DETAILED ACTION
Receipt of Applicant’s amendment filed 07/20/2026 is acknowledged.
Claims 1, 4, 5, 12-19, 21, and 22 have been amended.
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. Examiner may also include cited interpretations encompassed within parenthesis, e.g. (Examiner’s interpretation), for clarity. 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.
Response to Arguments
Claim Rejections under 35 U.S.C. § 112(b):
Acknowledgement is made of amended claims 4, 5, 13-15 and 17-21 to address indefiniteness issues. Previous rejections to claims 4, 5, 13-15, and 17-21 due to indefiniteness in Office Action dated 1/21/2026 are withdrawn. However, amendments to claims have introduced more rejections. See Claim Rejections - 35 U.S.C. § 112 section below.
Claim Rejections under 35 U.S.C. § 101:
Acknowledgement is made of amended claims. Applicant’ arguments have been fully considered but not persuasive. Significant claim amendments warrant new grounds of rejection. See Claim Rejections - 35 U.S.C. §101 section below. Rejections to claims 1-22 remain.
Applicant argues that the amended claims are not directed to mathematical concepts nor mental processes and cannot practically be per formed in the human mind under Step 2A Prong 1 of the Office’s Patent Subject Matter Eligibility test (i.e. Alice/Mayo test). The Examiner respectfully disagrees.
As shown in Claim Rejections – 35 U.S.C. §101 section below, several claim 1 limitations were identified as reciting mathematical concepts. Per MPEP 2106.04(a)(2)(I), the mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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. In addition, there are instances where a formula or equation is written in text format that should also be considered as falling within this grouping. 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, e.g., performing an arithmetic operation such as exponentiation. There is no particular word or set of words that indicates a claim recites a mathematical calculation. That is, a claim does not have to recite the word "calculating" in order to be considered a mathematical calculation. Additionally, per MPEP 2106.04(a)(2)(III) the courts consider a mental process (thinking) that "can be performed in the human mind, or by a human using a pen and paper" to be an abstract idea. Accordingly, the "mental processes" abstract idea grouping is defined as concepts performed in the human mind, and examples of mental processes include observations, evaluations, judgments, and opinions. The courts do not distinguish between mental processes that are performed entirely in the human mind and mental processes that require a human to use a physical aid (e.g., pen and paper or a slide rule) to perform the claim limitation. Nor do the courts distinguish between claims that recite mental processes performed by humans and claims that recite mental processes performed on a computer. Note that the complexity of a mathematical concept or the difficulty of a mental step does not, by itself, render the claim patent-eligible. Thus, Applicant’s argument not persuasive.
Applicant argues that under Step 2A Prong 2 of the Office’s Patent Subject Matter Eligibility test, the claims integrate the alleged exception into a practical application since the claims “provide a set of steps that improve computer-related technology” and cites Ex Parte Desjardins, Appeal No. 2024-000567, and Memorandum from Robert Bahr to the Patent Examining Corps dated November 2, 2016 as basis for argument. The Examiner respectfully disagrees.
Per MPEP 2106.05(a), “if the specification explicitly sets forth an improvement but in a conclusory manner (i.e., a bare assertion of an improvement without the detail necessary to be apparent to a person of ordinary skill in the art), the examiner should not determine the claim improves technology. An indication that the claimed invention provides an improvement can include a discussion in the specification that identifies a technical problem and explains the details of an unconventional technical solution expressed in the claim, or identifies technical improvements realized by the claim over the prior art.” After review of the Specification, arts of reference (see Claim Rejections – 35 U.S.C. §103), and after careful patent eligibility reanalysis, the Examiner respectfully disagrees that the claimed invention provides an unconventional technical solution to a technical problem and/or integrates into a practical application.
Applicant argues the amended claims present significantly more that the alleged abstract idea under Step 2B of the Office’s Patent Subject Matter Eligibility test and are “analogous to the self-referential table of Enfish”. The Examiner respectfully disagrees.
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 identified 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 Insignificant Extra-Solution Activity (i.e. mere data gathering). Per MPEP 2106.05(g), the addition of insignificant extra-solution activity does not amount to an inventive concept, particularly when the activity is well-understood or conventional. Per MPEP 2106.05(d), “[t]he courts have recognized the following (i.e. applicable) 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”. The identified additional limitation of receiving, at a classical computer, data characterizing physical system comprising a first-quantized physical system is considered well-understood, routine, and conventional. As Berkheimer evidence, see Cao/Jones in Claim Rejections – 35 U.S.C. §103 section below. Thus, Applicant’s argument not persuasive.
Applicant’s argument regarding “…the claim fails to recite details of how a solution to a problem is accomplished” is moot given new grounds of rejection necessitated by amendment.
Applicant argues amended independent claim 13 is not directed to an abstract idea because it “describe[s] a specific improvement that addresses a technical problem” and is “significantly more” than any alleged abstract idea. Per reasons previously discussed, Applicant’s argument not persuasive.
Applicant argues amended independent claim 22 is not directed to an abstract idea due to the “physical arrangement of elements of a quantum system”. The Examiner respectfully disagrees.
As shown in Claim Rejections – 35 U.S.C. §101 section below, the claim is directed towards Mathematical Concepts and/or Mental Processes performed on a computer. Physical arrangement of elements of a quantum system does not negate that the claim is directed towards an abstract idea. The additional of a quantum system to implement the abstract idea amounts to Field of Use and Technological Environment per MPEP 2106.05(h) under Step 2A Prong 2. Per MPEP 2106.05(h), “[a]s 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. Applicant’s argument not persuasive.
