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 .
Drawings
The drawings are objected to as failing to comply with 37 CFR 1.84(p)(5) because they do not include the following reference sign(s) mentioned in the description: "218" (estimated extremal eigenstates, described in at least ¶[0036], [0039], [0059], [0062], [0066] and shown in FIG. 2 as element 216) and "614" (single-state optimization algorithm step in the second iteration, described in ¶[0074] and shown in FIG. 6, which contains no box labeled 614). Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either "Replacement Sheet" or "New Sheet" pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
The drawings are objected to as failing to comply with 37 CFR 1.84(p)(5) because they include the following reference character(s) not mentioned in the description: "216" (FIG. 2, the box labeled "ESTIMATED EXTREMAL EIGENSTATES") and "608" (FIG. 6, the box reciting "IMPLEMENT A SINGLE-STATE OPTIMIZATION ALGORITHM IN THE FIRST ITERATION..."). Corrected drawing sheets in compliance with 37 CFR 1.121(d), or amendment to the specification to add the reference character(s) in the description in compliance with 37 CFR 1.121(b) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either "Replacement Sheet" or "New Sheet" pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Specification
The disclosure is objected to because of the following informalities: ¶[0060] refers to "the respective estimated eigenstate ESG," which appears to be a typographical error for "ES0" consistent with the remainder of the paragraph. Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of the first paragraph of 35 U.S.C. 112(a):
(a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention.
The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112:
The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention.
The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112:
The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention.
Claims 11-15 and 18-19 are rejected under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, at the time the application was filed, had possession of the claimed invention.
Claim 11 recites "implementing the limited multistate optimization algorithm in a second iteration to sequentially shift the state index and the orthogonality index to each tensor of a second one of the TTNSs...". The specification does not describe an "orthogonality index." The term does not appear anywhere in the written description. The only entity the specification describes as being sequentially shifted to each tensor together with the state index is the orthogonality center. See specification ¶[0019] ("The optimized state quantity also controls the size of the state index which can be sequentially shifted along with the orthogonality center (e.g., canonical center) of the bundled TTNS to each of the tensors during the sweep"); ¶[0043] ("the state index can be sequentially shifted along with the orthogonality center to each tensor of the bundled TTNS"); and ¶[0052] ("The site index controller 414 is configured to perform the sweeps across the bundled tensors 408 by moving the state index and the orthogonality center sequentially along each of the bundled tensors 408"). The specification's own description of the very method step recited in this limitation likewise recites the orthogonality center, not an orthogonality index. See ¶[0074] ("the limited multistate optimization algorithm is implemented in a second iteration to sequentially shift the state index and the orthogonality center to each tensor of a second one of the bundled TTNSs"). The corresponding first-iteration limitation of claim 11 itself recites "an orthogonality center." It is acknowledged that the phrase "THE ORTHOGONALITY INDEX" appears in box 610 of FIG. 6. That single, unexplained appearance in a flowchart box does not cure the deficiency. It is contradicted by ¶[0074], which is the specification's own description of box 610, and by box 606 of the same figure, which recites "AN ORTHOGONALITY CENTER." The disclosure nowhere describes what an orthogonality index is, how it is defined, how its size or position is determined, or how it differs from the orthogonality center. Accordingly, the disclosure does not reasonably convey to one of ordinary skill in the art that the inventor, at the time the application was filed, had possession of sequentially shifting an "orthogonality index" as an entity distinct from the orthogonality center. See MPEP § 2163.
Claims 12-15 depend from claim 11 and incorporate the deficient limitation. Claims 12-15 are therefore rejected for the same reason. No separate written description deficiency is identified in the limitations added by claims 12-15.
Examiner's note: This rejection may be overcome by amending "the orthogonality index" in claim 11 to "the orthogonality center," consistent with ¶[0074] and with box 606 of FIG. 6. Such an amendment would not introduce new matter. The same limitation additionally lacks antecedent basis and is addressed separately under 35 U.S.C. 112(b).
Claim 18 recites "wherein the limited multistate optimization algorithm is configured to provide the determined at least one of the extremal eigenstates of a given one of the iterations as an orthogonality constraint to the limited multistate optimization algorithm...". The specification does not describe the limited multistate optimization algorithm providing orthogonality constraints — either to itself or to any other component. Throughout the disclosure, the limited multistate optimization algorithm is described exclusively as a recipient of orthogonality constraints. See ¶[0035] ("The operation of limited multistate optimization algorithm 208, subject to the orthogonality constraints 212 and algorithm parameters 214 provided from the memory 206 as signals OC and PRM, respectively"); ¶[0040] ("the limited multistate optimization algorithm 208 can access the orthogonality constraints 212 from the memory 206, demonstrated by the signal OC"); and ¶[0051] ("The limited multistate optimization algorithm 402 is demonstrated as receiving orthogonality constraints OC"). FIG. 4 correspondingly depicts OC as an input to the limited multistate optimization algorithm 402. The specification uniformly attributes the generation of the orthogonality constraints to the single-state optimization algorithm. See ¶[0038] ("The converged extremal eigenstates of the bundled TTNS determined by the single-state optimization algorithm 210 are saved in the memory 206, demonstrated as a signal STCVG and in the memory 206 as the orthogonality constraints 212"); ¶[0030] ("The converged most extreme eigenstate(s) determined by the single-state optimization algorithm can be stored in the memory 108 as the orthogonality constraints 114 for the next iterations"); and ¶[0021] ("The converged extremal eigenstate(s) determined by the single-state optimization algorithm can thus be provided as orthogonality constraints to the limited multistate optimization algorithm in the next iteration"). The contrast with claim 6 is instructive. Claim 6 recites the same functional relationship but attributes it to "the processing unit," an attribution supported by ¶[0023], which describes the processing unit 106 as implementing the hybrid eigenstate determination algorithm 110 encompassing both sub-algorithms. Claim 6 is accordingly not rejected. Claim 18 instead attributes the function specifically to the limited multistate optimization algorithm, an actor to which the specification attributes only the receipt of orthogonality constraints. The specification therefore does not reasonably convey to one of ordinary skill in the art that the inventor, at the time the application was filed, had possession of a limited multistate optimization algorithm configured to supply orthogonality constraints to itself. See MPEP § 2163.
Claim 19 recites that "the limited multistate optimization algorithm is configured to determine if an estimated extremal eigenstate of a state set of a given one of the iterations is an estimated next higher or lower eigenstate relative to the determined at least one of the extremal eigenstates of a preceding one of the iterations," and that it "is configured to access an estimated next higher or lower eigenstate of a state set of the immediately preceding one of the iterations from the memory and to optimize the accessed estimated next higher or lower eigenstate to convergence via the single-state optimization algorithm in the given one of the iterations." The specification attributes each of these functions to the single-state optimization algorithm or to the processing unit, and never to the limited multistate optimization algorithm. See ¶[0039] ("the single-state optimization algorithm 210 can compare the eigenvalues of the estimated extremal eigenstates determined by the limited multistate optimization algorithm 208 in a given iteration with the eigenvalues of the saved estimated extremal eigenstates 218 determined by the limited multistate optimization algorithm 208 in an immediately preceding iteration ... the single-state optimization algorithm 210 can select one of the saved estimated extremal eigenstates 218 from the preceding iteration for convergence"); ¶[0054] ("the single-state optimization algorithm 404 can determine the redundancy of the estimated extremal eigenstates STEST, and can select at least one of the estimated extremal eigenstates STEST to converge in each iteration"); and ¶[0067] ("the processing unit 106 can identify that the lowest of the estimated eigenvalues in the third iteration ... is not the next higher eigenvalue relative to the converged lowest eigenvalue E3 ... the processing unit 106 can access the estimated lowest eigenstate ES4 from the memory 108 ... The single-state optimization algorithm 404 can thus select the estimated lowest eigenstate ES4 for convergence"). As with claim 18, the contrast with the corresponding system claim confirms the deficiency. Claim 7 recites the same three functions and attributes them to "the processing unit," consistent with ¶[0067]; claim 7 is accordingly not rejected. Claim 19 further requires the limited multistate optimization algorithm to be configured "to optimize the accessed estimated next higher or lower eigenstate to convergence via the single-state optimization algorithm" — that is, to carry out its recited function by means of the other sub-algorithm. The specification nowhere describes such an arrangement. The disclosure therefore does not reasonably convey to one of ordinary skill in the art that the inventor, at the time the application was filed, had possession of the subject matter of claim 19. See MPEP § 2163.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 4-7 and 11-20 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Claim 4 recites, at "at least one estimated extremal eigenstate in a given iteration after a first iteration is nominally common to a state set associated with a preceding sequential iteration," a relative term, "nominally common," which renders the claim indefinite. The term "nominally common" is not defined by the claim, and the specification does not use this term or provide a standard for ascertaining the requisite degree of correspondence between eigenstates that would satisfy "nominally common." The specification instead uses the term "redundant" (¶[0039]) to describe this relationship. One of ordinary skill in the art would not be reasonably apprised of the scope of the claim. For purposes of examination, "nominally common" is interpreted under BRI to mean "redundant," consistent with the specification's use of that term at ¶[0069], [0039].
Claims 5, 6, and 7 depend from claim 4 and are rejected for at least the reasons set forth above with respect to claim 4, from which the indefinite term "nominally common" is inherited.
Claim 11 recites the limitation "the orthogonality index" in the second-iteration limitation ("to sequentially shift the state index and the orthogonality index to each tensor of a second one of the TTNSs"). There is insufficient antecedent basis for this limitation in the claim. The corresponding first-iteration limitation introduces "an orthogonality center," not an "orthogonality index," and the specification does not use the term "orthogonality index" anywhere in the disclosure. For purposes of examination, "the orthogonality index" is interpreted under BRI to refer to the "orthogonality center" previously recited in claim 11, consistent with ¶[0019] and [0043] of the specification.
Claim 12 recites the limitations "the second bundled TTNS" and "the first bundled TTNS." There is insufficient antecedent basis for these limitations in the claim. Claim 11, from which claim 12 depends, introduces "a first one of the TTNSs" and "a second one of the TTNSs," not "a first bundled TTNS" or "a second bundled TTNS. For purposes of examination, "the first bundled TTNS" and "the second bundled TTNS" are interpreted under BRI to refer to "a first one of the TTNSs" and "a second one of the TTNSs" recited in claim 11, consistent with ¶[0024] of the specification.
Claims 13 and 14 depend from claim 12 and are rejected for at least the reasons set forth above with respect to claims 11 and 12, from which the antecedent-basis deficiencies are inherited. See the BRI interpretations provided for claims 11 and 12.
