DETAILED ACTION 1. The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA. 2. This communication is in response to the Applicant’s submission filed 11 December 2022 , where: Claims 1-20 are pending. Claims 1-20 are rejected. Drawings 3. 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: Fig. 2C, “ 202 ” not found in specification Fig. 3E, “ 311A ,” “ 311B ,” and “ 311N ” not found in specification 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 4. The disclosure is objected to because it contains an embedded hyperlink and/or other form of browser-executable code. Specification ¶ 0037 recites “the Unitary Inversion of Gates section in 'Quantum logic gate' entry in Wikipedia, available at 'en.wikipedia.org/wiki/ Quantum_logic_gate ' Applicant is required to delete the embedded hyperlink and/or other form of browser-executable code; references to websites should be limited to the top-level domain name without any prefix such as http:// or other browser-executable code. See MPEP § 608.01. 5. The disclosure is objected to because of the incorporation of essential material in the specification by reference to an unpublished U.S. application, foreign application or patent, or to a publication is improper. Applicant is required to amend the disclosure to include the material incorporated by reference, if the material is relied upon to overcome any objection, rejection, or other requirement imposed by the Office. The amendment must be accompanied by a statement executed by the applicant, or a practitioner representing the applicant, stating that the material being inserted is the material previously incorporated by reference and that the amendment contains no new matter. 37 CFR 1.57(g). The attempt to incorporate subject matter into this application by reference to “Unitary Inversion of Gates section in 'Quantum logic gate' entry in Wikipedia, available at 'en.wikipedia.org/wiki/ Quantum_logic_gate ', which is hereby incorporated by reference in its entirety for all purposes without giving rise to disavowment ” is ineffective because it is unclear which version of the non-patent literature is relied upon. Moreover, an incorporation by reference by hyperlink or other form of browser executable code is not permitted. (37 CFR § 1.57(e); MPEP § 608.01(p) sub I). The incorporation by reference will not be effective until correction is made to comply with 37 CFR 1.57(c), (d), or (e). If the incorporated material is relied upon to meet any outstanding objection, rejection, or other requirement imposed by the Office, the correction must be made within any time period set by the Office for responding to the objection, rejection, or other requirement for the incorporation to be effective. Compliance will not be held in abeyance with respect to responding to the objection, rejection, or other requirement for the incorporation to be effective. In no case may the correction be made later than the close of prosecution as defined in 37 CFR 1.114(b), or abandonment of the application, whichever occurs earlier. Claim Rejections - 35 U.S.C. § 101 6. 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. 7. 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 recites a method , which is a process, and thus one of the statutory categories of patentable subject matter. (35 U.S.C. § 101). However, under Step 2A Prong One , the claim recites the limitations of “ [(a)] computing , using a classical computer, a modified quantum state ,” “ [(b)] generating a modified quantum circuit based on the quantum circuit,” and “[(c.1.1)] wherein the modified sub-circuit is configured to apply an inverse transformation on the modified quantum state of the one or more qubits at one or more subsequent cycles of the modified quantum circuit.” The broadest reasonable interpretation of the claims covers simulations of quantum components through a classical computer, which is not inconsistent with the Applicant’s disclosure. (MPEP § 2111; see, e.g., Specification ¶ 0023 (“the executable quantum c1rcuit may comprise a machine representation that can be executed by a quantum hardware compiler, a logical program circuit that can be simulated by a classical computer or engine, or the like.”)). The activities of “[(a)] computing , ” “[(b)] generating, ” and “[(c.1.1)] apply ” contain limitations that can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groupings of abstract ideas. Also, the activities of “[(a) computing , ” [(b)] generating ,” and “[(c.1.1)] apply ” are mathematical relationships, mathematical formulas or equations, and mathematical calculations, and accordingly, are a mathematical concept, (MPEP § 2106.04(a)(2) sub I), which is also one of the groupings of abstract ideas. The claim also recited more details or specifics to the abstract idea of “ “[(a)] computing ” where “[(a.1)] the modified quantum state is computed based on an application of a transformation on an initial quantum state,” and “[(a.2)] the initial quantum state is associated with one or more qubits, a quantum circuit comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, are merely more specific to the abstract idea. The claim also recites more details or specifics of the abstract idea of “[(b)] generating ,” where “[(b.1)] the modified quantum circuit is configured to be executed by a quantum computer,” and “[(b.2)] the modified quantum circuit comprising the one or more qubits ,” and