Claim Rejections under 35 U.S.C. § 103:
Acknowledgement is made of amended claims. Applicant’ arguments have been considered, but are not persuasive. Significant claim amendments warrant new grounds of rejection. See Claim Rejections - 35 U.S.C. §103 section below. Rejections to claims 1-22 remain.
Applicant’ arguments with respect to Jones in view of Jerke (claims 1-17 and 20-21), i.e. the combination thereof and the use of classical vs quantum computers, have been considered but are moot because the new ground of rejection does not rely on any reference applied in the prior rejection of record for any teaching or matter specifically challenged in the argument. See Cao in view of Jones (claims 1-3, 13-17, and 20-22), See Cao in view of Jones in further view of Moll (claim 4), and Cao in view of Jones in further view of Jerke (claims 5-12) in Claim Rejections - 35 U.S.C. §103 section below.
In response to applicant's argument regarding claims 18 and 19 that Kassal’s disclosed use of Quantum Phase Estimation (QPE) differs from “the application of QPE in the claims”, a recitation of the intended use of the claimed invention must result in a structural difference between the claimed invention and the prior art in order to patentably distinguish the claimed invention from the prior art. If the prior art structure is capable of performing the intended use, then it meets the claim. Thus, Applicant’s argument not persuasive.
Applicants’ argument with respect to Babbush in view of Jones in further view of Brown (claim 22), i.e. the combination thereof, has been considered but moot because the new ground of rejection does not rely on any reference applied in the prior rejection of record for any teaching or matter specifically challenged in the argument. See Cao in view of Jones in Claim Rejections - 35 U.S.C. §103 section below.
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.
Claim 22 is 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 22, Ln.6 states “one or more quantum wavefunction and ancilla qubits”. It is unclear what a quantum wavefunction qubit is. Applicant fails to specifically disclose and/or define this term, rendering the claim indefinite. For purposes of compact prosecution, the examiner interprets this term to mean a probabilistic state of the ancilla qubit. Clarification is required.
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 an apparatus, as such these claims fall within the statutory category of machine.
Step 2A, Prong 1 (Claim 1):
The examiner submits that the foregoing claim limitations constitute abstract ideas, as the claims cover Mathematical Concepts and/or Mental Processes, 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:
representing, with the classical computer, wavefunctions associated with
the physical system, using a Cartesian component- separated tensor-product (As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.);
representing, with the classical computer, a Hamiltonian, associated with
the physical system, using a Cartesian component- separated tensor-product (As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.);
computing, with the classical computer, resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states (As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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, e.g., performing an arithmetic operation such as exponentiation. There is no particular word or set of words that indicates a claim recites a mathematical calculation. That is, a claim does not have to recite the word "calculating" in order to be considered a mathematical calculation.)
determining, with the classical computer, quantum resources required for a commensurate first-quantized calculation for a quantum computer (As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts and/or Mental Processes per MPEP 2106.04(a)(2)(I)/(III). The courts consider a mental process (thinking) that "can be performed in the human mind, or by a human using a pen and paper" to be an abstract idea. Accordingly, the "mental processes" abstract idea grouping is defined as concepts performed in the human mind, and examples of mental processes include observations, evaluations, judgments, and opinions. The courts do not distinguish between mental processes that are performed entirely in the human mind and mental processes that require a human to use a physical aid (e.g., pen and paper or a slide rule) to perform the claim limitation. Nor do the courts distinguish between claims that recite mental processes performed by humans and claims that recite mental processes performed on a computer. This limitation is interpreted as a calculation (i.e. Mathematical Concepts) of quantum resources, which the human mind can reasonably perform with/without the use of a physical aid, given the broadest reasonable interpretation.
establishing, with the classical computer, correct expected output for a quantum computer to verify an output from a quantum computer (As drafted and under its broadest reasonable interpretation, in light of the Specification, this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). Establishing correct expected output for a quantum computer is interpreted as calculating correct expected outputs, given Applicant’s disclosure [Spec. P.0012,13,136] and claim 5 limitations. Per MPEP 2106.04(a)(2)(I), it is important to note that a mathematical concept need not be expressed in mathematical symbols, because “[w]ords used in a claim operating on data to solve a problem can serve the same purpose as a formula.” 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.
Step 2A, Prong 2 (Claim 1):
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 Insignificant Extra-Solution Activity. In particular, the claim recites the additional limitations:
receiving, at a classical computer, data characterizing physical system comprising a first-quantized physical system (As drafted and under BRI, in light of the Specification, the additional limitation amounts to Insignificant Extra-Solution Activity (mere data gathering) per MPEP 2106.05(g). The term "extra-solution activity" can be understood as activities incidental to the primary process or product that are merely a nominal or tangential addition to the claim. Extra-solution activity includes both pre-solution and post-solution activity. An example of pre-solution activity is a step of gathering data for use in a claimed 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 (Claim 1):
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 Insignificant Extra-Solution Activity.
Per MPEP 2106.05(g), the addition of insignificant extra-solution activity does not amount to an inventive concept, particularly when the activity is well-understood or conventional. Per MPEP 2106.05(d), “[t]he courts have recognized the following (i.e. applicable) 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 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.
Per independent claim 13, the claim recites the limitations of:
establishing, with a quantum computer, a representation of a first-quantized physical system (As drafted and under its broadest reasonable interpretation in light of the Specification, this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.)
representing, with a quantum computer, an initial wavefunction |
ψ
(
0
)
of
the first-quantized physical system (As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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.);
representing, with a quantum computer, a Hamiltonian using a Cartesian
component- separated tensor-product of the first-quantized physical system (As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.);
computing, with a quantum computer, a time evolved wavefunction |
ψ
(
t
)
=
U
^
(
t
)
|
ψ
(
0
)
(As drafted and under its broadest reasonable interpretation this limitation amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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, e.g., performing an arithmetic operation such as exponentiation. There is no particular word or set of words that indicates a claim recites a mathematical calculation. That is, a claim does not have to recite the word "calculating" in order to be considered a mathematical calculation.)
