evolving the Hamiltonian in simulated time, achieved by applying the propagator
U
(t) = exp(−i
H
t) (setting
ℏ
= 1 and assuming
H
is time-independent), which solves the time-dependent Schrodinger equation [2]. This process is readily achieved using the split operator approximation, a form of Trotter–Suzuki decomposition [19, 27, 65, 66], where the kinetic and potential energy operators are simulated in alternating steps as
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59
444
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” Jones [Pg.20 P.2])
Jones discloses the limitations of claim 20 and maintains the same rationale for combination with Jerke as claim 13.
Regarding claim 21, Jones-Jerke disclose the method of claim 20, Jones further discloses wherein the one-particle and two-particle potential energy contributions to the Trotter approximation,
e
x
p
(
-
i
ε
V
^
e
x
t
)
|
ψ
1
⟩
and
e
x
p
(
-
i
ε
V
^
e
e
)
|
ψ
12
⟩
, respectively, are implemented using a Cartesian component-separated tensor-product (see Jerke claim 16) quantum circuit. (“This process is readily achieved using the split operator approximation, a form of Trotter–Suzuki decomposition [...]To make an algorithm fault-tolerant, its constituent operations must be decomposed into circuits of fault-tolerant primitive gates such as those in table 1. Consider the potential energy propagator
e
-
1
T
δ
t
as an example. Given a b-particle (i.e. one-particle and/or two-particle) wavefunction in the position basis as
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62
454
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where c(·) is the complex amplitude as a function of position in configuration space and subscripts correspond to particles in the system” Jones [Pg.20 P.2-3])
Jones-Jerke disclose the limitations of claim 21 and maintain the same rationale for combination as claim 13.
Claims 18 and 19 are rejected under 35 U.S.C. 103 as being unpatentable over Jones, N. Cody, et al. "Faster quantum chemistry simulation on fault-tolerant quantum computers." New Journal of Physics 14.11 (2012): 115023 (hereinafter referred to as “Jones”), in view of Jerke, Jonathan, and Bill Poirier. "Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions." The Journal of Chemical Physics 148, no. 10 (2018) (hereinafter referred to as “Jerke”), and in view of Kassal, Ivan, James D. Whitfield, Alejandro Perdomo-Ortiz, Man-Hong Yung, and Alán Aspuru-Guzik. "Simulating chemistry using quantum computers." Annual review of physical chemistry 62, no. 1 (2011): 185-207 (hereinafter referred to as “Kassal”).
Regarding claim 18, Jones-Jerke disclose the method of claim 13 but fail to specifically disclose the limitations of claim 18. However, Kassal discloses wherein applying the Quantum Phase Estimation algorithm provides a ground state energy level and eigenstate wavefunction. (“in order to measure an observable A, one would like to carry out a measurement in its eigenbasis {
|
e
k
⟩
}. This is achieved by the phase-estimation algorithm (PEA) [...] if the eigenstates are nondegenerate, the wave function will collapse to the eigenvector
|
e
k
⟩
” Kassal [Pg.194 P.2], “In the previous section, we describe how the PEA can be used to measure a quantum state in the eigenbasis of a Hermitian operator. This suggests a method for preparing a ground state: Measuring in the eigenbasis of the Hamiltonian will project a state
|
ψ
⟩
to the ground state
|
g
⟩
with probability
ψ
g
|
2.” Kassal [Pg.195 Sec.3.4.1]. See Fig.d below for ground state energy levels.)
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522
816
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Kassal is analogous art as it relates to quantum chemistry calculations / simulation. Kassal discloses “quantum algorithms for the exact, nonadiabatic simulation of chemical dynamics as well as for the full configuration interaction (FCI) treatment of electronic structure. We also discuss solving chemical optimization problems, such as lattice folding, using adiabatic quantum computation (AQC). Finally, we describe recent experimental implementations of these algorithms, including the first quantum simulations of chemical systems” [Pg.186 1.Introduction]. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have modified the Jones-Jerke combination to apply the Quantum Phase Estimation algorithm in order to efficiently find the eigenvalues (phases) of the disclosed quantum systems.
Regarding claim 19, Jones-Jerke disclose the method of claim 13, but fail to specifically disclose the limitations of claim 13. However, Kassal discloses wherein applying the Quantum Phase Estimation algorithm provides excited state energy levels and eigenstate wavefunctions. (“in order to measure an observable A, one would like to carry out a measurement in its eigenbasis {
|
e
k
⟩
}. This is achieved by the phase-estimation algorithm (PEA) [...] if the eigenstates are nondegenerate, the wave function will collapse to the eigenvector
|
e
k
⟩
” Kassal [Pg.194 P.2], “assuming the PEA can be implemented efficiently, we can prepare the thermal state of any classical or quantum Hamiltonian” Kassal [Pg.196 P.1]. See Fig.d above for exited state energy levels.)
Kassal discloses the limitations of claim 19 and maintains the same rationale for combination with Jones-Jerke as claim 18.