accordingly, are merely more specific to the abstract idea. The claim also recites more details or specifics to the abstract idea of “[(c.1.1)] . . . apply an inverse transformation ,” where “[(c.1.3)] the inverse transformation is configured to inverse the transformation ,” and “[(c.1.4)] whereby an application of the inverse transformation in the modified quantum circuit is configured to restore the initial quantum state or an approximation thereof ,” and accordingly, are merely more specific to the abstract idea. Thus, claim 1 recites an abstract idea. Under Step 2A Prong Two , the claim as a whole is not integrated into a practical application, because the additional elements recited in the claim beyond the identified judicial exception include a “ classical computer ,” a “ quantum circuit ,” an “ original sub-circuit ,” a “ modified quantum circuit ,” which are generic computer components recited at a high-level of generality, and are used to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. The claim recites more details or specifics to the additional element of “[(a.2)] quantum circuit ,” “comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, is merely more specific to the additional element. The claim also recites more details to the additional element of the “[(c)] modified quantum circuit ,” that “comprises a modified sub-circuit , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit,” and accordingly, is merely more specific to the additional element. Therefore, claim 1 is directed to the abstract idea. Finally, under Step 2B , the additional elements, taken alone or in combination, do not represent significantly more than the abstract idea itself. The additional elements include exception include a “ classical computer ,” a “ quantum circuit ,” an “ original sub-circuit ,” a “ modified quantum circuit ,” which are generic computer components recited at a high-level of generality, and are used to implement the abstract idea, (MPEP § 2106.05(f)), that does not amount to significantly more than the abstract idea. The claim recites more details or specifics to the additional element of “[(a.2)] quantum circuit ,” “comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, is merely more specific to the additional element. The claim also recites more details to the additional element of the “[(c)] modified quantum circuit ,” that “comprises a modified sub-circuit , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit,” and accordingly, is merely more specific to the additional element. Therefore, claim 1 is subject-matter ineligible. Claim 12 recites an apparatus , which is a product, and thus one of the statutory categories of patentable subject matter. (35 U.S.C. § 101). However, under Step 2A Prong One , the claim recites the limitations of “[(a)] compute , using a classical computer, a modified quantum state ,” “ [(b)] generating a modified quantum circuit based on the quantum circuit,” and “[(c.1.1)] wherein the modified sub-circuit is configured to apply an inverse transformation on the modified quantum state of the one or more qubits at one or more subsequent cycles of the modified quantum circuit.” The broadest reasonable interpretation of the claims covers simulations of quantum components through a classical computer, which is not inconsistent with the Applicant’s disclosure. (MPEP § 2111; see, e.g., Specification ¶ 0023 (“the executable quantum circuit may comprise a machine representation that can be executed by a quantum hardware compiler, a logical program circuit that can be simulated by a classical computer or engine, or the like.”)). The activities of “[(a)] computing , ” “[(b)] generating ,” and “[(c.1.1)] apply ” contain limitations that can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groupings of abstract ideas. Also, the activities of “[(a) computing” and “[(c.1.1)] apply ” are mathematical relationships, mathematical formulas or equations, and mathematical calculations, and accordingly, are a mathematical concept, (MPEP § 2106.04(a)(2) sub I), which is also one of the groupings of abstract ideas. The claim also recite s more details or specifics to the abstract idea of ““[(a)] compute ” where “[(a.1)] the modified quantum state is computed based on an application of a transformation on an initial quantum state,” and “[(a.2)] the initial quantum state is associated with one or more qubits, a quantum circuit comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, are merely more specific to the abstract idea. The claim also recites more details or specifics of the abstract idea of “[(b)] generating ,” where “[(b.1)] the modified quantum circuit is configured to be executed by a quantum computer,” and “[(b.2)] the modified quantum circuit comprising the one or more qubits ,” and accordingly, are merely more specific to the abstract idea. The claim also recites more details or specifics to the abstract idea of “[(c.1.1)] . . . apply an inverse transformation ,” where “[(c.1.3)] the inverse transformation is configured to inverse the transformation ,” and “[(c.1.4)] whereby an application of the inverse transformation in the modified quantum circuit is configured to restore the initial quantum state or an approximation thereof ,” and accordingly, are merely more specific to the abstract idea. Thus, claim 12 recites an abstract idea. Under Step 2A Prong Two , the claim as a whole is not integrated into