Step 2A, Prong 2 and Step 2B (Claim 13):
There are no additional elements, additional to the abstract idea itself, and therefore no additional elements which could integrate the abstract idea into a practical application (in Step 2A Prong 2) nor provide significantly more than the abstract idea itself (in Step 2B).
Therefore, 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 Mathematical Concepts and/or Mental Processes performed on a computer, 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 a time evolved wavefunction
PNG
media_image1.png
30
135
media_image1.png
Greyscale
(As drafted and under its broadest reasonable interpretation, this limitation amounts to Mathematical Concepts and/or Mental Processes performed on a computer per MPEP 2106.04(a)(2)(I)/(III). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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. Additionally, a person can reasonably compute / calculate a time evolved wavefunction with the use of a physical aid. 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 a quantum circuit comprising a plurality of quantum wires and a plurality of quantum gates; one or more quantum wavefunction and ancilla 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 a 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 representation of a physical system is accomplished/established. 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 an initial wavefunction
PNG
media_image2.png
34
50
media_image2.png
Greyscale
(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 an initial wavefunction is represented. 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 a 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), “[a]s 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), “[u]se 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 elaborates on the wavefunction, thus further amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 4, determining, with the classical computer, the number of qubits required for a commensurate calculation for a quantum computer; determining, with the classical computer, the number of quantum gates required for a commensurate calculation for a quantum computer; determining, with the classical computer, the circuit depth required for a commensurate calculation for a quantum computer; and determining, with the classical computer the quantum volume required for a commensurate calculation for a quantum computer. The additional elements amount to Mathematical Concepts and/or Mental Processes performed on a computer per MPEP 2106.04(a)(2)(I)/(III). 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. Note: per MPEP 2106.04(a)(2)(III), an example of “claims that recite mental processes include: a claim to "collecting information, analyzing it, and displaying certain results of the collection and analysis," where the data analysis steps are recited at a high level of generality such that they could practically be performed in the human mind”. Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 5, predicting, with the classical computer an expected output from a commensurate calculation for a quantum computer, using the resultant energy eigenvalues; predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using the resultant eigenstate wavefunctions; and predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using correlation functions obtained from the eigenstate wavefunctions. (As drafted and under its broadest reasonable interpretation in light of the Specification, these limitations amount to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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
PNG
media_image3.png
56
363
media_image3.png
Greyscale
. The additional element elaborates on the wavefunctions, thus is further directed towards Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 12, wherein one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
PNG
media_image4.png
44
484
media_image4.png
Greyscale
respectively. The additional element elaborates on the Hamilton, thus further amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). The mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. 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 14, wherein computing, with a quantum computer, the time evolved wavefunction
PNG
media_image1.png
30
135
media_image1.png
Greyscale
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 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 first-quantized 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 representation of the physical system, thus further amounts to Mathematical Concepts (mathematical relationships) per MPEP 2106.04(a)(2)(I). Therefore, the claim is rejected as not patent eligible under 35 U.S.C. 101.
Regarding Claim 16, wherein a kinetic energy is represented in a plane-wave basis representation, a potential energy is represented in component-separated tensor-product form in a plane-wave-dual grid-based representation, and the initial wavefunction
PNG
media_image2.png
34
50
media_image2.png
Greyscale
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 one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
PNG
media_image5.png
48
478
media_image5.png
Greyscale
respectively. The additional element elaborates on the Hamilton, thus further amounts to Mathematical Concepts per MPEP 2106.04(a)(2)(I). 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 18, applying a Quantum Phase Estimation algorithm, in conjunction with present potential energy quantum circuits, to provide 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, applying a Quantum Phase Estimation algorithm, in conjunction with present potential energy quantum circuits, to provide 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
PNG
media_image6.png
33
65
media_image6.png
Greyscale
operations with a small time step ε, using the Trotter approximation. The additional element elaborates on the wavefunction computation, 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 21, wherein one-particle and two-particle potential energy contributions to the Trotter approximation,
PNG
media_image7.png
31
117
media_image7.png
Greyscale
and
PNG
media_image8.png
35
125
media_image8.png
Greyscale
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). 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.
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.
The factual inquiries set forth in Graham V. John Deere Co., 383 U.S. 1, 148 USPQ 459 (1966), that are applied for establishing a background for determining obviousness under 35 U.S.C. 103(a) are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating
obviousness or nonobviousness.
Claims 1-3, 13-17, and 20-22 are rejected under 35 U.S.C. 103 as being unpatentable over Cao US Pat. No. 11169801 B2 (hereinafter referred to as “Cao”), 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”).
Regarding claim 1, Cao discloses A method for simulating performance of quantum computational chemistry, comprising: receiving, at a classical computer, data characterizing physical system (“The classical computer 402 generates 418 a reference state 420 based on the first Hamiltonian 406 and the basis set 408.” Cao [Col.24 Ln.3]); representing, with the classical computer, wavefunctions associated with the physical system (“To approximate the ground state of a Hamiltonian H, one uses a classical computer to optimize θ such that it minimizes energy of H:
PNG
media_image9.png
61
382
media_image9.png
Greyscale
, measured with respect to the ansatz state” Cao [Col.24 Ln.45]) representing, with the classical computer, a Hamiltonian, associated with the physical system (“the classical computer 402 of FIG. 4 includes a first Hamiltonian 406” Cao [Col.23 Ln.45]),
computing, with the classical computer, resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states (“The above construction depicted in FIG. 4 (see below) may also be expressed as a framework of variational quantum eigensolver (VQE) using noisy intermediate scale quantum devices in conjunction with a classical computer for approximately preparing the ground state of quantum Hamiltonians (of the form in Eqn. 44 above) as well as approximately measuring the ground state energy.” Cao [Col.24 Ln.35])
PNG
media_image10.png
469
635
media_image10.png
Greyscale
and establishing, with the classical computer, correct expected output for a quantum computer to verify an output from a quantum computer (“a classical computer may execute functionality for emulating a quantum computer and provide a subset of the functionality described herein” Cao [Col.35 Ln.45]. Note: The limitation of to verify an output is interpreted as intended use of the classical computer output, thus not given patentable weight.).