Claim 15 recites the limitation "the predefined algorithm parameters." There is insufficient antecedent basis for this limitation in the claim. Claim 11, from which claim 15 depends, recites only "algorithm parameters" without the modifier "predefined." Claim 15 is further rejected for at least the reasons set forth above with respect to claim 11, from which the "orthogonality index" antecedent-basis deficiency is inherited. For purposes of examination, "the predefined algorithm parameters" in claim 15 is interpreted under BRI to refer to the "algorithm parameters" recited in claim 11, consistent with ¶[0018] of the specification.
Claim 16 recites the limitation "the extremal eigenstates of the bundled TTNS." This claim language is used inconsistently with the specification, which consistently describes "extremal eigenstates" as belonging to the TTNO (the operator), not to a bundled TTNS (a candidate state used to estimate those eigenstates). See ¶[0004], [0016], [0025]. Independent claims 1 and 11 correctly recite "extremal eigenstates of the TTNO." The inconsistent usage in claim 16 renders the scope of the limitation unclear to one of ordinary skill in the art. For purposes of examination, "the extremal eigenstates of the bundled TTNS" is interpreted under BRI to mean the extremal eigenstates of the TTNO as estimated by and represented within the bundled TTNS, consistent with ¶[0024]-[0025] of the specification.
Claims 17, 18, 19, and 20 depend from claim 16 and are rejected for at least the reasons set forth above with respect to claim 16, from which the inconsistent-terminology deficiency is inherited. See the BRI interpretation provided for claim 16.
Claim 19 recites the limitation "the memory." There is insufficient antecedent basis for this limitation in the claim. Neither claim 16, nor intervening claims 17 and 18, recite a memory. For purposes of examination, "the memory" in claim 19 is interpreted under BRI to refer to any memory associated with the processing circuitry executing the machine-readable instructions of claim 16, consistent with ¶[0006] and [0036] of the specification.
Claim 19 recites the limitation "the immediately preceding one of the iterations," which was not itself previously introduced in the claim; the claim earlier introduces only "a preceding one of the iterations." It is unclear whether "the immediately preceding one of the iterations" refers back to the previously-recited "a preceding one of the iterations" or designates a distinct antecedent. For purposes of examination, "the immediately preceding one of the iterations" is interpreted under BRI as referring back to "a preceding one of the iterations" recited earlier in claim 19, consistent with ¶[0039]-[0040] of the specification.
Appropriate correction 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 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
CLAIM 1
Step 1: Claim 1 recites “A system comprising: a non-transitory memory that stores machine-readable instructions; and a processing unit that accesses the memory and executes the machine-readable instructions,” which falls within the statutory category of a machine. See MPEP 2106.03. Accordingly, claim 1 satisfies Step 1 of the eligibility analysis.
Step 2A, Prong 1: Claim 1 is directed to an abstract idea. Specifically, claim 1 recites a mathematical concept. The claim recites a hybrid eigenstate determination algorithm comprising “a limited multistate optimization algorithm configured to determine a state set comprising estimated extremal eigenstates of a bundled tree tensor network state (TTNS) based on predefined algorithm parameters and orthogonality constraints, the bundled TTNS being associated with a tree tensor network operator (TTNO) to be determined” and “a single-state optimization algorithm configured to select at least one estimated extremal eigenstate of the determined state set and to sequentially optimize the selected at least one estimated extremal eigenstate of the state set to convergence to determine a respective at least one of the extremal eigenstates of the TTNO.” These limitations set forth and describe mathematical relationships and mathematical calculations, namely the determination of the eigenstates associated with the extremal eigenvalues of an operator — which the specification identifies as a Hermitian or real symmetric matrix (specification ¶[0013]; ¶[0022]) — represented as a tree tensor network, by two named numerical optimization procedures operating subject to orthogonality constraints. The specification confirms the mathematical character of the recited optimization by expressly defining the term: “the term ‘optimize’ (and forms thereof) refers to minimizing or maximizing the Rayleigh quotient associated with the operator defined by the TTNO” (specification ¶[0026]). Claim 1 therefore recites subject matter within the “mathematical concepts” grouping of abstract ideas. See MPEP 2106.04(a)(2), subsections I–III.
Claim 1 recites, rather than merely involves, the mathematical concept. See MPEP 2106.04, subsection II(A)(1). Unlike the limitation “training the neural network in a first stage using the first training set” of USPTO Subject Matter Eligibility Example 39, which does not set forth or describe any mathematical relationship, calculation, formula, or equation, the present limitations name the specific calculations to be performed — multistate optimization of a state set of estimated extremal eigenstates of a bundled TTNS subject to orthogonality constraints, followed by sequential single-state optimization of a selected estimated extremal eigenstate to convergence — in the manner of claim 2 of USPTO Example 47. See also Memorandum, “Reminders on evaluating subject matter eligibility of claims under 35 U.S.C. 101” (Aug. 4, 2025), § II(A).
Step 2A, Prong 2: The claim recites additional elements: “a non-transitory memory that stores machine-readable instructions” and “a processing unit that accesses the memory and executes the machine-readable instructions.”
The judicial exception is not integrated into a practical application. The additional elements, considered individually and as an ordered combination, do not integrate the judicial exception into a practical application. The specification has been consulted to determine whether the disclosed invention improves the functioning of a computer or any other technology or technical field, and whether the claim reflects any such improvement. See MPEP 2106.04(d)(1) and 2106.05(a); Ex Parte Desjardins, Appeal No. 2024-000567 (PTAB September 26, 2025, Appeals Review Panel Decision) (precedential). The specification identifies a computational objective and describes a mechanism for achieving it: the background states that prior algorithms either “can operate rapidly to determine some extremal (e.g., low-lying) eigenstates but can omit states” or “can be computationally expensive and can take an impractically long time to determine such eigenstates” (specification ¶[0003]), and the disclosure explains that selecting the algorithm parameters to optimize a proper subset of the desired eigenstates and to bound the optimization “can minimize run-time while mitigating skipped eigenstates” (¶[0019]; see also ¶[0043], ¶[0044]). The asserted benefit, however, resides entirely within the recited mathematics. Each disclosed source of the run-time reduction is a reduction in the quantity of arithmetic performed: fewer eigenstates are optimized in each iteration (¶[0043]), the optimization is truncated at a capped bond dimension or sweep count before convergence (¶[0044]; page {5}, ¶[0028]), and previously converged eigenstates are re-used as orthogonality constraints so that they are not re-optimized (page {8}, ¶[0040]). The specification describes no corresponding change to the computer that performs those calculations. The computer system is described only as functional blocks that “can each correspond diagrammatically to software, hardware, a combination of software and hardware, and/or collections of data” (page {4}, ¶[0022]; see also ¶[0023]), and the specification states that the eigensolver “implemented … for calculating the eigenproblem at each tensor can be any of a variety of software or hardware eigenproblem resolvers” (page {7}, ¶[0034]). An improvement in the abstract idea itself is not an improvement in technology. See MPEP 2106.05(a) (citing Trading Technologies Int’l v. IBG LLC, 921 F.3d 1084, 1093-94 (Fed. Cir. 2019)). The present facts are the converse of those in Ex Parte Desjardins, where the credited improvements were “tantamount to how the machine learning model itself would function in operation and therefore not subsumed in the identified mathematical calculation”; here, every asserted benefit is subsumed within the identified mathematical calculation.
The specification asserts a second benefit of a different character, and it likewise is not an improvement in technology. The background identifies the omission, or “skipping,” of eigenstates as the defect of the prior rapid algorithms, which “can omit states if the random initial states are close to other eigenstates of the tensor network matrix” (specification ¶[0003]), and the disclosure states that by saving the estimated extremal eigenstates the algorithm “can provide a more robust determination of the extremal eigenstates of the TTNO” (¶[0039]; see also ¶[0036]). That asserted benefit is an improvement in the completeness and accuracy of the numerical result that the recited mathematics produces. It is not a change in the operation of the processing unit, the memory, or any other component, and the specification describes none. An improvement in the information that a computer produces or stores is not an improvement in the functioning of the computer. See MPEP 2106.05(a) (citing BSG Tech LLC v. Buyseasons, Inc., 899 F.3d 1281, 1287-88 (Fed. Cir. 2018) (“an improvement to the information stored by a database is not equivalent to an improvement in the database’s functionality”); Trading Technologies Int’l v. IBG LLC, 921 F.3d 1084, 1093-94 (Fed. Cir. 2019)). Accordingly, neither asserted benefit is an improvement in the functioning of a computer or in any other technology or technical field.
Even were the disclosure treated as setting forth an improvement in technology, the claim would additionally have to reflect that improvement, that is, include the components or steps of the invention that provide the improvement described in the specification. See MPEP 2106.05(a) (citing Intellectual Ventures I LLC v. Symantec Corp., 838 F.3d 1307, 1316 (Fed. Cir. 2016)). Claim 1 recites the two optimization algorithms only by the results they produce. The “predefined algorithm parameters” that the specification identifies as the source of the run-time reduction are recited without any constraint on what they are or on how they bound the optimization; claim 1 does not recite the optimized state quantity as a proper subset, does not recite any limit parameter, does not recite a plurality of iterations, and does not recite any output, use, or application of the determined extremal eigenstates. The TTNO is likewise unconstrained; the specification states that it “can correspond to any of a variety of Hermitian matrices” (¶[0022]). Under the broadest reasonable interpretation, claim 1 reads on determining extremal eigenstates of any Hermitian matrix, for any purpose. A claim having such broad applicability across many fields of endeavor does not provide meaningful limitations that integrate a judicial exception into a practical application. See MPEP 2106.05(f), subsection (3). The specification confirms that breadth, listing “superconducting circuits, qubits, quantum chemistry simulations, conformal field theory, and/or disordered systems,” “chemical reaction networks, traffic modeling and optimization control, glassy dynamics, and/or computational fluid dynamics,” and “artificial intelligence and/or machine learning applications” as interchangeable uses (¶[0015]) — none of which is recited in claim 1.