a practical application, because the additional elements recited in the claim beyond the identified judicial exception include a “a processor ” “ coupled memory ,” a “ classical computer ,” a “ quantum circuit ,” an “ original sub-circuit ,” a “ modified quantum circuit ,” which are generic computer components recited at a high-level of generality used to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. The claim recites more details or specifics to the additional element of a “[(a.2)] quantum circuit ,” “comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, is merely more specific to the additional element. The claim also recites more details to the additional element of the “[(c)] modified quantum circuit ,” that “comprises a modified sub-circuit , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit,” and accordingly, is merely more specific to the additional element. Therefore, claim 12 is directed to the abstract idea. Finally, under Step 2B , the additional elements, taken alone or in combination, do not represent significantly more than the abstract idea itself. The additional elements include exception include a “ processor ,” “ coupled memory ,” a “ classical computer ,” a “ quantum circuit ,” an “ original sub-circuit ,” a “ modified quantum circuit ,” which are recited at a high-level of generality, and are used to implement the abstract idea, (MPEP § 2106.05(f)), that does not amount to significantly more than the abstract idea. The claim recites more details or specifics to the additional element of “[(a.2)] quantum circuit ,” “comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, is merely more specific to the additional element. The claim also recites more details to the additional element of the “[(c)] modified quantum circuit ,” that “comprises a modified sub-circuit , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit,” and accordingly, is merely more specific to the additional element. Therefore, claim 12 is subject-matter ineligible. Claim 20 recites a computer program product , which is a product, and thus one of the statutory categories of patentable subject matter. (35 U.S.C. § 101). However, under Step 2A Prong One , the claim recites the limitations of “[(a)] compute , using a classical computer, a modified quantum state ,” “ [(b)] generating a modified quantum circuit based on the quantum circuit,” “[(c.1.1)] wherein the modified sub-circuit is configured to apply an inverse transformation on the modified quantum state of the one or more qubits at one or more subsequent cycles of the modified quantum circuit.” The broadest reasonable interpretation of the claims covers simulations of quantum components through a classical computer, which is not inconsistent with the Applicant’s disclosure. (MPEP § 2111; see, e.g., Specification ¶ 0023 (“the executable quantum circuit may comprise a machine representation that can be executed by a quantum hardware compiler, a logical program circuit that can be simulated by a classical computer or engine, or the like.”)). The activities of “[(a)] computing , ” “[(b)] generating ,” and “[(c.1.1)] apply ” contain limitations that can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groupings of abstract ideas. Also, the activities of “[(a) computing” and “[(c.1.1)] apply ” are mathematical relationships, mathematical formulas or equations, and mathematical calculations, and accordingly, are a mathematical concept, (MPEP § 2106.04(a)(2) sub I), which is also one of the groupings of abstract ideas. The claim also recited more details or specifics to the abstract idea of ““[(a)] compute ” where “[(a.1)] the modified quantum state is computed based on an application of a transformation on an initial quantum state,” and “[(a.2)] the initial quantum state is associated with one or more qubits, a quantum circuit comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, are merely more specific to the abstract idea. The claim also recites more details or specifics of the abstract idea of “[(b)] generating ,” where “[(b.1)] the modified quantum circuit is configured to be executed by a quantum computer,” and “[(b.2)] the modified quantum circuit comprising the one or more qubits ,” and accordingly, are merely more specific to the abstract idea. The claim also recites more details or specifics to the abstract idea of “[(c.1.1)] . . . apply an inverse transformation ,” where “[(c.1.3)] the inverse transformation is configured to inverse the transformation ,” and “[(c.1.4)] whereby an application of the inverse transformation in the modified quantum circuit is configured to restore the initial quantum state or an approximation thereof ,” and accordingly, are merely more specific to the abstract idea. Thus, claim 20 recites an abstract idea. Under Step 2A Prong Two , the claim as a whole is not integrated into a practical application, because the additional elements recited in the claim beyond the identified judicial exception include a “ non-transitory computer readable medium retaining program instructions, which program instructions when read by a processor ,” where the instructions executed on generic computer components does not serve to integrate the abstract idea into a practical application. (MPEP § 2106.05(f)). Also, the claim recites a “ classical computer ,” a “ quantum circuit ,” an “ original sub-circuit ,” a “ modified quantum circuit ,” which are generic computer