Cao fails to specifically disclose comprising a first quantized physical system, using a Cartesian component-separated tensor-product, and determining, with the classical computer, quantum resources required for a commensurate first-quantized calculation for a quantum computer.
However, Jones discloses comprising a first quantized physical system, representing wavefunctions using a Cartesian component-separated tensor-product; representing the Hamiltonian using a Cartesian component-separated tensor-product (“First-quantized molecular simulation represents the simulated system wavefunction on a Cartesian grid, and the Hamiltonian is calculated with digital arithmetic acting on this coordinate Space [ ] Each position register can be decomposed in Cartesian components |
r
= |
x
|
y
|
z
, so for a pair of particles we calculate
PNG
media_image11.png
36
330
media_image11.png
Greyscale
” Jones [Pg.31-32 Appendix C]); determining, with the classical computer, quantum resources required for a commensurate first-quantized calculation for a quantum computer (“A gate approximation sequence uses a stream of fault-tolerant single-qubit gates to approximate an arbitrary phase rotation, such as that in equation (1). For context, a common set of fault tolerant gates is listed in table 1. Such sequences must be calculated using a classical algorithm (i.e. using a classical computer)” Jones [Pg.7 Sec.2.2]. Also see Jones [Pg.25 4.3 Resource analysis for first-quantized molecular simulations]).
Cao and Jones are analogous art as they both relate to quantum chemistry simulation. Cao discloses “[a] hybrid quantum classical (HQC) computer, which includes both a classical computer component and a quantum computer component, solves linear systems. The HQC decomposes the linear system to be solved into subsystems that are small enough to be solved by the quantum computer component, under control of the classical computer component. The classical computer component synthesizes the outputs of the quantum computer component to generate the complete solution to the linear system” [Abstract]. And Jones discloses “[w]e 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]. It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include a first quantized physical system utilizing Cartesian component-separated tensor-products, along with quantum resource determination, as Jones discloses, since a “first-quantized simulation algorithm is in some ways more complex than the second quantized algorithm, but for problems in chemistry larger than a handful of particles, it is computationally faster.” Jones [Pg.19 Sec.4].
Regarding claim 2, Cao fails to specifically disclose 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.
However, Jones 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. (“we transform the representation of the system wavefunction from position basis {x, y, z} (i.e. Cartesian component-separated tensor-product. See Jones Pg.31-32 Appendix C) to momentum basis {kx , ky, kz} (i.e. plane-wave-dual grid)” Jones [Pg.21 P.2]. Momentum basis is interpreted as plane-wave-dual grid due to Applicant’s disclosure [Spec. P.60])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include a first quantized physical system utilizing Cartesian component-separated tensor-products on a plane-wave-dual grid, as Jones discloses, since a “first-quantized simulation algorithm is in some ways more complex than the second quantized algorithm, but for problems in chemistry larger than a handful of particles, it is computationally faster.” Jones [Pg.19 Sec.4].
Regarding claim 3, Cao fails to specifically disclose 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.
However, Jones 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. (“The complete Hamiltonian in first-quantized form can be expressed as the sum of the kinetic (
T
^
) and potential (
V
^
) operators
PNG
media_image12.png
58
320
media_image12.png
Greyscale
where the indices i and j run over all particles (electrons and nuclei) of any given molecule [ ] The core of the algorithm is evolving the Hamiltonian in simulated time, achieved by applying the propagator
U
(t) = exp(−i
H
t) [ ] where the kinetic and potential energy operators are simulated in alternating steps as
PNG
media_image13.png
44
302
media_image13.png
Greyscale
[ ] The operators
e
-
i
V
^
δ
t
and
e
-
i
T
^
δ
t
are diagonal in the position and momentum bases (i.e. plane-wave-dual grid), respectively. One can switch the encoded configuration space representation between these two bases by applying the QFT (i.e. plane-wave-dual grid. See Spec. P.0060) to each spatial dimension of the wavefunction” Jones [Pg.20 P.3-4])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include a first quantized physical system utilizing Cartesian component-separated tensor-products on a plane-wave-dual grid, as Jones discloses, since a “first-quantized simulation algorithm is in some ways more complex than the second quantized algorithm, but for problems in chemistry larger than a handful of particles, it is computationally faster.” Jones [Pg.19 Sec.4].
Regarding independent claim 13, Cao discloses A method for performing first-quantized quantum computational chemistry comprising: representing, with a quantum computer, an initial wave function
|
ψ
0
⟩
of physical system; (“The quantum computer 252 starts in the initial state 266, and evolves its state according to the annealing schedule 270 following the time-dependent Schrödinger equation, a natural quantum-mechanical time evolution of physical systems (FIG. 2B, operation 268).” Cao [Col.29 Ln.63]) representing, with a quantum computer, a Hamiltonian (“More specifically, the state of the quantum computer 252 undergoes time evolution under a time-dependent Hamiltonian, which starts from the initial Hamiltonian 260 and terminates at the final Hamiltonian 262.” Cao [Col.29 Ln.67]); and computing, with a quantum computer, a time evolved wavefunction
ψ
t
=
U
^
t
|
ψ
0
⟩
. (“More specifically, the state of the quantum computer 252 undergoes time evolution under a time-dependent Hamiltonian, which starts from the initial Hamiltonian 260 and terminates at the final Hamiltonian 262.” Cao [Col.29 Ln.67])
Cao fails to specifically disclose establishing, with a quantum computer, a representation of a first-quantized physical system; and using a Cartesian component-separated tensor-product of the first-quantized physical system.