The additional elements individually, the “processing unit” and the “non-transitory memory that stores machine-readable instructions” are recited at a high level of generality and do no more than instruct that the mathematical concept be carried out on a general purpose computer. A mathematical algorithm applied on a general purpose computer is the paradigmatic “apply it” recitation. See MPEP 2106.05(f), subsection (2)(i) (citing Alice Corp. Pty. Ltd. v. CLS Bank Int’l, 573 U.S. 208, 223 (2014); Gottschalk v. Benson, 409 U.S. 63, 64 (1972); Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334 (Fed. Cir. 2015)). The recited components are not a particular machine that imposes meaningful limits, because the specification states that the eigenproblem may be calculated by “any of a variety of software or hardware eigenproblem resolvers” (¶[0034]). See MPEP 2106.05(b). The claim effects no transformation or reduction of a particular article to a different state or thing; the only things changed are numerical values representing eigenstates. See MPEP 2106.05(c). The memory’s storage of the machine-readable instructions, and the processing unit’s access to them, is the ordinary manner in which a stored-program computer is directed to perform a calculation and is part of the “apply it” recitation rather than a meaningful limitation upon it. See MPEP 2106.05(f). Considered as an ordered combination, the additional elements amount to a processing unit that reads instructions from a memory and executes them, which is the conventional arrangement and operation of a stored-program computer and does not change the analysis. Accordingly, claim 1 does not satisfy Step 2A, Prong 2.
Step 2B: The claim does not include additional elements that amount to significantly more than the judicial exception. The “processing unit” performing the recited eigenproblem calculations is a generic computer employed for the performance of repetitive calculations, which the courts have recognized as well-understood, routine, and conventional. See MPEP 2106.05(d)(II)(ii) (citing Parker v. Flook, 437 U.S. 584, 594 (1978); Bancorp Servs., L.L.C. v. Sun Life Assurance Co., 687 F.3d 1266, 1278 (Fed. Cir. 2012) (“The computer … is employed only for its most basic function, the performance of repetitive calculations, and as such does not impose meaningful limits on the scope of those claims.”)); see also Alice Corp., 573 U.S. at 225-26. The “non-transitory memory that stores machine-readable instructions” and the processing unit’s access of that memory constitute storing and retrieving information in memory, which the courts have likewise recognized as well-understood, routine, and conventional. See MPEP 2106.05(d)(II)(iv) (citing Versata, 793 F.3d at 1334; OIP Techs., Inc. v. Amazon.com, Inc., 788 F.3d 1359, 1363 (Fed. Cir. 2015)). These findings are further supported by the specification itself, which describes the computer system generically as functional blocks corresponding to “software, hardware, a combination of software and hardware, and/or collections of data” ¶[0022]) and states that the eigenproblem may be calculated by “any of a variety of software or hardware eigenproblem resolvers” (¶[0034]). See MPEP 2106.05(d)(I) (an express statement in the specification may demonstrate the well-understood, routine, and conventional nature of an additional element); Intellectual Ventures I LLC v. Symantec Corp., 838 F.3d 1307, 1317 (Fed. Cir. 2016) (“The written description is particularly useful in determining what is well-known or conventional”). The ordered combination of the processing unit and the memory adds nothing further, as the components interact in their ordinary and expected fashion, with the processing unit fetching and executing instructions held in the memory. Accordingly, claim 1 does not satisfy Step 2B and is rejected under 35 U.S.C. 101.
CLAIM 2
Step 1: Claim 2 depends from claim 1 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 2 incorporates all the limitations of claim 1 and is therefore directed to the same abstract idea identified in claim 1. Claim 2 additionally recites that “the predefined algorithm parameters comprise an optimized state quantity that defines a quantity of the estimated extremal eigenstates in the state set that is a proper subset of the quantity of extremal eigenstates of the TTNO and that determines a size of a state index, the state index being sequentially shifted along with an orthogonality center to each of a plurality of tensors of the bundled TTNS during a sweep of the bundled TTNS to optimize the quantity of the estimated extremal eigenstates of the extremal eigenstates of the TTNO associated with the bundled TTNS as defined by the optimized state quantity.” These are mathematical constraints on the recited calculation: a cardinality constraint defining a proper subset of the eigenstates to be optimized, a dimensional constraint on the size of an index, and the sequential relocation of that index and of the orthogonality center among the tensors during a sweep, which is the numerical bookkeeping by which the recited eigenproblem is evaluated. See MPEP 2106.04(a)(2). No new additional elements are introduced.
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
CLAIM 3
Step 1: Claim 3 depends from claim 1 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 3 incorporates all the limitations of claim 1 and is therefore directed to the same abstract idea identified in claim 1. Claim 3 additionally recites that “the hybrid eigenstate determination algorithm is configured to operate in a plurality of iterations comprising the limited multistate optimization algorithm followed by the single-state optimization algorithm, such that the limited multistate optimization algorithm is configured to determine the state set in each of the iterations, the state set being different in each of the iterations,” and that the single-state optimization algorithm operates on the state set of the respective iteration to determine the extremal eigenstates of the TTNO. This limitation specifies only that the recited mathematical operations are repeated in sequence over a plurality of iterations on successively different state sets. The iterative repetition of a mathematical calculation remains a mathematical concept. See MPEP 2106.04(a)(2). No new additional elements are introduced.
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
CLAIM 4
Step 1: Claim 4 depends from claim 3 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 4 incorporates all the limitations of claims 1 and 3 and is therefore directed to the same abstract idea identified in claim 1. Claim 4 additionally recites that “at least one estimated extremal eigenstate in a given iteration after a first iteration is nominally common to a state set associated with a preceding sequential iteration,” which sets forth a mathematical relationship between the state sets of successive iterations and is therefore part of the recited abstract idea. See MPEP 2106.04(a)(2).
Step 2A, Prong 2: Claim 4 further recites the additional elements: “the processing unit is configured to store the estimated extremal eigenstates of each state set in each of the iterations in the memory, and to store the determined at least one of the extremal eigenstates in each of the iterations in the memory.” The additional elements in claim 4 are the processing unit and memory of claim 1, together with the newly recited functions of “stor[ing] the estimated extremal eigenstates of each state set … in the memory” and “stor[ing] the determined at least one of the extremal eigenstates … in the memory.”
The judicial exception is not integrated into a practical application. For the same reasons as discussed in the Step 2A, Prong 2 analysis of claim 1, the processing unit and the memory do not integrate the judicial exception into a practical application.
With respect to the newly recited storing functions, writing the results of the recited calculations into the memory is post-solution activity that is ancillary to the mathematical concept and does not impose any meaningful limit on it. See MPEP 2106.05(g). The claim recites only that the computed eigenstates are stored; it does not recite any use or application of the stored values that would effect an improvement in the functioning of the computer or in any other technology. Storing computed values in a generic memory so that they may be read back in a later iteration is the ordinary, expected use of a memory and amounts to no more than an instruction to implement the mathematical concept on a generic computer. See MPEP 2106.05(f). Accordingly, claim 4 does not satisfy Step 2A, Prong 2. It is acknowledged that the specification attributes a purpose to this retention of data: the estimated extremal eigenstates are saved “to provide redundancy” (¶[0036]) so that the single-state optimization algorithm may fall back on a stored eigenstate from a preceding iteration and thereby mitigate state-skipping (¶[0039]). That purpose is served by supplying data to the recited mathematics; it is not a change in how the memory or the processing unit operates, and the specification describes no such change. An improvement in the information a computer stores or produces is not an improvement in the functioning of the computer. See MPEP 2106.05(a) (citing BSG Tech LLC v. Buyseasons, Inc., 899 F.3d 1281, 1287-88 (Fed. Cir. 2018)).
Step 2B: The claim does not include additional elements that amount to significantly more than the judicial exception. For the same reasons as discussed in the Step 2B analysis of claim 1, the processing unit and the memory are well-understood, routine, and conventional. With respect to the newly recited functions of storing the estimated extremal eigenstates and the determined extremal eigenstates in the memory, storing and retrieving information in memory has been recognized by the courts as well-understood, routine, and conventional activity. See MPEP 2106.05(d)(II)(iv) (citing Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334 (Fed. Cir. 2015); OIP Techs., Inc. v. Amazon.com, Inc., 788 F.3d 1359, 1363 (Fed. Cir. 2015)). The ordered combination of calculating values and then storing them in a memory for later retrieval adds nothing beyond the conventional operation of a stored-program computer. Accordingly, claim 4 does not satisfy Step 2B and is rejected under 35 U.S.C. 101.
CLAIM 5
Step 1: Claim 5 depends from claim 4 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 5 incorporates all the limitations of claims 1, 3, and 4 and is therefore directed to the same abstract idea identified in claim 1. Claim 5 additionally recites that “the processing unit is configured to compare the estimated extremal eigenstates of a state set associated with a given one of the iterations with the estimated extremal eigenstates of a state set associated with a preceding sequential iteration to determine redundancy.” The comparison of computed eigenstates in order to determine redundancy is an evaluation of the results of the recited calculation and is itself part of the mathematical concept. See MPEP 2106.04(a)(2).
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
CLAIM 6
Step 1: Claim 6 depends from claim 4 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 6 incorporates all the limitations of claims 1, 3, and 4 and is therefore directed to the same abstract idea identified in claim 1. Claim 6 additionally recites that “the processing unit is configured to provide the determined at least one of the extremal eigenstates of a given one of the iterations as an orthogonality constraint to the limited multistate optimization algorithm, such that the limited multistate optimization algorithm is configured to determine the estimated extremal eigenstates of a state set associated with a next one of the iterations as having higher or lower eigenstates relative to the at least one of the extremal eigenstates of the given one of the iterations.” Constraining a subsequent eigenproblem calculation to solutions orthogonal to previously determined eigenstates, and thereby to eigenstates of successively higher or lower eigenvalue, sets forth a mathematical relationship governing the recited calculation. See MPEP 2106.04(a)(2).
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
CLAIM 7
Step 1: Claim 7 depends from claim 4 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 7 incorporates all the limitations of claims 1, 3, and 4 and is therefore directed to the same abstract idea identified in claim 1. Claim 7 additionally recites “determin[ing] if an estimated extremal eigenstate of a state set of a given one of the iterations is an estimated next higher or lower eigenstate relative to the determined at least one of the extremal eigenstates of a preceding sequential iteration” and, if not, “to optimize the accessed estimated next higher or lower eigenstate to convergence via the single-state optimization algorithm in the given one of the iterations.” Determining the ordinal relationship between computed eigenvalues and optimizing a selected eigenstate to convergence are mathematical evaluations and calculations forming part of the recited abstract idea. See MPEP 2106.04(a)(2).
Step 2A, Prong 2: The additional elements in claim 7 are the processing unit and memory of claim 1, together with the newly recited function of being “configured to access an estimated next higher or lower eigenstate of a state set of the preceding sequential iteration from the memory.” The judicial exception is not integrated into a practical application. For the same reasons as discussed in the Step 2A, Prong 2 analysis of claim 1, the processing unit and the memory do not integrate the judicial exception into a practical application.
With respect to the newly recited function of accessing a previously stored estimated eigenstate from the memory, the retrieval of previously stored data for use in a subsequent calculation is pre-solution data gathering that is ancillary to the mathematical concept and imposes no meaningful limit on it. See MPEP 2106.05(g). Reading a stored value back from a generic memory is the ordinary, expected use of a memory and amounts to no more than an instruction to implement the mathematical concept on a generic computer. See MPEP 2106.05(f). Accordingly, claim 7 does not satisfy Step 2A, Prong 2.