components recited at a high-level of generality, and are used to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. The claim recites more details or specifics to the additional element of a “[(a.2)] quantum circuit ,” “comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, is merely more specific to the additional element. The claim also recites more details to the additional element of the “[(c)] modified quantum circuit ,” that “comprises a modified sub-circuit , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit,” and accordingly, is merely more specific to the additional element. Therefore, claim 20 is directed to the abstract idea. Finally, under Step 2B , the additional elements, taken alone or in combination, do not represent significantly more than the abstract idea itself. The additional elements include exception include a “non-transitory computer readable medium retaining program instructions, which program instructions when read by a processor,” where the instructions executed on generic computer components does not serve to integrate the abstract idea into a practical application. (MPEP § 2106.05(f)). Also, the claim recites a “ classical computer ,” a “ quantum circuit ,” an “ original sub-circuit ,” a “ modified quantum circuit ,” which are generic computer components recited at a high-level of generality, and are used to implement the abstract idea, (MPEP § 2106.05(f)), that does not amount to significantly more than the abstract idea. The claim recites more details or specifics to the additional element of “[(a.2)] quantum circuit ,” “comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits,” and accordingly, is merely more specific to the additional element. The claim also recites more details to the additional element of the “[(c)] modified quantum circuit ,” that “comprises a modified sub-circuit , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit,” and accordingly, is merely more specific to the additional element. Therefore, claim 20 is subject-matter ineligible. Claims 2, 4, 6, 8, and 9 depend directly or indirectly from claim 1. Claims 13, 16, and 17 depend directly or indirectly from claim 12. The claims recite more details or specifics to the abstract idea of “[(a)] said computing the modified quantum state,” where ( claims 2 and 13: [(a)] wherein said computing the modified quantum state comprises: [(a.1.1)] applying the transformation on the initial quantum state, to thereby obtain a transformed quantum state; and [(a.1.2)] compressing the transformed quantum state to obtain the modified quantum state”; claim 4: [(a.3.1)] wherein the one or more coefficients are [(a.3.1.1)] selected to be removed by said compressing based on a determination that the one or more coefficients are insignificant”; claim 6 and 16: “[(a.3)] wherein execution of the quantum circuit utilizes a quantum resource, . . .”; claims 8, 9, and 17: [(a)] wherein the modified quantum state comprises [(a.3)] a scarce representation of the initial quantum state”; claim 9: “[(a.1)] wherein the initial quantum state is represented by a first set of coefficients over a first state base, and [(a.3.1)] the scarce representation utilizes a second set of coefficients over a second state base, [(a.3.2)] wherein the first set of coefficients comprises a greater number of coefficients than the second set of coefficients”), and accordingly, are merely more specific to the abstract idea. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Thus, claims 2, 4, 6, 8, 9, 13, 16, and 17 are subject-matter ineligible. Claim 3 depends directly or indirectly from claim 1. Claim 14 depends directly or indirectly from claim 12. The claims recite more details or specifics to the abstract idea of “[(a.3)] the transformed quantum state ” where ( claims 3 and 14: “[(a.3)] wherein the transformed quantum state is [(a.3.1)] represented by a set of coefficients in a state base,” and “[(a.4)] said compressing comprises removing one or more coefficients from the set of coefficients”), and accordingly, are merely more specific to the abstract idea. The claims also recite more details or specifics of the abstract idea of “[(c.1.1)] . . . apply an inverse transformation ,” ( claims 3 and 14: “[(c.1.1)] whereby the inverse transformation enables to provide a partial reconstruction of the initial quantum state and not a full reconstruction of the initial quantum state”), and accordingly, is merely more specific to the abstract idea. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Thus, claims 3 and 14 are subject-matter ineligible. Claim 5 depends directly or indirectly from claim 1. Claim 15 depends directly or indirectly from claim 12. The claims recite further recite “ [(d)] selecting the transformation from a set of potential transformations.” The activity of “[(d)] selecting” can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groupings of abstract ideas. The claim also recites more details or specifics of the abstract idea of “ [(d)] selecting ,” “wherein said selecting is performed based on at least one of: [(d.2)] a first amount of quantum resources required for setting the modified quantum state on the one or more qubits,” and “[(d.3)] a second amount of quantum resources required for applying the inverse transformation on the one or more qubits at one or more subsequent cycles of the modified quantum circuit,” and accordingly, are merely more specific to the abstract idea. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Thus, claims 5 and 15 are subject-matter ineligible. Claim 7 depends directly or indirectly from claim 1. The claim recites more details or specifics of the abstract idea of “[(b)] generating the modified quantum circuit ,” “[(b)] wherein said generating the modified quantum circuit comprises [(b.3)] setting the modified quantum state on the one or more qubits using one or more quantum state setters , ” and accordingly, is merely more specific to the abstract idea. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Thus, claim 7 is subject-matter ineligible. Claim 10 depend s directly or indirectly from claim 1. Claim 18 depend s directly or indirectly from claim 12. The claims further recite “[(d)] executing, by the quantum computer, the modified quantum circuit ,” which is the use of a generic computer component ( quantum computer ) to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application, nor amounts to significantly more than the abstract idea. Thus, claims 10 and 18 are subject-matter ineligible . Claim 11 depends directly or indirectly from claim 1. Claim 19 depends directly or indirectly from claim 12. The claims further recite “[(d)] determining the initial quantum state , wherein the initial quantum state is determined by executing the quantum circuit or a representation thereof , ” which is a pre-processing insignificant extra - solution activity of data gathering, (MPEP § 2106.05(g)), that does not serve to integrate the abstract idea into a practical solution. Also, this is a well-understood, routine, and conventional activity of data retrieval, (MPEP § 2106.05(d) sub II.iv ), that does not amount to significantly more than the abstract idea. Thus, claims 11 and 19 are subject-matter ineligible. Claim Rejections - 35 U.S.C. § 102 8. The following is a quotation of the appropriate paragraphs of 35 U.S.C . § 10 2 that form the basis for the rejections under this section made in this Office action: A person shall be entitled to a patent unless – (a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention. (a)(2) the claimed invention was described in a patent issued under section 151, or in an application for patent published or deemed published under section 122(b), in which the patent or application, as the case may be, names another inventor and was effectively filed before the effective filing date of the claimed invention. 9. Claims 1, 7, 10-12, and 18-20 are rejected under 35 U.S.C . § 10 2 (a)(1) as being anticipated by US Published Application 20190197426 to Kawano et al. [hereinafter Kawano ]. Regarding claims 1, 12, and 20, Kawano teaches [a] method ( Kawano ¶ teaches “a method through a classical computer and a method through a quantum computer are separately described”) of claim 1, [an] apparatus c om pri si ng a processor and coupled memory ( Kawano ¶ 0533 teaches “the computer including a processor (hardware processor), such as a CPU (central processing unit), and memories, such as a RAM (random-access memory) and a ROM (read-only memory)”) of claim 12, and [a] computer program product comprising a non-transitory computer readable medium ( Kawano ¶ 0546 teaches a computer (a classical computer and a quantum computer), the processing details of functions to be included in each apparatus are written in a program. Execution of the program on the computer achieves the processing functions on the computer.”) of claim 20, comprising: [(a)] computing, using a classical computer ( Kawano ¶ 0104 teaches “a transformation apparatus 1 . . . includes classical computers 11 and 13 (first and second classical computers), a quantum computer 12, and a controller 14 [)that is, using a classical computer )]”) , a modified quantum state, [(a.1)] the modified quantum state is computed based on an application of a transformation on an initial quantum state ( Kawano ¶ 0222 teaches “[t]he computation apparatus 5 of this embodiment receives n-dimensional vectors a j =(a 1 J , . . . , a nj ) T , g=(g 1 , . . . , gn ) T and an integer N 1 as inputs, and obtains and outputs, as the difference vector t ( d ) , (d 1 , . . . , d n ) T , satisfying the aforementioned Formula (10) representing [learning with errors (LWE)]. The difference vector t ( d ) is the solution of the modified LWE represented in Formula (5) [(that is, the “difference vector” is an initial quantum state )]; Kawano ¶ 0224 teaches the “basis setter 51 sets the LLL-reduced basis [(that is, an application of a transformation on an initial quantum state )] computed from {a 1 . . . , a m , N’ε 1 , . . . N’ε n } as the basis B, and further outputs t=g=(g 1 , . . . , g n ) T (step S51)”) , [(a.2)] the initial quantum state is associated with one or more qubits, a quantum circuit comprising the one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits ( Kawano ¶ 0534 teaches a “quantum gate type quantum computer applies, to the quantum bits, a manipulation [(that is, “manipulation” is inherently an original sub-circuit that is configured to set the initial quantum state on the one or more qubits )] corresponding to the quantum gate. This application sequentially changes the encoded quantum state in the set of quantum bits (qubits) [(that is, “changes the encoded quantum state” is the initial quantum state is associated with one or more qubits and an original sub-circuit that is configured to