However, Jones discloses establishing, with a quantum computer, a representation of a first-quantized physical system; (Jones [Pg.19 4. Simulating chemical structure and dynamics in a first-quantized representation]) representing, with a quantum computer, an initial wave function
|
ψ
0
⟩
of the first-quantized physical system; (“After preparing an initial state |ψ0
⟩
, the system is evolved” Jones [Pg.4 Figure 1]) representing, with a quantum computer, a Hamiltonian using a Cartesian component-separated tensor-product of the first-quantized physical system (“First-quantized molecular simulation represents the simulated system wavefunction on a Cartesian grid, and the Hamiltonian is calculated with digital arithmetic acting on this coordinate Space [ ] Each position register can be decomposed in Cartesian components |ri = |xi |yi |zi, so for a pair of particles we calculate
PNG
media_image11.png
36
330
media_image11.png
Greyscale
” Jones [Pg.31-32 Appendix C])
Cao and Jones are analogous art as they both relate to quantum chemistry simulation. Cao discloses “[a] hybrid quantum classical (HQC) computer, which includes both a classical computer component and a quantum computer component, solves linear systems. The HQC decomposes the linear system to be solved into subsystems that are small enough to be solved by the quantum computer component, under control of the classical computer component. The classical computer component synthesizes the outputs of the quantum computer component to generate the complete solution to the linear system” [Abstract]. And Jones discloses “[w]e 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]. Thus, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include a first quantized physical system utilizing Cartesian component-separated tensor-products, as Jones discloses, since a “first-quantized simulation algorithm is in some ways more complex than the second quantized algorithm, but for problems in chemistry larger than a handful of particles, it is computationally faster.” Jones [Pg.19 Sec.4].
Regarding claim 14, Cao fails to specifically disclose wherein computing, with a quantum computer, 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, with a quantum computer.
However, Jones discloses wherein computing, with a quantum computer, 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])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include computing resultant energy eigenvalues and eigenstate wavefunctions of the Hamiltonian for one or more quantum states, as Jones discloses, in order to “simulate chemistry with an efficient use of resources”, i.e. “solving novel problems for less computational cost than a classical computer.” Jones [Pg.3 Ln.2-6].
Regarding claim 15, Cao fails to specifically disclose the representation of the first-quantized 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.
However, Jones discloses the representation of the first-quantized 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 (“A first-quantized simulation is essentially a finite-difference method for solving the Schrodinger equation. Configuration space is discretized into a Cartesian grid (i.e. coordinate grid spacing), and each particle (e.g. electron) has a wavefunction expressed in a quantum register that encodes a probability amplitude at each coordinate on the grid. For example, let us imagine that we form a position-basis representation for a single electron on a 2p ×2p ×2p grid (i.e. min/max coordinate values), which requires only 3p qubits. Explicitly, the electronic wavefunction is represented as
PNG
media_image14.png
91
523
media_image14.png
Greyscale
” Jones [Pg.19-20 Sec.4]. The configuration space disclosed by Jones is interpreted as plane-wave-dual due to Applicant’s disclosure “Elements of the first-quantized Hamiltonian may be written in the following basis representations: [ ] plane wave dual (i.e. grid-based, Sinc, or position-space)” Spec. [P.0060]).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include a first quantized physical system represented as a plane-wave-dual grid, as Jones discloses, since a “first-quantized simulation algorithm is in some ways more complex than the second quantized algorithm, but for problems in chemistry larger than a handful of particles, it is computationally faster.” Jones [Pg.19 Sec.4].
Regarding claim 16, Cao fails to specifically disclose wherein a kinetic energy is represented in a plane-wave basis representation, a potential energy is represented in component-separated tensor-product form in a plane-wave-dual grid-based representation, and the initial wavefunction |
ψ
0
⟩
is represented in a plane-wave-dual grid-based representation.
However, Jones discloses wherein a 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]), a potential energy is represented in component-separated tensor-product form in a plane-wave-dual grid-based representation (See Jones [Pg.31-32 Appendix C. Quantum circuits for potential and kinetic energy operators in first-quantized molecular Hamiltonians]), and the initial wavefunction |
ψ
0
⟩
is represented in a plane-wave-dual grid-based representation. (“After preparing an initial state |
ψ
0
⟩
, the system is evolved in simulated time by solving the time-dependent Schrodinger equation.” Jones [Pg.4 Figure 1]. The initial wavefunction |
ψ
0
⟩
is interpreted to be represented in a plane-wave-dual grid-based representation due to Applicant’s disclosure [Spec. P.0018] “a plane-wave-dual grid-based representation comprising coordinate grid spacing, minimum and maximum coordinate values, and a number of grid points” and Jones disclosure [Pg.19-20 Sec.4] “A first-quantized simulation is essentially a finite-difference method for solving the Schrodinger equation. Configuration space is discretized into a Cartesian grid, and each particle (e.g. electron) has a wavefunction expressed in a quantum register that encodes a probability amplitude at each coordinate on the grid. For example, let us imagine that we form a position-basis representation for a single electron on a 2p ×2p ×2p grid, which requires only 3p qubits. Explicitly, the electronic wavefunction is represented as
PNG
media_image15.png
73
434
media_image15.png
Greyscale
where c (x, y, z) is the complex probability amplitude for the electron to occupy the volume element centered at the position r
≡
(x, y, z).”)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to represent kinetic/potential energies and initial waveform as Jones discloses, in order for “efficient chemical simulation on quantum computers” Jones [Pg.29 Sec.6 Conclusions].