Claim 22 is rejected under 35 U.S.C. 103 as being unpatentable over
Babbush US Pub. No. 20200117698 (hereinafter referred to as “Babbush”), in view of
Jones, N. Cody, et al. "Faster quantum chemistry simulation on fault-tolerant quantum computers." New Journal of Physics 14.11 (2012): 115023 (hereinafter referred to as “Jones”), in view of Brown, James, and James D. Whitfield. "Basis set convergence of Wilson basis functions for electronic structure." The Journal of Chemical Physics 151, no. 6 (2019) (hereinafter referred to as “Brown”).
Regarding independent claim 22, Babbush discloses An apparatus comprising: quantum hardware, the quantum hardware further comprising a quantum system comprising one or more qubits, and one or more control devices configured to operate the quantum system wherein the apparatus is configured to perform operations comprising: (“the quantum hardware 102 may include a quantum system 110 and control devices 112 for controlling the quantum system 112. The quantum system 110 may include one or more multi-level quantum subsystems, e.g., qubits or qudits.” Babbush [P.0037-38])
establishing the representation of a physical system; (“The input data may include data representing a first Hamiltonian characterizing the physical system that is to be modeled or simulated.” Babbush [P.0035])
Babbush fails to specifically disclose representing the initial wavefunction, representing the Hamilton using Cartesian component-separated tensor-product, and computing the time evolved wavefunction.
However, Jones discloses representing the initial wavefunction |
ψ
0
⟩
; (“After preparing an initial state |
ψ
0
⟩
” Jones [Pg.4 Fig.1])
and computing the time evolved wavefunction
ψ
t
=
U
^
t
|
ψ
0
⟩
; (“the system is evolved in simulated time by solving the time-dependent Schrodinger equation.” Jones [Pg.4 Fig.1])
Babbush and Jones are analogous art as they both relate to quantum chemistry computation. Babbush discloses “methods and systems for performing second quantized simulations of interacting electrons using a plane wave dual basis” [P.0003] and Jones discloses “efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time.” [Abstract]. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have combined the apparatus of Babbush with the methods, as taught by Jones, in order to “substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault tolerant quantum computers” Jones [Abstract].
Babbush and Jones fail to specifically disclose representing the Hamilton using Cartesian component-separated tensor-product.
However, Brown discloses representing the Hamilton using Cartesian component-separated tensor-product; (“This section outlines all the integrals needed to define the Hamiltonian representation [...] Exploiting grid based basis sets and a sum-of-product decomposition of the Hamiltonian into its three Cartesian product has been applied to the electronic structure, using a multiresolution disjoint Legendre polynomial basis, and a tensor decomposed sinc function basis.” Brown [Pg.4 Sec.III])
Brown is analogous art as it relates to numerical representation of the electronic structure of chemical systems. Brown discloses “To calculate electronic energies of a variety of small molecules and states, we utilize the sum-of-products form, Gaussian quadratures, and introduce methods for selecting sample points from a grid of phase-space localized Wilson basis” [Abstract]. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to have represented the Hamilton using Cartesian component-separated tensor-products, as Brown discloses, with the Babbush-Jones combination since “This reduces memory requirements and can be used to perform matrix-vector products more efficiently using sequential summation” Brown [Pg.2 P.2].
Conclusion
The prior art made of record, listed on form PTO-892, and not relied upon is
considered pertinent to applicant's disclosure:
Rubin (Simulating Quantum Systems With Quantum Computation – US Pub. No 10984152 B2). “The quantum system is simulated by operating the set of models on a computer system that includes a classical processor unit and multiple unentangled quantum processor units (QPUs), and the unentangled QPUs operate the respective subsystem models. In some examples, density matrix embedding theory (DMET) is used to compute an approximate ground state energy for the quantum system” [Abstract]
Pednault et al. (Simulating Quantum Circuits – US Pub. No 11250190 B2). “The present invention relates generally to quantum circuits, and more particularly to simulating quantum circuits.” [P.0001]
Cao et al. (Hybrid Quantum-classical Computer System And Method For Optimization – US Patent No 11488049 B2). “A hybrid quantum-classical computing method for solving optimization problems though applications of non-unitary transformations.” [Col.2 Ln.21]
Hastings et al. (Classical Simulation Constants And Ordering For Quantum Chemistry Simulation – US Patent No 10417370 B2). “Quantum computations based on second quantization are performed by applying one body and two body terms in a selected order. Typically, terms associated with operators that commute are applied prior to application of other terms.” [Abstract]
Cao, Yudong, Jonathan Romero, Jonathan P. Olson, Matthias Degroote, Peter D. Johnson, Mária Kieferová, Ian D. Kivlichan et al. "Quantum chemistry in the age of quantum computing." Chemical reviews 119, no. 19 (2019): 10856-10915. “This article is an overview of the algorithms and results that are relevant for quantum chemistry.” [Abstract]
Kassal, Ivan, et al. "Polynomial-time quantum algorithm for the simulation of chemical dynamics." Proceedings of the National Academy of Sciences 105.48 (2008): 18681-18686. “we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time.” [Abstract]
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/ANTHONY CHAVEZ/ Examiner, Art Unit 2186
/RENEE D CHAVEZ/Supervisory Patent Examiner, Art Unit 2186