set the initial quantum state on the one or more qubits )]”) ; and [(b)] generating a modified quantum circuit based on the quantum circuit ( Kawano , Fig. 6, teaches a quantum circuit of the quantum computer 12 of Fig. 5 [Examiner annotations in dashed-line text boxes): Kawano ¶ 0271 teaches “[t]he quantum state generator 72a performs quantum manipulation corresponding to the following transformation, for the first register that stores the quantum state of Formula (11), and a quantum bit (second register) in a newly prepared initialized quantum bit in the quantum state | φ ”; [ Examiner notes that the broadest reasonable interpretation of a “ modified quantum circuit ” is one that is based on modifying quantum states, which is not inconsistent with the Applicants’ specification. (MPEP § 2111; see, e.g., Specification ¶ 0028 (“a modified quantum circuit may be generated., in which the modified states are prepared on the respective qubits instead of the initial states”))]) , [(b.1)] the modified quantum circuit is configured to be executed by a quantum computer ( Kawano ¶ 0001 teaches “a quantum computing technology that performs operations by a quantum computer [(that is, the modified quantum circuit is configured to be executed by a quantum computer ) ]”) , [(b.2)] the modified quantum circuit comprising the one or more qubits (see Kawano ¶ 0534 teaches a “quantum gate type quantum computer applies, to the quantum bits, a manipulation corresponding to the quantum gate. This application sequentially changes the encoded quantum state [(that is, the modified quantum circuit )] in the set of quantum bits (qubits) [(that is, the modified quantum circuit comprising the one or more qubits )]”) , [(b.2.1)] wherein the modified quantum circuit excludes the original sub-circuit ( Kawano ¶ 0224 teaches a “basis setter 51 sets the LLL-reduced basis [(that is, the modified quantum state )] computed from {a1, . . . , am, N′ε1, . . . , N′εn } as the basis B, and further outputs t=g=(g 1 , . . . , g n ) T (step S51)”) ([ Examiner notes that the broadest reasonable interpretation of a “ modified quantum circuit ” is one that is based on modifying quantum states, which is not inconsistent with the Applicants’ specification. (MPEP § 2111; see, e.g., Specification ¶ 0028 (“a modified quantum circuit may be generated, in which the modified states are prepared on the respective qubits instead of the initial states”)), and inherently, the modified quantum circuit excludes the original sub-circuit )] , [(c)] wherein the modified quantum circuit comprises a modified sub-circuit ( Kawano , Fig. 6, teaches a modified sub-circuit [Examiner annotations in dashed-line text boxes]:” Kawano ¶ 0127 teaches a “subset of the data register 121 b that includes in units of each ceil( log2 N) quantum bit is called a data sub-register 121 b- i [(that is, a “data sub-register” pertains to the modified quantum circuit comprises a modified sub-circuit )]”) , [(c.1)] the modified sub-circuit is configured to set the modified quantum state on the one or more qubits of the modified quantum circuit during one or more cycles of the modified quantum circuit ( Kawano ¶ 0218 teaches “computation (quantum computation) by the quantum computer and computation (classical computation) by the classical computer use, as a subroutine, the processes (third embodiment) of computing the solution of GapCVPγ for the modified [learning with errors (LWE)] transformed in the second embodiment to compute the solution of LWE (FIG. 3) [(that is, the modified quantum state )]”; Kawano ¶¶ 0224-25 teaches “[t]he basis setter 51 sets the LLL-reduced basis [(that is, an application of a transformation on an initial quantum state )] computed from {a 1 , . . . , a m , N′ε 1 , . . . , N′ε n } as the basis B [(that is, the modified sub-circuit is configured to set the modified quantum state on the one or more bits of the modified quantum circuit during one or more cycles of the modified quantum circuit )], and further outputs t=g=(g 1 , . . . , g n ) T (step S51). Hereinafter, the operations identical to those in the fourth embodiment are performed, thereby obtaining and outputting the difference vector t (d) ”; Kawano ¶ 0010 teaches “an object to provide a method of combining a classical computer and a quantum computer in a hybrid manner to solve a lattice problem at higher speed than conventional methods. That is, the object is to provide a method that can be achieved even by a quantum computer incapable of having a long execution time period [(that is, “time period” is during one or more cycles of the modified quantum circuit )] owing to decoherence due to noise and can solve the lattice problem in a shorter time period than conventional methods, by causing the classical computer to deal with light tasks in the entire computation process and by causing the quantum computer to deal with heavy tasks therein”), [(c.1.1)] wherein the modified sub-circuit is configured to apply an inverse transformation on the modified quantum state of the one or more qubits at one or more subsequent cycles of the modified quantum circuit ( Kawano ¶ 0130 teaches “[t]he observer 125a observes the index register 121a after the execution through the inverse quantum Fourier transformation unit 126 [(that is, the modified sub-circuit is configured to apply an inverse transformation on the modified quantum state of the one or more qubits at