Regarding claim 17, Cao fails to specifically disclose wherein one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
PNG
media_image5.png
48
478
media_image5.png
Greyscale
respectively.
However, Jones discloses wherein one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
PNG
media_image5.png
48
478
media_image5.png
Greyscale
respectively. (“Firstly, equation (15) calculates the potential energy as a function of position coordinates (i.e. one-particle potential energy) (note that
V
^
is diagonal in this basis) and stores the result in a quantum register |V(r1, r2, …, rb
)
to some finite precision [ ] Secondly, equation (16) uses the |V(r1, r2, …, rb
)
register in a ‘quantum variable’ phase rotation that imparts a phase to each grid point of the wavefunction in position basis proportional to the potential energy at those coordinates.” Jones [Pg.21 P.1]. “First-quantized molecular simulation represents the simulated system wavefunction on a Cartesian grid, and the Hamiltonian is calculated with digital arithmetic acting on this coordinate space. [ ] The potential energy operator is diagonal in position basis, and is the sum of Coulomb interactions between electrons and nuclei (i.e. two-particle potential energy) in the system
PNG
media_image16.png
86
228
media_image16.png
Greyscale
(C.1) and qj is the charge of particle j . The prefactor on the rhs of equation (C.1) is a constant for any given pair of particles, and we can later encode this scaling factor into the QVR.” Jones [Pg.31 Appendix C.])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method with one-particle and two-particle potential energy contributions to the Hamiltonian, as Jones discloses, in order for “efficient chemical simulation on quantum computers” Jones [Pg.29 Sec.6 Conclusions].
Regarding claim 20, Cao fails to specifically disclose 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.
However, Jones 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
PNG
media_image17.png
59
444
media_image17.png
Greyscale
” Jones [Pg.20 P.2])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include using the Trotter approximation to compute the time-evolved wavefunction since “it is computationally faster” Jones [Pg.19 Sec.4].
Regarding claim 21, Cao fails to specifically disclose wherein 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 quantum circuit.
However, Jones further discloses wherein 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 quantum circuit. (“Configuration space is discretized into a Cartesian grid, and each particle (e.g. electron) has a wavefunction expressed in a quantum register that encodes a probability amplitude at each coordinate on the grid [ ] 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
PNG
media_image18.png
62
454
media_image18.png
Greyscale
where c(·) is the complex amplitude as a function of position in configuration space and subscripts correspond to particles in the system” Jones [Pg.19-20 Sec.4])
Jones discloses the limitations of claim 21 and maintains the same rationale for combination with Cao as claim 20, from which this claim depends.
Regarding independent claim 22, Cao discloses An apparatus comprising: quantum hardware, the quantum hardware further comprising a quantum system comprising (“The system 250 includes both a quantum computer 252 and a classical computer 254.” Cao [Col.29 Ln.45]): a quantum circuit comprising a plurality of quantum wires and a plurality of quantum gates (“There may be any number of gates in a quantum circuit. However, in some embodiments the number of gates may be at least proportional to the number of qubits 104 in the quantum computer 102.”) Cao [Col.31 Ln.4]. Note: The quantum circuit is interpreted to include quantum wires since “In embodiments in which some or all of the qubits 104 are implemented as semiconducting material (e.g., nanowires), the control unit 106 may be microfabricated gates” Cao [Col.32 Ln.27]); ,
and one or more control devices configured to operate the quantum system wherein the apparatus is configured to perform operations comprising (“The quantum computer 102 includes a control unit 106, which may include any of a variety of circuitry and/or other machinery for performing the functions disclosed herein.” Cao [Col.31 Ln.24]): establishing a representation of a physical system; representing an initial wavefunction |
ψ
0
⟩
(“The quantum computer 252 starts in the initial state 266, and evolves its state according to the annealing schedule 270 following the time-dependent Schrödinger equation, a natural quantum-mechanical time evolution of physical systems” Cao [Col.29 Ln.63]), representing a Hamilton , and computing a time evolved wavefunction
ψ
t
=
U
^
t
|
ψ
0
⟩
; (“More specifically, the state of the quantum computer 252 undergoes time evolution under a time-dependent Hamiltonian, which starts from the initial Hamiltonian 260 and terminates at the final Hamiltonian 262.” Cao [Col.29 Ln.67])
Cao fails to specifically disclose one or more quantum wavefunction and ancilla qubits and representing a Hamilton using Cartesian component-separated tensor-product.
However, Jones discloses one or more quantum wavefunction and ancilla qubits (Note: See examiner’s interpretation of this limitation in Claim Rejections – 35 USC § 112 section above. “we construct a phase kickback ancilla register
PNG
media_image19.png
35
85
media_image19.png
Greyscale
of size n = p + q qubits” Jones [Pg.22 P.2]) representing a Hamilton using Cartesian component-separated tensor-product (“First-quantized molecular simulation represents the simulated system wavefunction on a Cartesian grid, and the Hamiltonian is calculated with digital arithmetic acting on this coordinate Space [ ] Each position register can be decomposed in Cartesian components |ri = |xi |yi |zi, so for a pair of particles we calculate
PNG
media_image11.png
36
330
media_image11.png
Greyscale
” Jones [Pg.31-32 Appendix C]).