It is acknowledged that the specification attributes a purpose to this retention of data: the estimated extremal eigenstates are saved “to provide redundancy” (¶[0036]) so that the single-state optimization algorithm may fall back on a stored eigenstate from a preceding iteration and thereby mitigate state-skipping (¶[0039]). That purpose is served by supplying data to the recited mathematics; it is not a change in how the memory or the processing unit operates, and the specification describes no such change. An improvement in the information a computer stores or produces is not an improvement in the functioning of the computer. See MPEP 2106.05(a) (citing BSG Tech LLC v. Buyseasons, Inc., 899 F.3d 1281, 1287-88 (Fed. Cir. 2018)).
Step 2B: The claim does not include additional elements that amount to significantly more than the judicial exception. For the same reasons as discussed in the Step 2B analysis of claim 1, the processing unit and the memory are well-understood, routine, and conventional. With respect to the newly recited function of accessing an estimated extremal eigenstate from the memory, storing and retrieving information in memory has been recognized by the courts as well-understood, routine, and conventional activity. See MPEP 2106.05(d)(II)(iv) (citing Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334 (Fed. Cir. 2015); OIP Techs., Inc. v. Amazon.com, Inc., 788 F.3d 1359, 1363 (Fed. Cir. 2015)). The ordered combination of retrieving a stored value and then performing further calculations upon it adds nothing beyond the conventional operation of a stored-program computer. Accordingly, claim 7 does not satisfy Step 2B and is rejected under 35 U.S.C. 101.
CLAIM 8
Step 1: Claim 8 depends from claim 1 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 8 incorporates all the limitations of claim 1 and is therefore directed to the same abstract idea identified in claim 1. Claim 8 additionally recites that “the predefined algorithm parameters comprise a maximum bond dimension of the tensors of the bundled TTNS during operation of the limited multistate optimization algorithm in each iteration of the hybrid eigenstate determination algorithm.” The bond dimension is the dimension of the virtual index interconnecting the tensors of the tensor network representation (¶[0016]), and a maximum value therefore is a numerical bound on the recited calculation. Such a numerical parameter of the recited computation is mathematical in nature and is part of the recited abstract idea. See MPEP 2106.04(a)(2).
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
CLAIM 9
Step 1: Claim 9 depends from claim 1 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 9 incorporates all the limitations of claim 1 and is therefore directed to the same abstract idea identified in claim 1. Claim 9 additionally recites that “the predefined algorithm parameters comprise a maximum number of sweeps during operation of the limited multistate optimization algorithm in each iteration of the hybrid eigenstate determination algorithm.” A maximum number of sweeps is a numerical bound on how many times the recited optimization is iterated over the tensors before it is terminated. Such a numerical parameter of the recited computation is mathematical in nature and is part of the recited abstract idea. See MPEP 2106.04(a)(2).
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
CLAIM 10
Step 1: Claim 10 depends from claim 1 and recites a system, which falls within the statutory category of a machine. See MPEP 2106.03.
Step 2A, Prong 1: Claim 10 incorporates all the limitations of claim 1 and is therefore directed to the same abstract idea identified in claim 1. Claim 10 additionally recites that “the predefined algorithm parameters comprise a quantity of the estimated extremal eigenstates of each state set that is selected to be optimized to convergence by the single-state optimization algorithm in each iteration of the hybrid eigenstate determination algorithm.” A quantity of eigenstates selected for further optimization is a cardinality constraint on the recited calculation. Such a numerical parameter of the recited computation is mathematical in nature and is part of the recited abstract idea. See MPEP 2106.04(a)(2).
Step 2A, Prong 2 & Step 2B: No additional elements are introduced, the analysis from the parent claim is maintained.
Claims 11, 12, 13, 14 and 15 are substantially similar in scope and spirit to claims 1+2+3, 4, 6, 7 and 8+9, respectively. Therefore, the 35 U.S.C. 101 rejections of claims 1+2+3, 4, 6, 7 and 8+9 are applied accordingly. Claims 11, 12, 13, 14, 15 only differ from claims 1+2+3, 4, 6, 7 and 8+9 in the Step 1 analysis, wherein the former recites “A method for determining a plurality of extremal eigenstates of a tree tensor network operator (TTNO),” comprising a series of steps, which falls within the statutory category of a process. See MPEP 2106.03. Accordingly, claims 11, 12, 13, 14 and 15 satisfies Step 1 of the eligibility analysis.
Claims 16, 17, 18, 19 and 20 are substantially similar in scope and spirit to claims 1+3, 2, 6, 7 and 8+9, respectively. Therefore, the 35 U.S.C. 101 rejections of claims 1+3, 2, 6, 7 and 8+9 are applied accordingly. Claims 16, 17, 18, 19 and 20 only differ from claims 1+3, 2, 6, 7 and 8+9 in the Step 1 analysis, wherein the former recites
“A non-transitory computer readable medium comprising machine-readable instructions,” which falls within the statutory category of an article of manufacture. See MPEP 2106.03. Accordingly, claim 16, 17, 18, 19 and 20 satisfies Step 1 of the eligibility analysis.
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 for establishing a background for determining obviousness under 35 U.S.C. 103 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.
This application currently names joint inventors. In considering patentability of the claims the examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the examiner to consider the applicability of 35 U.S.C. 102(b)(2)(C) for any potential 35 U.S.C. 102(a)(2) prior art against the later invention.
Claims 1-3, 8-11, 15-18 and 20 are rejected under 35 USC 103 as being unpatentable over Computing vibrational eigenstates with tree tensor network states (TTNS) to Larsson (hereinafter Larsson) in view of Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond to Zhai et al. (hereinafter Zhai).
Per claim 1, Larsson discloses A system (Larsson: Abstract, p. 1…Larsson describes a computational scheme that determines the extremal eigenstates of an operator represented as a loop-free tensor network by a density-matrix-renormalization-group sweep algorithm, which constitutes the system limitation under BRI, "We present how to compute vibrational eigenstates with tree tensor network states (TTNS), the underlying ansatz behind the multilayer multi-configuration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group (DMRG)"; § III B, p. 10…the scheme is embodied in a concrete executable program rather than in the abstract, so what Larsson discloses is a working computational system, "The program we used is implemented in Python and makes use of NumPy"), comprising:
…
a limited multistate optimization algorithm configured to determine a state set comprising estimated extremal eigenstates of a bundled tree tensor network state (TTNS) based on predefined algorithm parameters and orthogonality constraints, the bundled TTNS being associated with a tree tensor network operator (TTNO) to be determined (Larsson: § III B, p. 9…the first step of Larsson's procedure is a deliberately loosened state-average optimization that carries twenty states at once and is cut off by a predefined sweep limit, so that it returns estimates rather than converged eigenstates, which constitutes the limited multistate optimization algorithm…to determine a state set comprising estimated extremal eigenstates…based on predefined algorithm parameters limitation under BRI, "Do a (loose) state average calculation with 20 states for maximal seven sweeps (as shown in Fig. 10). This gives a rough estimate of the eigenstates"; § II D 3, p. 7…the several states are carried simultaneously in a single tensor network by adding a state-indicating bond to it, which is the bundling recited by the bundled tree tensor network state (TTNS) limitation under BRI, "It can be achieved by adding to the root node an additional “physical” bond that indicates the particular state"; § III B, p. 9…every such optimization is constrained by the eigenstates already determined so that it cannot re-converge them, which constitutes the orthogonality constraints limitation under BRI, "Throughout, the Hamiltonian was shifted by the previously computed states (see Eq. (14))"; § II C 1, p. 5…the operator whose eigenstates are sought is itself decomposed into a loop-free tensor network form, which Larsson expressly names a tree tensor network operator and which constitutes the tree tensor network operator (TTNO) to be determined limitation under the BRI supplied by the specification's own lexicographic definition at ¶[0013], "Most optimal decompositions would probably be decompositions of the Hamiltonian using similar tree tensor networks (tree tensor network operators)"); and
…
Larsson does not expressly disclose, but Zhai does teach:
a non-transitory memory that stores machine-readable instructions (Zhai: Abstract, p. 1…Zhai distributes the sweep algorithms as an open-source code, i.e. as instructions fixed in a form a machine can read and execute, which constitutes the non-transitory memory that stores machine-readable instructions limitation under BRI, "block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms"; § II B, p. 5…the tensors operated on at each step of the sweep are held in memory during execution, confirming an addressable store that the algorithm reads and writes, "tensors required at the given one or two sites in an iteration of the sweep algorithm are loaded into memory"); and
a processing unit that accesses the memory and executes the machine-readable instructions, the machine-readable instructions comprising a hybrid eigenstate determination algorithm (Zhai: FIG. 1 caption, p. 2…Zhai reports the measured wall time of a sweep on a stated number of processor cores, which establishes that the stored instructions are fetched and executed by processing hardware, and therefore constitutes the processing unit that accesses the memory and executes the machine-readable instructions limitation under BRI, "The scaling of DMRG wall time (using 24 CPU cores) per sweep with respect to the MPS bond dimension"; § II A 3, p. 3…the instructions so executed carry out a state-by-state optimization that is itself run together with the multistate state-averaged optimization, so that the two solvers operate as one composite procedure rather than as alternatives, which constitutes the hybrid eigenstate determination algorithm limitation under BRI, "where |Ψi⟩ are the converged states below the targeted excited state |Ψk⟩, and wi are the energy level shifts. This can be combined with the state-averaged ansatz to determine batches of states at a time") comprising: …
a single-state optimization algorithm configured to select at least one estimated extremal eigenstate of the determined state set and to sequentially optimize the selected at least one estimated extremal eigenstate of the state set to convergence to determine a respective at least one of the extremal eigenstates of the TTNO (Zhai: § II A 3, p. 2…Zhai teaches taking the states produced by the multistate state-averaged calculation and refining each one individually, as its own separate tensor network and with the lower-lying states projected out, which is an optimization of a single selected state and therefore constitutes the single-state optimization algorithm…to select at least one estimated extremal eigenstate of the determined state set and to sequentially optimize limitation under BRI, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site"; § II A 3, pp. 2-3…Zhai teaches a second single-state form in which the states are taken one at a time against a Hamiltonian shifted by the states already converged, and expressly identifies those already-converged states as the eigenstates handed forward, which constitutes the recited optimization to convergence to determine a respective at least one of the extremal eigenstates of the TTNO, "Here, we compute the ground and excited states one-by-one with a modified level-shifted Hamiltonian defined as…"; § II A 3, p. 3…the states so converged are the ones the next pass is constrained by, and the procedure is run group by group until the spectrum is built up, "where |Ψi⟩ are the converged states below the targeted excited state |Ψk⟩, and wi are the energy level shifts. This can be combined with the state-averaged ansatz to determine batches of states at a time").