one or e more subsequent cycles of the modified quantum circuit )], and obtains an observation result r j0 (step S126)”) , [(c.1.2)] the one or more subsequent cycles of the modified quantum circuit are subsequent to the one or more cycles ( Kawano , claim 1, teaches “the inverse quantum Fourier transformation unit is configured to execute M-dimensional inverse quantum Fourier transform on the index register that stores the quantum state after observation by the second observer [(that is, a subsequent inverse transformation is the one or more subsequent cycles of the modified quantum circuit are subsequent to the one or more cycles )]”) , [(c.1.3)] the inverse transformation is configured to inverse the transformation ( Kawano ¶ 0081 teaches execution of N-dimensional quantum Fourier transform; Kawano ¶ 0130 teaches “observer 125a observes the index register 121a after the execution through the inverse quantum Fourier transformation unit 126, and obtains an observation result r j0 ”; [ Examiner notes that a Fourier transform transforms a function of time (or space) into a function of frequency, and accordingly, an inverse Fourier transform transforms a function of frequency into a function of time (or space)]) , [(c.1.4)] whereby an application of the inverse transformation in the modified quantum circuit is configured to restore the initial quantum state or an approximation thereof ( Kawano ¶ 0081 teaches execution of N-dimensional quantum Fourier transform; Kawano ¶ 0130 teaches “observer 125a observes the index register 121a after the execution through the inverse quantum Fourier transformation unit 126, and obtains an observation result r j0 ”; [ Examiner notes that a Fourier transform transforms a function of time (or space) into a function of frequency, and accordingly, an inverse Fourier transform transforms a function of frequency into a function of time (or space) [(that is, to return to the “time domain” inherently is whereby an application of the inverse transformation in the modified quantum circuit is configured to restore . . . an approximation thereof )]]) . Regarding claims 6 and 16, Kawano teaches all of the limitations of claims 1 and 12, respectively, as described above in detail . Kawano teaches - [(a.3)] wherein execution of the quantum circuit utilizes a quantum resource ( Kawano ¶¶ 0117-18 teaches “[t]he classical computer 11 outputs (L, n, M, N, R, B, t) (step S119). That is, the classical computer 11 uses the classical computer to generate (L, n, M, N, R, B, t) [(that is, the “classical computer” is the initial quantum state is determined by executing . . . a representation thereof )], which are parameters required to start computation on the quantum computer from the input (B, t)”; Kawano ¶ 0120 teaches “[t]he quantum computer 12 (FIGS. 4 to 6) receives (L, n, M, N, R, B, t) as inputs [(that is, receives the initial quantum state )]”) , [(b.3)] wherein execution of the modified quantum circuit does not utilize the quantum resource ( Kawano ¶ 0099 teaches “the [closest vector problem (CVP)] is transformed into the modified [learning with errors (LWE)] by an operation (quantum computation) through a quantum computer and an operation (classical computation) through a classical computer (FIG. 2) [(that is, “LWE” is the modified quantum circuit, where the “classical computer” is execution of the modified quantum circuit does not utilize the quantum resource )]”) . Regarding claim 7, Kawano teaches all of the limitations of claim 1 as described above in detail Kawano teaches - [(b)] wherein said generating the modified quantum circuit comprises [(b.3)] setting the modified quantum state on the one or more qubits using one or more quantum state setters Kawano ¶¶ 0224-25 teaches “[t]he basis setter 51 sets the LLL-reduced basis [(that is, an application of a transformation on an initial quantum state )] computed from {a 1 , . . . , a m , N′ε 1 , . . . , N′ε n } as the basis B [(that is, generating the modified quantum circuit comprises setting the modified quantum state on the one or more qubits using one or quantum state setters )], and further outputs t=g=(g 1 , . . . , g n ) T (step S51). Hereinafter, the operations identical to those in the fourth embodiment are performed, thereby obtaining and outputting the difference vector t (d) ””) . Regarding claims 10 and 18, Kawano teaches all of the limitations of claims 1 and 12, respectively, as described above in detail . Kawano teaches - [(d)] executing, by the quantum computer, the modified quantum circuit ( Kawano ¶ 0120 teaches a “quantum computer 12 (FIGS. 4 to 6) receives (L, n, M, N, R, B, t) as inputs, sets (prepares) a register string . . . and executes quantum computation m times on the string [(that is, executing, by the quantum computer, the modified quantum circuit )]”) . Regarding claims 11 and 19, Kawano teaches all of the limitations of claims 1 and 12, respectively, as described above in detail . Kawano teaches - further comprises [(d)] determining the initial quantum state, [(d.1)] wherein the initial quantum state is determined by executing the quantum circuit or a representation thereof ( Kawano ¶¶ 0117-18 teaches “[t]he classical computer 11 outputs (L, n, M, N, R, B, t) (step S119). That is, the classical computer 11 uses the classical computer to generate (L, n, M, N, R, B, t) [(that is, the “classical computer” is the initial quantum state is determined by executing . . . a representation thereof )], which are parameters required to start computation on the quantum computer from the input (B, t)”; Kawano ¶ 0120 teaches “[t]he quantum computer 12 (FIGS. 4 to 6) receives (L, n, M, N, R, B, t) as inputs [(that is, receives the initial quantum state )]”) . Claim Rejections – 35 U.S.C. § 103 10. The following is a quotation of 35 U.S.C . § 10 3 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. 