Cao and Jones are analogous art as they both relate to quantum chemistry simulation. Cao discloses “[a] hybrid quantum classical (HQC) computer, which includes both a classical computer component and a quantum computer component, solves linear systems. The HQC decomposes the linear system to be solved into subsystems that are small enough to be solved by the quantum computer component, under control of the classical computer component. The classical computer component synthesizes the outputs of the quantum computer component to generate the complete solution to the linear system” [Abstract]. And Jones discloses “[w]e 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]. Thus, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao’s hybrid classical / quantum system and method to include one or more quantum wavefunction and ancilla qubits and representing a Hamilton using Cartesian component-separated tensor-product, as Jones discloses, since the “phase kickback (i.e. wavefunction/ancilla qubit) uses substantially fewer T gates than the bitwise approach, as shown in figure 16, while having comparable circuit depth” Jones [Pg.23 Ln.3] and because “it is computationally faster” Jones [Pg.19 Sec.4], respectively.
Claim 4 is rejected under 35 U.S.C. 103 as being unpatentable over Cao US Pat. No. 11169801 B2 (hereinafter referred to as “Cao”), 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 further view of Moll, Nikolaj, et al. "Quantum optimization using variational algorithms on near-term quantum devices." Quantum Science and Technology 3.3 (2018): 030503 (hereinafter referred to as “Moll”).
Regarding claim 4, Cao-Jones fail to specifically disclose determining, with the classical computer, the number of qubits required for a commensurate calculation for a quantum computer; and determining, with the classical computer, the number of quantum gates required for a commensurate calculation for a quantum computer, determining, with the classical computer, the circuit depth required for a commensurate calculation for a quantum computer ; and determining, with the classical computer the quantum volume required for a commensurate calculation for a quantum computer.
However, Moll discloses determining, with the classical computer, the number of qubits required for a commensurate calculation for a quantum computer; and determining, with the classical computer, the number of quantum gates required for a commensurate calculation for a quantum computer; determining, with the classical computer, the circuit depth required for a commensurate calculation for a quantum computer ; and determining, with the classical computer, the quantum volume required for a commensurate calculation for a quantum computer (“To define a suitable metric, we first note that a quantum computer's performance depends on five main hardware parameters: (i) Number of physical qubits
N
, (ii) Connectivity between qubits, (iii) Number of gates that can be applied before errors or decoherence mask the result, (iv) Available hardware gate set
(v) Number of operations that can be run in parallel. With the goal to quantify a quantum computer's power with a single parameter, we would like to consider a metric based on the question ‘can this device run a given algorithm?'. For any given instance of a quantum algorithm, there is a lower bound on the number of qubits
N
required to run the algorithm, as well as the necessary number of steps (or circuit depth)
d
. We therefore define a quantum volume VQ that takes into account both the number of qubits
N
and the allowable depth
d
of quantum circuits that can be run on a near-term quantum device.” Moll [Pg.5 Sec.2])
Moll is analogous art as it relates to quantum computing/optimization and chemical applications. Moll discloses “the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization
problems as well as for problems in quantum chemistry” [Abstract]. It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the Cao-Jones combination to include quantum computer component determination, as Moll discloses, in order “to quantify a quantum computer’s power (i.e. performance)” Moll [Pg.5 P.2].
Claims 5-12 are rejected under 35 U.S.C. 103 as being unpatentable over Cao US Pat. No. 11169801 B2 (hereinafter referred to as “Cao”), 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 further 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 5, Cao-Jones fails to specifically disclose predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using the resultant energy eigenvalues; predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using the resultant eigenstate wavefunctions; and predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using correlation functions obtained from the eigenstate wavefunctions.
However, Jerke discloses predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using the resultant energy eigenvalues; predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using the resultant eigenstate wavefunctions (“In Fig. 7 (see below), we have integrated the full 6D probability density |
Ψ
|2, for the 1s2p (3P) state” Jerke [Pg.13 Col.1 P.1]);
PNG
media_image20.png
258
381
media_image20.png
Greyscale
and predicting, with the classical computer, an expected output from a commensurate calculation for a quantum computer, using correlation functions obtained from the eigenstate wavefunctions (“In Fig. 6 (see below), we present radial correlation functions [ ] 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—are novel, to our knowledge.” Jerke [Pg.12 Col.2 P.1])
PNG
media_image21.png
309
379
media_image21.png
Greyscale
Jerke is analogous art as it relates to computation of chemical systems using a classical computer. Jerke discloses “In this paper, we are concerned with solving the quantum mechanical time-independent Schrodinger equation (TISE) — specifically, as applied to electronic structure” [Pg.2 Intro.]. It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao-Jones to include Jerke’s output prediction method, in order “to compute the ground and several excited electronic states (K
≈
10) [ ] to chemical accuracy—i.e., to within 1–2 mhartree or better.” Jerke [Pg.8 IV.Results].
Regarding claim 6, Cao-Jones fail to specifically disclose 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.
However, Jerke discloses 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. (“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])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao-Jones to include Jerke’s approach to establishing optimal component-separated basis sets since “the Hilbert space of
the new basis has now expanded so that the eigenvectors of the new matrix representation H0—obtained through another set of block Krylov cycles—are more accurate than the old.” Jerke [Pg.7 Col.2 P.5].
Regarding claim 7, Cao-Jones fail to specifically disclose 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.
However, Jerke 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])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao-Jones to include Jerke’s approach to determining tensor-product Hamiltonian-wavefunction matrix-vector products since the approach “reduces RAM requirements tremendously” Jerke [Pg.1 Col.2 P.3].
Regarding claim 8, Coa-Jones fail to specifically disclose 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.
However, Jerke discloses 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. (“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.6 Col.1 P.4])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao-Jones to include applying block Krylov iteration, as Jerke discloses, since a “key advantage of block Krylov over simple Krylov is that a smaller M is required to attain convergence—leading to much less linear dependence and smaller ranks” Jerke [Pg.6 Col.2 P.1])
Regarding claim 9, Cao-Jones fail to specifically disclose 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.