Larsson and Zhai are analogous art because they are from the same field of endeavor, specifically the determination of extremal eigenstates of an operator represented as a loop-free tensor network by density-matrix-renormalization-group sweep algorithms. They are further reasonably pertinent to the same problem with which the inventor was involved, namely obtaining a large number of the extremal eigenstates of such an operator accurately, in eigenvalue order and without skipping states, at an acceptable computational cost.
Before the effective filing date of the claimed invention, it would have been obvious to a PHOSITA to follow the loose, parameter-limited state-average step of Larsson with the per-state projected refinement of Zhai, and to store the eigenstates so converged as the orthogonality constraints for the next pass, as claimed.
The suggestion/motivation for doing so would have been provided by Zhai itself, which identifies the output of a state-averaged calculation as the very input its per-state refinement is meant to improve, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site" (Zhai: § II A 3, p. 2), and which expressly cites Larsson as a source of that refinement approach, "Larsson, H. R. Computing vibrational eigenstates with tree tensor network states (TTNS). The Journal of Chemical Physics" (Zhai: Ref. 61, p. 16). Zhai further states the deficiency that makes the refinement worth adding, teaching that a state-averaged optimization loses accuracy as the number of states it carries grows, "This algorithm is normally a robust and convenient choice for tens of roots, but for a given bond dimension, the accuracy decreases as the number of roots is increased" (Zhai: § II A 3, p. 2). Larsson supplies the corresponding suggestion from its own side, teaching that optimizing the states individually is an available alternative and that the state-average step is retained only because it is faster, "In principle, one could also avoid the state average calculations at all and perform optimizations state by state" (Larsson: § III B, p. 9). Lastly, this is the application of a known technique to a known method ready for improvement to yield predictable results, the rationale of MPEP § 2143.01(D), and the combination does no more than yield the predictable result each reference already attributes to it, namely converged extremal eigenstates obtained faster than by refining every state from the outset.
Per claim 2, Larsson combined with Zhai discloses claim 1. Larsson further teaches wherein the predefined algorithm parameters comprise an optimized state quantity that defines a quantity of the estimated extremal eigenstates in the state set that is a proper subset of the quantity of extremal eigenstates of the TTNO and that determines a size of a state index, the state index being sequentially shifted along with an orthogonality center to each of a plurality of tensors of the bundled TTNS during a sweep of the bundled TTNS to optimize the quantity of the estimated extremal eigenstates of the extremal eigenstates of the TTNO associated with the bundled TTNS as defined by the optimized state quantity (Larsson: § III B, p. 9…the run as a whole seeks eighty-four eigenstates, so the quantity programmed into any one pass is a proper subset of the eigenstates sought, "To obtain the lowest 84 eigenstates, we iterated the following procedure, both for TTNS and MPS:"; § III B, p. 9…the quantity so programmed is twenty, which constitutes the optimized state quantity…that is a proper subset of the quantity of extremal eigenstates of the TTNO limitation under BRI, "Do a (loose) state average calculation with 20 states for maximal seven sweeps"; § II D 3, p. 7…that quantity is carried as a dedicated bond on the network whose dimension is the number of states, which constitutes the claimed "state index" whose size the optimized state quantity determines, "It can be achieved by adding to the root node an additional “physical” bond that indicates the particular state"; § II D 3, p. 7…because the canonical root node advances from tensor to tensor over the course of the sweep, the state-indicating bond must be carried along with it, which constitutes the state index being sequentially shifted along with an orthogonality center to each of a plurality of tensors of the bundled TTNS during a sweep limitation under BRI, "To make the optimization stable, it is required to move the state dimension from one node to another").
Per claim 3, Larsson combined with Zhai discloses claim 1. Larsson further teaches wherein the hybrid eigenstate determination algorithm is configured to operate in a plurality of iterations comprising the limited multistate optimization algorithm followed by the single-state optimization algorithm, such that the limited multistate optimization algorithm is configured to determine the state set in each of the iterations, the state set being different in each of the iterations (Larsson: § III B, p. 9…the multistate step is not run once but is repeated as the first stage of a procedure that is iterated until the whole set of eigenstates is obtained, which constitutes the recited plurality of iterations under BRI, "To obtain the lowest 84 eigenstates, we iterated the following procedure, both for TTNS and MPS:"; § III B, p. 9…the first stage of each such pass is the loose twenty-state calculation that returns estimates, "Do a (loose) state average calculation with 20 states for maximal seven sweeps"; § II D 2, p. 7…the constraint carried into each successive pass is what forces the newly returned states to differ from those already obtained, which constitutes the recited state set being different in each of the iterations, "Note that after the optimization, the newly computed eigenstate is orthogonal to the previously computed states"), and …
Larsson does not expressly disclose, but Zhai does teach: such that the single-state optimization algorithm is configured to select the at least one estimated extremal eigenstate of the state set associated with the respective iteration and to sequentially optimize the selected at least one estimated extremal eigenstate of the state set associated with the respective one of the iterations to convergence to determine the at least one of the extremal eigenstates in each of the iterations to determine the extremal eigenstates of the TTNO (Zhai: § II A 3, p. 2…Zhai teaches refining each state produced by the state-averaged pass on its own, with the lower-lying states projected out, which constitutes the recited per-iteration selection and sequential optimization of a single estimated eigenstate under BRI, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site"; § II A 3, p. 3…Zhai runs that state-by-state optimization together with the state-averaged ansatz so that the spectrum is built up a group at a time, each group being converged before the next is sought, which constitutes the recited determination of the extremal eigenstates in each of the iterations, "where |Ψi⟩ are the converged states below the targeted excited state |Ψk⟩, and wi are the energy level shifts. This can be combined with the state-averaged ansatz to determine batches of states at a time"). The rationale to combine Zhai with Larsson is the same as set forth for claim 1.
Per claim 8, Larsson combined with Zhai discloses claim 1. Larsson further teaches wherein the predefined algorithm parameters comprise a maximum bond dimension of the tensors of the bundled TTNS during operation of the limited multistate optimization algorithm in each iteration of the hybrid eigenstate determination algorithm (Larsson: § III B, p. 9…among the parameters set before each state-average run is an explicit ceiling on the bond dimension the network tensors may reach, which constitutes the maximum bond dimension of the tensors of the bundled TTNS limitation under BRI, "we fixed the maximally allowed bond dimension nmax and also set a minimal bond dimension of nmin = 3").
Per claim 9, Larsson combined with Zhai discloses claim 1. Larsson further teaches wherein the predefined algorithm parameters comprise a maximum number of sweeps during operation of the limited multistate optimization algorithm in each iteration of the hybrid eigenstate determination algorithm (Larsson: § III B, p. 9…the multistate step of each pass is halted at a sweep count fixed in advance, which is what makes that step "loose" and leaves its output as estimates, and which constitutes the maximum number of sweeps limitation under BRI, "Do a (loose) state average calculation with 20 states for maximal seven sweeps (as shown in Fig. 10). This gives a rough estimate of the eigenstates").
Per claim 10, Larsson combined with Zhai discloses claim 1. Larsson further teaches wherein the predefined algorithm parameters comprise a quantity of the estimated extremal eigenstates of each state set that is selected to be optimized to convergence by the single-state optimization algorithm in each iteration of the hybrid eigenstate determination algorithm (Larsson: § III B, p. 9…after each twenty-state estimate Larsson divides the estimated states into groups by a threshold fixed in advance, and it is that programmed threshold which fixes how many of the estimated states are carried into the converging stage on each pass, which constitutes the recited predefined algorithm parameters compris[ing] a quantity of the estimated extremal eigenstates of each state set that is selected to be optimized to convergence under BRI, "Cluster the 20 states in groups whose energy differ by maximal 2 cm-1. Discard the last cluster as this may overlap with higher lying states"; § III B, p. 9…each such group is then taken to convergence on that same pass, so the programmed quantity is the quantity optimized to convergence in each iteration, "For each cluster, do an additional (refined) state average calculation for maximal ten sweeps. This gives the converged states").
Per claim 11, Larsson discloses A method for determining a plurality of extremal eigenstates of a tree tensor network operator (TTNO) (Larsson: § III B, p. 9…Larsson sets out a procedure whose stated object is to obtain the eighty-four lowest eigenstates of the tensor-network-represented Hamiltonian, which constitutes the method for determining a plurality of extremal eigenstates of a tree tensor network operator (TTNO) limitation under BRI, "To obtain the lowest 84 eigenstates, we iterated the following procedure, both for TTNS and MPS:"; § II C 1, p. 5…that Hamiltonian is itself put into a loop-free tensor network form, which the specification's own definition at ¶[0013] makes a TTNO, "can be decomposed as a sum of direct products of one-dimensional operators or matrices in finite basis representation (SOP)"), the method comprising:
defining algorithm parameters comprising an optimized state quantity that defines a quantity of extremal eigenstates that is a proper subset of the extremal eigenstates of the TTNO and that determines a size of a state index for each of a plurality of bundled tree tensor network states (TTNSs) associated with the TTNO (Larsson: § III B, p. 9…twenty states are programmed into each state-average pass out of the eighty-four sought overall, so the programmed quantity is a proper subset, which constitutes the optimized state quantity…that is a proper subset limitation under BRI, "Do a (loose) state average calculation with 20 states for maximal seven sweeps"; § II D 3, p. 7…that same quantity fixes the dimension of the state-indicating bond added to the network, which constitutes the recited determination of a size of a state index, "It can be achieved by adding to the root node an additional “physical” bond that indicates the particular state"); and
implementing a hybrid eigenstate determination algorithm comprising a plurality of iterations, wherein implementing the hybrid eigenstate determination algorithm comprises:
implementing a limited multistate optimization algorithm in a first iteration to sequentially shift the state index and an orthogonality center to each tensor of a first one of the TTNSs to determine a first state set comprising first estimated extremal eigenstates having the quantity of extremal eigenstates defined by the optimized state quantity (Larsson: § III B, p. 9…the procedure is expressly iterated, and its first stage on each pass is the loose twenty-state calculation that yields the estimated eigenstates, which constitutes the recited first-iteration limited multistate optimization under BRI, "Do a (loose) state average calculation with 20 states for maximal seven sweeps (as shown in Fig. 10). This gives a rough estimate of the eigenstates"; § II D 3, p. 7…the canonical root node moves from tensor to tensor over the sweep and the state-indicating bond is carried with it, which constitutes the recited sequential shifting of "the state index and an orthogonality center to each tensor", "To make the optimization stable, it is required to move the state dimension from one node to another");
…
implementing the limited multistate optimization algorithm in a second iteration to sequentially shift the state index and the orthogonality index to each tensor of a second one of the TTNSs to determine a second state set comprising second estimated extremal eigenstates having the quantity of extremal eigenstates defined by the optimized state quantity (Larsson: § III B, p. 9…because the same procedure is iterated with the Hamiltonian shifted by everything already computed, the second pass runs the identical twenty-state sweep on a second network and returns a second, different set of estimates, which constitutes the recited second-iteration limited multistate optimization under BRI, "Throughout, the Hamiltonian was shifted by the previously computed states (see Eq. (14))"; § II D 2, p. 7…the shift is what guarantees the second pass returns states other than those already obtained, "Note that after the optimization, the newly computed eigenstate is orthogonal to the previously computed states");
Larsson does not expressly disclose, but Zhai does teach:
implementing a single-state optimization algorithm in the first iteration to select at least one of the first estimated extremal eigenstates of the determined first state set and to sequentially optimize the selected at least one of the first estimated extremal eigenstates of the first state set to convergence to determine a respective first converged set of at least one converged extremal eigenstate of the TTNO (Zhai: § II A 3, p. 2…Zhai teaches taking the states that the state-averaged pass produced and refining each selected state on its own, as a separate tensor network with the lower states projected out, which constitutes the recited selection and sequential optimization to convergence under BRI, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site"; § II A 3, p. 3…Zhai identifies the states that this stage yields as the converged states, which constitutes the recited "converged set of at least one converged extremal eigenstate of the TTNO", "where |Ψi⟩ are the converged states below the targeted excited state |Ψk⟩, and wi are the energy level shifts. This can be combined with the state-averaged ansatz to determine batches of states at a time").