11. The factual inquiries for establishing a background for determining obviousness under 35 U.S.C . § 10 3 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 . 12. 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 . § 10 2(b)(2)(C) for any potential 35 U.S.C . § 10 2(a)(2) prior art against the later invention. 13. Claims 2-5 and 13-15 are rejected under 35 U.S.C . § 10 3 as being unpatentable over US Published Application 20190197426 to Kawano et al. [hereinafter Kawano ] in view of US Published Application 20060123363 to Williams et al. [hereinafter Williams ] . Regarding claims 2 and 13, Kawano teaches all of the limitations of claims 1 and 12, respectively, as described above in detail . Kawano teaches - [(a)] wherein said computing the modified quantum state comprises: [(a.3)] applying the transformation on the initial quantum state, to thereby obtain a transformed quantum state ( Kawano ¶ 0224 teaches the “basis setter 51 sets the LLL-reduced basis [(that is, applying the transformation on the initial quantum state, to thereby obtain a transformed quantum state )] computed from {a 1 . . . , a m , N’ε 1 , . . . N’ε n } as the basis B, and further outputs t=g=(g 1 , . . . , g n ) T (step S51)” [ Examiner notes that the term “modification” and “transformation” are synonymous , and accordingly, a “ modified quantum state ,” introduced in claim 1, is synonymous to a “ transformed quantum state ”]) ; and * * * Though Kawano teaches transforming an initial state via a LLL-reduced basis algorithm, Kawano , however, does not explicitly teach – * * * and [(a.4)] compressing the transformed quantum state to obtain the modified quantum state. But Williams teaches – * * * and [(a.4)] compressing ( Williams ¶ 0083 teaches “compactification techniques for reducing the number of gates [(that is, “compactification” is compressing )]”; [ Examiner notes that the broadest reasonable interpretation of “compressing” is synonymous with compacting, which is not inconsistent with the Applicant’s disclosure (MPEP § 2111), and accordingly, covers the teachings of Williams ]) and [ (a.4) compressing] the transformed quantum state to obtain the modified quantum state ( Williams ¶ 0048 teaches “[a] systematic algebraic approach to quantum circuit design is used in the present invention to find a quantum circuit for an arbitrary unitary transformation [(that is, an “arbitrary unitary transformation” serves to produce the transformed quantum state to obtain the modified quantum state )]”) . Kawano and Williams are from the same or similar field of endeavor. Kawano teaches combining a classical computer and a quantum computer in a hybrid manner of applying an algorithm involving a transformation of a quantum state to a modified quantum state. Williams teaches a desired quantum computation which can then be mapped into equivalent circuit fragments, and describes a number of rules allowing such circuits to be compactified. Thus, it would have been obvious to a person having ordinary skill in the art as of the effective filing date of the Applicant’s effective filing date to modify Kawano pertaining to a modified quantum state with the compactification rules of Williams . The motivation to do so is to “join these quantum circuit fragments together, while applying circuit compactification rules to minimize the size of the resulting circuit. The net result is a quantum circuit capable of implementing any (real or complex) unitary matrix, specialized to use one of several types of 2-qubit gates, appropriate for different physical implementations of quantum computing hardware.” ( Williams ¶ 0060). Regarding claims 3 and 14, the combination of Kawano and Williams teaches all of the limitations of claims 2 and 13, respectively, as described above in detail. Williams teaches - [(a.3)] wherein the transformed quantum state is [(a.3.1)] represented by a set of coefficients in a state base ( Williams ¶ 0007 teaches “a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient which when squared in absolute value, represents the probability for each state [(that is, generally with a state, “ the transformed quantum statis represented by a set of coefficients in a state base )]”) , [(a.4)] said compressing comprises [(a.4.1)] removing one or more coefficients from the set of coefficients ( Williams ¶ 0076 teaches “compactification rules eliminate unnecessary gate operations [(that is, to “eliminate” is removing one or more coefficients from the set of coefficients )] including rotations and phase shifts through an angle of zero or 2nπ, combine contiguous sequences of Ph-, R y -, or R z -gate operations, accumulate phase gates into an overall phase, compress sequences of CNOT gates having the same embedding, and implement bit-reversals by explicitly rewiring the circuit (rather than implementing such operations computationally). . . . [K] nown "special case" unitary operators (such as the [quantum Fourier transform (QFT)]) are foun