However, Jerke discloses 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. (“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])
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao-Jones to include projecting the Hamiltonian onto the Krylov vectors, as Jerke discloses, in order “[t]o address the situation” of “a rather rapid growth in the total number of terms (i.e. from the block Krylov algorithm)” Jerke [Pg.7 Sec.D P.1].
Regarding claim 10, Cao-Jones fail to specifically disclose 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.
However, Jerke 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)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao-Jones to include band-pass staging, as Jerke discloses, in order “[t]o address the situation” of “a rather rapid growth in the total number of terms (i.e. from the block Krylov algorithm)” Jerke [Pg.7 Sec.D P.1].
Regarding claim 11, Cao-Jones fail to specifically disclose wherein the wavefunctions comprise a Cartesian component-separated tensor product of the form
PNG
media_image3.png
56
363
media_image3.png
Greyscale
.
However, Jerke discloses wherein the wavefunctions comprise a Cartesian component-separated tensor product of the form
PNG
media_image3.png
56
363
media_image3.png
Greyscale
. (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
). 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.)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao to include wavefunctions comprising a Cartesian component-separated tensor product, as Jerke discloses, since the form “reduces RAM requirements tremendously” Jerke [Pg.1 Col.2 P.3].
Regarding claim 12, Cao-Jones fail to specifically disclose wherein one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
PNG
media_image4.png
44
484
media_image4.png
Greyscale
respectively.
However, Jerke discloses wherein one-particle and two-particle potential energy contributions to the Hamiltonian comprise Cartesian component-separated tensor products of the form
PNG
media_image4.png
44
484
media_image4.png
Greyscale
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. Gaussian-Sinc form is interpreted as Cartesian component-separated tensor products due to Applicant’s disclosure [Spec. P.0060]. Therefore, Jerke’s disclosed one/two-particle potential energy contributions are interpreted to be in the form of the cited expressions.)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify Cao to include one/two particle energy contributions to the Hamilton comprising a Cartesian component-separated tensor products, as Jerke discloses, since the form “reduces RAM requirements tremendously” Jerke [Pg.1 Col.2 P.3].
Claims 18 and 19 are rejected under 35 U.S.C. 103 as being unpatentable over Cao US Pat. No. 11169801 B2 (hereinafter referred to as “Cao”), 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 further 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, Cao fails to specifically disclose applying a Quantum Phase Estimation algorithm, in conjunction with present potential energy quantum circuits, to provide a ground state energy level and eigenstate wavefunction.
However, Kassal discloses applying a Quantum Phase Estimation algorithm, in conjunction with present potential energy quantum circuits, to provide 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.4d below for ground state energy levels. Note: The phase estimation algorithm disclosed by Kassal is interpreted to be in conjunction with present potential energy quantum circuits since “Figure 4 describes the experiment and the potential
energy surfaces that were obtained.” Kassal [Pg.199 Sec.5.2])
PNG
media_image22.png
598
156
media_image22.png
Greyscale
PNG
media_image23.png
522
816
media_image23.png
Greyscale
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 Cao to apply a Quantum Phase Estimation algorithm in order to efficiently find the eigenvalues (phases) of the disclosed quantum systems.
Regarding claim 19, Cao fails to specifically disclose applying a Quantum Phase Estimation algorithm, in conjunction with present potential energy quantum circuits, to provide excited state energy levels and eigenstate wavefunctions.
However, Kassal discloses applying a Quantum Phase Estimation algorithm, in conjunction with present potential energy quantum circuits, to provide 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.)
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 Cao to apply a Quantum Phase Estimation algorithm in order to efficiently find the eigenvalues (phases) of the disclosed quantum systems.
Conclusion
The prior art made of record, listed on form PTO-892, and not relied upon is
considered pertinent to applicant's disclosure:
Hilton et al. (Hybrid Classical-quantum Computer Architecture For Molecular Modeling – US Pub. No 2005/0273306 A1). “the classical computer is capable of implementing the hybrid algorithm, coordinating one or more quantum processors, and comparing the results” [P.0161]
Poirier, Lionel William. Optimal separable bases and molecular collisions. University of California, Berkeley, 1997. “In the DVR formalism, a finite grid of points is laid out over the region of interest in configuration space; and the density and extent of the points are presumed sufficient to adequately represent the underlying continuous coordinates for a given application. This DVR grid can then be used to obtain approximate, position-like representations of quantum mechanical operators and wavefunctions. An operator is represented in the DVR as an N x N matrix, where N is the total number of grid points. Similarly, a wavefunction is represented by a vector of length N.” [Pg.48 Sec.3.2.1].
Neukart et al. (Simulating Electronic Structure With Quantum Annealing Devices And Artificial Neural Networks – US Pat. No 11776666 B2). “System 100 further comprises one or more classical computers 106 that operates with one or more (non-quantum) computing processors to perform classical computations (e.g., Hartree-Fock methods, quantum Monte Carlo methods, density functional theory or configuration interaction methods, etc.) to derive classically determined results 118 that include classically computed molecular electronic structural information.” [Col.4 Ln.65].
Applicant’s amendment necessitated the new ground(s) of rejection presented in this Office Action. Accordingly, THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Anthony Chavez whose telephone number is (571) 272-1036. The examiner can normally be reached Monday - Thursday, 8 a.m. - 5 p.m. ET.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner' s supervisor, Renee Chavez can be reached at (571) 270-1104. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/ANTHONY CHAVEZ/ Examiner, Art Unit 2186
/RENEE D CHAVEZ/Supervisory Patent Examiner, Art Unit 2186