…
implementing the single-state optimization algorithm in the second iteration to select at least one of the second estimated extremal eigenstates of the determined second state set and to sequentially optimize the selected at least one of the second estimated extremal eigenstates of the second state set to convergence to determine a respective second converged set of at least one converged extremal eigenstate of the TTNO (Zhai: § II A 3, p. 2…the same per-state refinement is what Zhai applies to whichever state-averaged set is at hand, so it is applied again to the second set, "one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site"; § II A 3, p. 3…Zhai expressly contemplates repeating the procedure group after group until the spectrum is built up, "This can be combined with the state-averaged ansatz to determine batches of states at a time").
Larsson and Zhai are analogous art because they are from the same field of endeavor, specifically the determination of extremal eigenstates of an operator represented as a loop-free tensor network by density-matrix-renormalization-group sweep algorithms. They are further reasonably pertinent to the same problem with which the inventor was involved, namely obtaining a large number of the extremal eigenstates of such an operator accurately, in eigenvalue order and without skipping states, at an acceptable computational cost.
Before the effective filing date of the claimed invention, it would have been obvious to a PHOSITA to carry out Larsson's iterated procedure with Zhai's per-state projected refinement supplying the converging stage of each iteration, as claimed.
The suggestion/motivation for doing so would have been provided by Zhai itself, which identifies the output of a state-averaged calculation as the very input its per-state refinement is meant to improve, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site" (Zhai: § II A 3, p. 2), and which expressly cites Larsson as a source of that refinement approach, "Larsson, H. R. Computing vibrational eigenstates with tree tensor network states (TTNS). The Journal of Chemical Physics" (Zhai: Ref. 61, p. 16). Zhai further states the deficiency that makes the refinement worth adding, teaching that a state-averaged optimization loses accuracy as the number of states it carries grows, "This algorithm is normally a robust and convenient choice for tens of roots, but for a given bond dimension, the accuracy decreases as the number of roots is increased" (Zhai: § II A 3, p. 2). Larsson supplies the corresponding suggestion from its own side, teaching that optimizing the states individually is an available alternative and that the state-average step is retained only because it is faster, "In principle, one could also avoid the state average calculations at all and perform optimizations state by state" (Larsson: § III B, p. 9). Furthermore, the combination is the application of a known technique to a known method ready for improvement and produces only the predictable result the references already ascribe to it.
Per claim 15, Larsson combined with Zhai discloses claim 11. Larsson further teaches wherein the predefined algorithm parameters comprise at least one of a maximum bond dimension of the tensors of the bundled TTNS and a maximum number of sweeps during operation of the limited multistate optimization algorithm in each iteration of the hybrid eigenstate determination algorithm (Larsson: § III B, p. 9…both alternatives recited are fixed in advance for every state-average pass, a ceiling on the tensors’ bond dimension and a ceiling on the sweep count, either of which satisfies the recited at least one of under BRI, "we fixed the maximally allowed bond dimension nmax and also set a minimal bond dimension of nmin = 3"); § III B, p. 9…"Do a (loose) state average calculation with 20 states for maximal seven sweeps").
Per claim 16, Larsson discloses …machine-readable instructions, the machine-readable instructions being executed to implement a hybrid eigenstate determination algorithm in each of a plurality of iterations, the hybrid eigenstate determination algorithm being configured to (Larsson: § III B, p. 10…the procedure is carried out by an actual program written in Python and C++, i.e. by machine-readable instructions that are executed, which constitutes the machine-readable instructions…being executed limitation under BRI, "The program we used is implemented in Python and makes use of NumPy"; § III B, p. 9…the procedure those instructions carry out is expressly iterated, which constitutes the recited execution in each of a plurality of iterations, "To obtain the lowest 84 eigenstates, we iterated the following procedure, both for TTNS and MPS"):
generate a bundled tree tensor network state (TTNS) associated with a tree tensor network operator (TTNO) in each of the iterations (Larsson: § II D 3, p. 7…a fresh state-averaged tree network carrying the several states on a state-indicating bond is set up for the calculation, which constitutes the generation of a bundled tree tensor network state (TTNS) under BRI, "Another, well-known way to obtain excited states is to describe several eigenstates simultaneously with the same tensor network. This is known as state averaging"; § II C 1, p. 5…the network is set up against the Hamiltonian in loop-free tensor network form, which the specification’s definition at ¶[0013] makes the claimed TTNO, "Most optimal decompositions would probably be decompositions of the Hamiltonian using similar tree tensor networks (tree tensor network operators)");
implement a limited multistate optimization algorithm configured to determine a state set in each of the iterations, the state set being different in each of the iterations and comprising estimated extremal eigenstates of the bundled TTNS based on predefined algorithm parameters (Larsson: § III B, p. 9…each pass runs the same loose twenty-state, seven-sweep calculation and returns estimates, which constitutes the recited per-iteration determination of a state set of estimated extremal eigenstates based on predefined algorithm parameters under BRI, "Do a (loose) state average calculation with 20 states for maximal seven sweeps (as shown in Fig. 10). This gives a rough estimate of the eigenstates"; § II D 2, p. 7…because every optimization is constrained by the states already computed, the set a later pass returns is necessarily other than the sets already returned, which constitutes the recited state set being different in each of the iterations, "Note that after the optimization, the newly computed eigenstate is orthogonal to the previously computed states"); and …
Larsson does not expressly disclose, but Zhai does teach:
A non-transitory computer readable medium comprising… (Zhai: Abstract, p. 1…Zhai distributes the eigenstate algorithms as an open-source code, which is instructions fixed in a machine-readable article rather than a transient signal, and therefore constitutes the "non-transitory computer readable medium" limitation under BRI, "block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms"; § II B, p. 5…the stored contents are read into working memory as execution proceeds, confirming a tangible store, "tensors required at the given one or two sites in an iteration of the sweep algorithm are loaded into memory")…
implement a single-state optimization algorithm configured to select at least one estimated extremal eigenstate of the determined state set associated with the respective one of the iterations and to sequentially optimize the selected at least one estimated extremal eigenstate of the state set associated with the respective one of the iterations to convergence to determine a respective at least one of the extremal eigenstates of the bundled TTNS in each of the iterations to determine the extremal eigenstates of the TTNO (Zhai: § II A 3, p. 2…Zhai teaches selecting from the state-averaged set and refining each such state on its own, as a separate tensor network with the lower states projected out, which constitutes the recited single-state optimization to convergence under BRI, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site"; § II A 3, p. 3…and teaches repeating that refinement group by group until the spectrum is determined, which constitutes performing it in each of the iterations to determine the extremal eigenstates of the TTNO, "This can be combined with the state-averaged ansatz to determine batches of states at a time").
Larsson and Zhai are analogous art because they are from the same field of endeavor, specifically the determination of extremal eigenstates of an operator represented as a loop-free tensor network by density-matrix-renormalization-group sweep algorithms. They are further reasonably pertinent to the same problem with which the inventor was involved, namely obtaining a large number of the extremal eigenstates of such an operator accurately, in eigenvalue order and without skipping states, at an acceptable computational cost.
Before the effective filing date of the claimed invention, it would have been obvious to a PHOSITA to store on a non-transitory medium, as Zhai does, instructions that carry out Larsson's iterated loose state-average stage followed by Zhai's per-state projected refinement, as claimed.
The suggestion/motivation for doing so would have been provided by Zhai itself, which identifies the output of a state-averaged calculation as the very input its per-state refinement is meant to improve, "To improve the quality of the states obtained from the state-averaged DMRG, one can further refine each excited state (as an independent MPS) by projecting out lower-lying states when optimizing the central site" (Zhai: § II A 3, p. 2), and which expressly cites Larsson as a source of that refinement approach, "Larsson, H. R. Computing vibrational eigenstates with tree tensor network states (TTNS). The Journal of Chemical Physics" (Zhai: Ref. 61, p. 16). Zhai further states the deficiency that makes the refinement worth adding, teaching that a state-averaged optimization loses accuracy as the number of states it carries grows, "This algorithm is normally a robust and convenient choice for tens of roots, but for a given bond dimension, the accuracy decreases as the number of roots is increased" (Zhai: § II A 3, p. 2). Larsson supplies the corresponding suggestion from its own side, teaching that optimizing the states individually is an available alternative and that the state-average step is retained only because it is faster, "In principle, one could also avoid the state average calculations at all and perform optimizations state by state" (Larsson: § III B, p. 9). Furthermore, reducing an already-disclosed computational procedure to distributable stored instructions is the use of a known technique to improve a similar method in the same way, with an entirely predictable result.
Per claim 17, Larsson combined with Zhai discloses claim 16. Larsson further teaches wherein the predefined algorithm parameters comprise an optimized state quantity that defines a quantity of the estimated extremal eigenstates in the state set that is a proper subset of the quantity of extremal eigenstates of the TTNO and that determines a size of a state index, the state index being sequentially shifted along with an orthogonality center to each of a plurality of tensors of the bundled TTNS during a sweep of the bundled TTNS to optimize the quantity of the estimated extremal eigenstates of the extremal eigenstates of the TTNO associated with the bundled TTNS in the limited multistate optimization algorithm in each of the iterations as defined by the optimized state quantity (Larsson: § III B, p. 9…twenty states are programmed into a pass that forms part of a run seeking eighty-four, so the programmed quantity is a proper subset of the eigenstates sought, "Do a (loose) state average calculation with 20 states for maximal seven sweeps"; § II D 3, p. 7…that quantity fixes the dimension of the state-indicating bond, and because the canonical root node advances tensor by tensor across the sweep that bond must travel with it, which constitutes the recited shifting of the state index along with an orthogonality center to each of a plurality of tensors, "To make the optimization stable, it is required to move the state dimension from one node to another"; § III B, p. 9…the twenty-state pass is not run once but is the first stage of a procedure Larsson expressly iterates, which constitutes the recited operation of the limited multistate optimization algorithm in each of the iterations, "To obtain the lowest 84 eigenstates, we iterated the following procedure, both for TTNS and MPS:").
Per claim 18, Larsson combined with Zhai discloses claim 16. Larsson further teaches wherein the limited multistate optimization algorithm is configured to provide the determined at least one of the extremal eigenstates of a given one of the iterations as an orthogonality constraint to the limited multistate optimization algorithm, such that the limited multistate optimization algorithm is configured to determine the estimated extremal eigenstates of a state set associated with a next one of the iterations as having higher or lower eigenstates relative to the at least one of the extremal eigenstates of the given one of the iterations (Larsson: § III B, p. 9…the eigenstates converged on a pass are fed back as a shift applied to the operator on every later pass, which is precisely the recited provision of the determined eigenstates as an orthogonality constraint under BRI, "Throughout, the Hamiltonian was shifted by the previously computed states (see Eq. (14))"; § II D 2, p. 7…the effect of that constraint is that the states returned next are orthogonal to, and therefore lie beyond, those already determined, which constitutes the recited determination of the next state set as having higher or lower eigenstates relative to the eigenstates already found, "Note that after the optimization, the newly computed eigenstate is orthogonal to the previously computed states").
Per claim 20, Larsson combined with Zhai discloses claim 16. Larsson further teaches wherein the predefined algorithm parameters comprise at least one of a maximum bond dimension of the tensors of the bundled TTNS and a maximum number of sweeps during operation of the limited multistate optimization algorithm in each iteration of the hybrid eigenstate determination algorithm (Larsson: § III B, p. 9…each state-average pass is bounded in advance both by a ceiling on bond dimension and by a ceiling on sweep count, either of which satisfies the recited at least one of under BRI, "we fixed the maximally allowed bond dimension nmax and also set a minimal bond dimension of nmin = 3"; § III B, p. 9…"Do a (loose) state average calculation with 20 states for maximal seven sweeps").
Claims 4-6, 12, 13 are rejected under 35 USC 103 as being unpatentable over Larsson in view of Zhai, as applied in the rejection of claims 1-3, 8-11, 15-18 and 20 above, and further in view of Excited state geometry optimization with the density matrix renormalization group as applied to polyenes to Hu et al. (hereinafter Hu).
Per claim 4, Larsson combined with Zhai discloses claim 3.
Larsson combined with Zhai does not expressly disclose, but with Hu does teach:
wherein at least one estimated extremal eigenstate in a given iteration after a first iteration is nominally common to a state set associated with a preceding sequential iteration (Hu: § V B, p. 10…Hu carries a state forward from one iteration to the next by matching each newly obtained solution against the solution held from the preceding iteration, an operation that presupposes and requires that the same state appear in both sets, which constitutes the recited eigenstate nominally common to a state set associated with a preceding sequential iteration under BRI, "we ensure that at each block iteration we always pick the Davidson solution with maximum overlap with the ex"). Larsson corroborates that the same state recurs between successive passes of a multistate procedure of the kind claimed (Larsson: § III B, p. 9…Larsson discards the highest-energy group of each twenty-state estimate precisely because those estimated states may recur among the states the later passes are still to determine, "Discard the last cluster as this may overlap with higher lying states"), wherein the processing unit is configured to store the estimated extremal eigenstates of each state set in each of the iterations in the memory, and to store the determined at least one of the extremal eigenstates in each of the iterations in the memory (Hu: § V B, pp. 10-11…Hu directs that the whole set of state vectors produced by the multistate pass be written to storage, which constitutes storing the estimated extremal eigenstates of each state set…in the memory under BRI, "Store the wavefunction vectors {ci} (for i = 1, 2, ..., n) at the middle of the sweep"; § V B, p. 11…Hu directs separately that each solution settled on for the targeted state be written to storage as well, which constitutes storing the determined at least one of the extremal eigenstates…in the memory, "Store the vector cxsol as the new solution"; § V B, p. 11…Hu expressly repeats the storing step on every later pass of its procedure, which constitutes performing both storing operations in each of the iterations, "Repeat Step. 2 in further geometry optimization steps").
Larsson, Zhai and Hu are analogous art because all three are from the same field of endeavor, specifically the determination of extremal eigenstates of an operator represented as a loop-free tensor network by density-matrix-renormalization-group sweep algorithms. Hu is further reasonably pertinent to the particular problem with which the inventor was involved, namely keeping an iterative eigenstate search from skipping a state as it advances through the spectrum.
Before the effective filing date of the claimed invention, it would have been obvious to a PHOSITA to add to the Larsson-Zhai procedure the storage and cross-iteration comparison of Hu, so that the states estimated on each pass are retained and the state carried into the converging stage is confirmed against the preceding pass, as claimed.
The suggestion/motivation for doing so would have been provided by Hu itself, which identifies the failure mode the technique cures, teaching that the state being sought is reliably present only at the middle of a sweep and can be lost where the retained space is small, "the desired excited state can usually be found in the eigenspectrum at the middle of the sweep (when the renormalized Hilbert space is largest) but can be lost at the edges of the sweep when the renormalized Hilbert space is small" (Hu: § V, p. 10), and which states the cure in the same breath, teaching that the state is held on course by matching each new solution against the one retained from the previous iteration, "we ensure that at each block iteration we always pick the Davidson solution with maximum overlap with the excited state solution at the previous block iteration" (Hu: § V, p. 10). Larsson supplies the same concern from its own side, warning that a group of estimated states may reach into the states not yet converged, "Discard the last cluster as this may overlap with higher lying states" (Larsson: § III B, p. 9). Furthermore, this is the use of a known technique to improve a similar method in the same way, and its result, an eigenstate sequence that does not skip a state, is exactly what Hu reports the technique achieving.
Per claim 5, Larsson combined with Zhai and Hu discloses claim 4. Hu further teaches wherein the processing unit is configured to compare the estimated extremal eigenstates of a state set associated with a given one of the iterations with the estimated extremal eigenstates of a state set associated with a preceding sequential iteration to determine redundancy (Hu: § V, p. 11…Hu computes the overlap of each solution vector of the current iteration against the corresponding vector carried from the preceding iteration, and a high overlap is precisely a finding that the two are the same state, which constitutes the recited comparison to determine redundancy under BRI, "Compute overlaps between vectors {cisol} and {ciguess}, and align the phases when needed"). The rationale to combine Hu with Larsson and Zhai is the same as the parent claim.
Per claim 6, Larsson combined with Zhai and Hu discloses claim 4. Larsson further teaches wherein the processing unit is configured to provide the determined at least one of the extremal eigenstates of a given one of the iterations as an orthogonality constraint to the limited multistate optimization algorithm, such that the limited multistate optimization algorithm is configured to determine the estimated extremal eigenstates of a state set associated with a next one of the iterations as having higher or lower eigenstates relative to the at least one of the extremal eigenstates of the given one of the iterations (Larsson: § III B, p. 9…the eigenstates converged on a pass are applied to the operator as a shift on every subsequent pass, which constitutes the recited provision of those eigenstates as an orthogonality constraint to the limited multistate optimization algorithm under BRI, "Throughout, the Hamiltonian was shifted by the previously computed states (see Eq. (14))"; § II D 2, p. 7…the constraint operates so that what the next pass returns is orthogonal to what was already determined and therefore lies beyond it in the spectrum, "Note that after the optimization, the newly computed eigenstate is orthogonal to the previously computed states").
Per claim 12, Larsson combined with Zhai discloses claim 11.
Larsson combined with Zhai does not expressly disclose, but with Hu does teach: wherein at least one of the second estimated extremal eigenstates in the second bundled TTNS is redundant with at least one of the first estimated extremal eigenstates in the first bundled TTNS (Hu: § V, p. 10…Hu matches each solution of the current iteration to the solution retained from the preceding one and follows the match, an operation that has meaning only because a state recurs in both sets, which constitutes the recited redundancy between the second and first estimated eigenstates under BRI, "we ensure that at each block iteration we always pick the Davidson solution with maximum overlap with the excited state solution at the previous block iteration"), the method further comprising: storing the first and second estimated extremal eigenstates in a memory; and storing the determined first and second converged sets in the memory (Hu: § V B, p. 10…Hu writes the complete set of estimated state vectors produced by the multistate pass to storage, which constitutes storing the first and second estimated extremal eigenstates in a memory under BRI, "Store the wavefunction vectors {ci} (for i = 1, 2, ..., n) at the middle"; § V B, p. 11…Hu writes each settled solution for the targeted state to storage separately, which constitutes storing the determined first and second converged sets in the memory, "Store the vector c x sol as the new solution"; § V B, p. 11…Hu repeats both storing steps on each later pass, so both the first and the second sets are stored, "Repeat Step. 2 in further geometry optimization steps").
Before the effective filing date of the claimed invention, it would have been obvious to a PHOSITA to add to the Larsson-Zhai method of claim 11 the storage and cross-pass state comparison of Hu, so that the estimated eigenstates of each pass are retained and the state carried into the converging stage of the second pass is confirmed against the first, as claim 12 recites.
The suggestion/motivation is supplied by Hu itself, which states the failure mode the technique cures, "the desired excited state can usually be found in the eigenspectrum at the middle of the sweep (when the renormalized Hilbert space is largest) but can be lost at the edges of the sweep when the renormalized Hilbert space is small" (Hu: § V B, p. 10), and states the cure in the same breath, "we ensure that at each block iteration we always pick the Davidson solution with maximum overlap with the ex" (Hu: § V B, p. 10). Larsson supplies the same concern from its own side, warning that a group of estimated states may reach into states not yet converged, "Discard the last cluster as this may overlap with higher lying states" (Larsson: § III B, p. 9). Furthermore, this is the application of a known technique to a known method ready for improvement to yield predictable results, the rationale of MPEP § 2143.01(D).
Per claim 13, Larsson combined with Zhai and Hu discloses claim 12. Larsson further teaches further comprising providing the determined first converged set as an orthogonality constraint to the limited multistate optimization algorithm, wherein implementing the limited multistate optimization algorithm in the second iteration comprises determining the second estimated extremal eigenstates of the second state set as having higher or lower eigenstates relative to the first converged set (Larsson: § III B, p. 9…what a pass converges is applied to the operator as a shift for every pass that follows, which constitutes the recited provision of the determined first converged set as an orthogonality constraint to the limited multistate optimization algorithm under BRI, "Throughout, the Hamiltonian was shifted by the previously computed states (see Eq. (14))"; § II D 2, p. 7…the effect of that shift is that the states the next pass returns are orthogonal to the converged set and so lie beyond it in the spectrum, "Note that after the optimization, the newly computed eigenstate is orthogonal to the previously computed states").
Claims 7 and 14 are rejected under 35 USC 103 as being unpatentable over Larsson in view of Zhai and Hu, as applied above, and further in view of TRPL+K: Thick-Restart Preconditioned Lanczos+K Method for Large Symmetric Eigenvalue Problems to Wu et al. (hereinafter Wu).
Per claim 7, Larsson combined with Zhai and Hu discloses claim 4. Larsson combined with Zhai and Hu does not expressly disclose, but Wu does teach: wherein the processing unit is configured to determine if an estimated extremal eigenstate of a state set of a given one of the iterations is an estimated next higher or lower eigenstate relative to the determined at least one of the extremal eigenstates of a preceding sequential iteration, and in response to determining that the estimated extremal eigenstate of the state set of the given one of the iterations is not the estimated next higher or lower eigenstate of the preceding sequential iteration, is configured to access an estimated next higher or lower eigenstate of a state set of the preceding sequential iteration from the memory and to optimize the accessed estimated next higher or lower eigenstate to convergence via the single-state optimization algorithm in the given one of the iterations (Wu: § 2.1, p. 3…Wu identifies the very condition the limitation is directed to, that each pass of a restarted extremal-eigenstate procedure discards part of what it had and so may fail to carry forward the state that should come next, and identifies the answer as recovering that state from what the preceding pass held, which constitutes the recited determination that the current iteration's estimate is not the estimated next higher or lower eigenstate of the preceding sequential iteration under BRI, "restarting inevitably impairs the optimality of unrestarted Lanczos since it discards part of the information. Various techniques [24, 35, 33, 16, 20] attempt to partially recover the lost information due to restarting"; § 2.2, p. 4…Wu indexes its estimated eigenvectors by eigenvalue rank, so that a given index denotes the next eigenstate in the extremal sequence, which is the ordering the recited estimated next higher or lower eigenstate presupposes, "xi,2 is the approximate eigenvector for the second smallest eigenvalue at the end of cycle i"; § 2.2, p. 4…Wu takes the estimated eigenvector of the corresponding rank that was retained in storage from the immediately preceding pass and puts it back into the current pass's optimization, which is precisely the recited access of an estimated next higher or lower eigenstate of a state set of the preceding sequential iteration from the memory, "In +K restarting, U is then augmented by l Ritz vectors from the previous step"; § 2.2, p. 4…Wu states which vector is so retrieved, namely the estimate of the same eigenvalue rank produced by the preceding pass, "where xi,j is the j-th Ritz vector from cycle i, {rj} is its residual, and xi−1,j is the corresponding Ritz vector from cycle i−1"; § 2.1, p. 3…and Wu carries the retrieved estimate forward into the current pass's optimization until the wanted eigenpair is obtained, which constitutes optimizing the accessed estimated next higher or lower eigenstate to convergence…in the given one of the iterations, "This is a key feature for our proposed method where we augment the restarted space with Ritz vectors from a previous cycle").
Per claim 14, Larsson combined with Zhai and Hu discloses claim 12. Larsson combined with Zhai and Hu does not expressly disclose, but Wu does teach: further comprising: determining if a most extreme of the second estimated extremal eigenstates is an estimated next higher or lower eigenstate relative to the determined first converged set; in response to determining that the most extreme of the second estimated extremal eigenstates is not the estimated next higher or lower eigenstate relative to the determined first converged set, accessing an estimated next higher or lower eigenstate of the first state set from the memory; and optimizing the accessed estimated next higher or lower eigenstate to convergence via the single-state optimization algorithm in the second iteration (Wu: § 2.1, p. 3…Wu identifies the condition the limitation is directed to, that a restarted pass discards part of what the preceding pass held and may therefore fail to deliver the state that should come next, "restarting inevitably impairs the optimality of unrestarted Lanczos since it discards part of the information. Various techniques [24, 35, 33, 16, 20] attempt to partially recover the lost information due to restarting"; § 2.2, p. 4…Wu's estimates are indexed by eigenvalue rank, so the estimate of a given rank is the next eigenstate in the extremal sequence, which constitutes the ordering the recited "estimated next higher or lower eigenstate" presupposes, "xi,2 is the approximate eigenvector for the second smallest eigenvalue at the end of cycle i"; § 2.2, p. 4…Wu retrieves from storage the estimate of the corresponding rank produced by the first pass and returns it to the second pass's optimization, which constitutes the recited accessing an estimated next higher or lower eigenstate of the first state set from the memory, "where xi,j is the j-th Ritz vector from cycle i, {rj} is its residual, and xi−1,j is the corresponding Ritz vector from cycle i−1"; § 2.1, p. 3…and the retrieved estimate is carried into that pass's optimization until the wanted eigenpair is obtained, which constitutes optimizing the accessed estimated next higher or lower eigenstate to convergence…in the second iteration, "This is a key feature for our proposed method where we augment the restarted space with Ritz vectors from a previous cycle").
Claim 19 is rejected under 35 USC 103 as being unpatentable over Larsson in view of Zhai, as applied in the rejection of claim 16 above, and further in view of Wu.
Larsson combined with Zhai discloses claim 16. Larsson combined with Zhai does not expressly disclose, but Wu does teach: wherein the limited multistate optimization algorithm is configured to determine if an estimated extremal eigenstate of a state set of a given one of the iterations is an estimated next higher or lower eigenstate relative to the determined at least one of the extremal eigenstates of a preceding one of the iterations, and in response to determining that the estimated extremal eigenstate of the state set of the given one of the iterations is not the estimated next higher or lower eigenstate of the immediately preceding one of the iterations, is configured to access an estimated next higher or lower eigenstate of a state set of the immediately preceding one of the iterations from the memory and to optimize the accessed estimated next higher or lower eigenstate to convergence via the single-state optimization algorithm in the given one of the iterations (Wu: § 2.1, p. 3…Wu identifies the condition the limitation addresses, that each restarted pass discards part of the information the preceding pass held, and identifies the answer as recovering it, "restarting inevitably impairs the optimality of unrestarted Lanczos since it discards part of the information. Various techniques [24, 35, 33, 16, 20] attempt to partially recover the lost information due to restarting"; § 2.2, p. 4…Wu keeps in storage, at each restart, the estimated eigenvectors of the states still wanted, which constitutes the memory from which the recited access is made, "At restart, thick restarting keeps at least the p wanted Ritz vectors"; § 2.2, p. 4…Wu indexes those estimates by eigenvalue rank so that a given index denotes the next eigenstate in the extremal sequence, "xi,2 is the approximate eigenvector for the second smallest eigenvalue at the end of cycle i"; § 2.2, p. 4…and Wu returns the estimate of the corresponding rank held from the immediately preceding pass into the current pass's optimization, which constitutes the recited access of an estimated next higher or lower eigenstate of a state set of the immediately preceding one of the iterations from the memory and its optimization to convergence there, "where xi,j is the j-th Ritz vector from cycle i, {rj} is its residual, and xi−1,j is the corresponding Ritz vector from cycle i−1").
As it pertains to claims 7, 14 and 19, Larsson, Zhai, Hu and Wu are analogous art because all four are from the same field of endeavor, specifically the determination of the extremal eigenstates of a large sparse Hermitian operator by iterative subspace sweep algorithms that carry several estimated states at once. Wu is further reasonably pertinent to the particular problem with which the inventor was involved, namely keeping an iterative eigenstate search from losing or skipping a state as it advances through the spectrum, a problem Wu states in terms of the information a restarted pass discards.
Before the effective filing date of the claimed invention, it would have been obvious to a PHOSITA to add to the Larsson-Zhai-Hu procedure the retained-estimate restart of Wu, so that where the pass in hand does not yield the eigenstate that should come next, the estimate of that state held from the preceding pass is taken back out of storage and carried to convergence, as claimed.
The suggestion/motivation for doing so would have been provided by Wu itself, which states the deficiency that makes the technique worth adding, teaching that each restarted pass throws away part of what the preceding pass had established, "restarting inevitably impairs the optimality of unrestarted Lanczos since it discards part of the information" (Wu: § 2.1, p. 3), and which states the cure in the same breath, teaching that the estimates the preceding pass produced are kept and put back into the pass that follows, "At restart, thick restarting keeps at least the p wanted Ritz vectors" (Wu: § 2.2, p. 4) and "This is a key feature for our proposed method where we augment the restarted space with Ritz vectors from a previous cycle" (Wu: § 2.1, p. 3). Larsson and Hu supply the corresponding suggestion from their own side. Larsson warns that a group of estimated states may reach into states not yet converged and must therefore be set aside, "Discard the last cluster as this may overlap with higher lying states" (Larsson: § III B, p. 9), and Hu states the failure mode in terms of a wanted state going missing from the set the current pass returns, "the desired excited state can usually be found in the eigenspectrum at the middle of the sweep (when the renormalized Hilbert space is largest) but can be lost at the edges of the sweep when the renormalized Hilbert space is small" (Hu: § V B, p. 10). A PHOSITA reading Larsson's and Hu's statements of the problem alongside Wu's statement of the answer would have had reason to apply Wu's retained-estimate restart, and a reasonable expectation of success in doing so, because all four references converge estimated eigenstates of the same kind of operator by the same kind of iterative sweep. Furthermore, this is the application of a known technique to a known method ready for improvement to yield predictable results, the rationale of MPEP § 2143.01(D), and it yields no more than the result Wu already attributes to it.
Conclusion
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/ALAN CHEN/Primary Examiner, Art Unit 2125
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