DETAILED ACTION
This Office Action is in response to a communication filed on November 10, 2025 for Application No. 17/738,944, in which claims 1, 3, and 5-6 are presented for examination. The amendments filed on November 10, 2025 have been entered, where claims 1 and 3 are amended and claims 2 and 4 are canceled.
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 .
Claim Objections
Claim 1 is objected to because of the following informalities:
“n is positive integer” should be “n is a positive integer” (Claim 1, Ln. 16).
Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
Claim 3 is rejected under 35 U.S.C. 112(b) as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention.
Specifically, Claim 3 recites the limitation “the two same 2n x 2n unitary matrices . . . and the two same 2n x 2n unitary matrices” (ln. 18-19). There is insufficient antecedent basis for this limitation in the claim. Therefore, Claim 3 is rejected. The claim should be amended to clarify that “the two same 2n x 2n unitary matri[ces]” are the two “Q2n” matrices (Pg. 14, Ln. 7-14, 16). As opposed to another two 2n x 2n unitary matrices, such as the two “P2n” components of “Q2n” (Fig. 5D). Alternatively, the claim could be amended in a manner similar to the amendment to Claim 1, where “the” was removed.
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, 3, and 5-6 are rejected under 35 U.S.C. 101 because the claimed invention is directed to abstract ideas without significantly more.
Regarding Claim 1:
Step 1: Claim 1 is a machine claim. Therefore, it is directed to a statutory category of eligible subject matter.
Step 2A Prong 1: If a claim limitation, under its broadest reasonable interpretation, covers mathematical relationships, mathematical formulas or equations, or mathematical calculations but for the recitation of generic computer components, then it falls within the "Mathematical Concepts" grouping of abstract ideas. Here, steps of the claimed method are mathematical concepts. Specifically, the claim recites
“Daubechies-6 (D6) wavelet transform . . . generate a first intermediate result, wherein the first part comprises data of (n-1)th dimension and data of nth dimension of the n-dimensional data . . . generating a second intermediate result corresponding to the first intermediate result and a first result corresponding to the second part, wherein the second part comprises data of 1st dimension to data of (n-2)th dimension of the n-dimensional data . . . generate a second result according to the second intermediate result . . . the n is positive integer . . . Daubechies-6 (D6) wavelet transform” (mathematical concepts – amounts to the recitation of a mathematical formula for D6 wavelet transform to transfer a state amplitude, see Pg. 7, Ln. 4-10,
“
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”; which “may be further decomposed into: (I2 n−2 ⊗A)·Q2 n ·Q2 n ·(I2 n−2 ⊗B) . . . the aforementioned formula”, see Pg. 7, Ln. 11-16);
“to implement a 4 x 4 parameter matrix . . .another 4 x 4 parameter matrix” (mathematical concepts – amounts to the recitation of a specific elements in a formula for D6 wavelet transform, see Pg 8, Ln. 4-5,
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”); and
“to implement a dot product of two same 2n x 2n unitary matrices” (mathematical concepts – amounts to the recitation of a mathematical operation on specific elements in a formula for D6 wavelet transform, see Pg. 8, Ln. 1,
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”);
“(UAl ⊗ UA2) ⋅ M ⋅ (Aai ⊕ Aa2) ⋅ Mt⋅ (VA1 ⊗ VA2) . . . (UBl ⊗ UB2) ⋅ M ⋅ (Abi ⊕ Ab2) ⋅ Mt⋅ (VB1 ⊗ VB2)” (mathematical concepts – amounts to the recitation of mathematical formulas);
“Aa1 is Rz(
π
2
)⋅ Ry(1.15909π) ⋅ Rz(
-
π
2
)” (mathematical concepts – amounts to the recitation of a formula for an element in a larger mathematical formula) (“Aa1” is used as a representative example for the elements contained in amended claim 1, this analysis applies equally to elements “Aa2” through “VB2” which are similarly found to be mathematical concepts); and
“a matrix form of M is
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, a matrix form of the Mt is a conjugate transpose matrix of the matrix form of the M, the 2n x 2n unitary matrix is
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” (mathematical concepts – amounts to the recitation of a formula for an element in a larger mathematical formula).
Step 2A Prong 2: This judicial exception is not integrated into a practical application.
The claim recites the additional elements:
“a quantum circuit for . . . comprising . . . a B quantum circuit . . . a Q2n⋅Q2n quantum circuit . . . the Q2n⋅Q2n quantum circuit coupled to the B quantum circuit . . . the Q2n"Q2n quantum circuit . . . an A quantum circuit coupled to the Q2n⋅Q2n quantum circuit . . . wherein the B quantum circuit and the A quantum circuit is configured . . . the Q2n⋅Q2n quantum circuit is configured . . . configured to transfer a state amplitude. . . the quantum circuit for . . . wherein the A quantum circuit is implement as . . . the B quantum circuit is implement as” (Field of use – recitation of quantum circuit components amounts to merely generally linking the use of well-defined mathematical concepts to a particular field of use) and
“configured to receive a first part of n-dimensional data . . . configured to receive a second part of the n-dimensional data . . . to receive the first intermediate result . . . to receive the second intermediate result . . . a set of the first result and the second result serves as an output” (Insignificant extra-solution activity – receiving and transmitting data across computer components by unspecified means is incidental to the claimed functionality of the wavelet transform operations).
Step 2B: The claim does not include additional elements considered individually and in combination that are sufficient to amount to significantly more than the judicial exception.
The claim recites the additional elements:
“a quantum circuit for . . . comprising . . . a B quantum circuit . . . a Q2n⋅Q2n quantum circuit . . . the Q2n⋅Q2n quantum circuit coupled to the B quantum circuit . . . the Q2n"Q2n quantum circuit . . . an A quantum circuit coupled to the Q2n⋅Q2n quantum circuit . . . wherein the B quantum circuit and the A quantum circuit is configured . . . the Q2n⋅Q2n quantum circuit is configured . . . configured to transfer a state amplitude. . . the quantum circuit for . . . wherein the A quantum circuit is implement as . . . the B quantum circuit is implement as” (Field of use – recitation of quantum circuit components do not impose meaningful limitations on the use of the mathematical concepts because it merely refers to a pre-existing coupling structure for quantum circuit decomposition used in quantum wavelet transform mathematical operations, see generally Mayo Collaborative Servs. v. Prometheus Labs. Inc., 566 U.S. 66, 78, 101 USPQ2d 1961, 1968 (2012)) and
“configured to receive a first part of n-dimensional data . . . configured to receive a second part of the n-dimensional data . . . to receive the first intermediate result . . . to receive the second intermediate result . . . a set of the first result and the second result serves as an output” (receiving and transmitting data across computer components is well‐understood, routine, and conventional, see buySAFE, Inc. v. Google, Inc., 765 F.3d 1350, 1355, 112 USPQ2d 1093, 1096 (Fed. Cir. 2014); Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334, 115 USPQ2d 1681, 1701 (Fed. Cir. 2015); OIP Techs., 788 F.3d at 1363, 115 USPQ2d at 1092-93; which is recited here with a high level of generality, and remains insignificant extra-solution activity even upon reconsideration).
For the reasons above, Claim 1 is rejected as being directed to an abstract idea without significantly more.
Regarding Claim 3:
Step 1: Claim 3 is a machine claim. Therefore, Claim 3 is directed to a statutory category of eligible subject matter.
Step 2A Prong 1: If a claim limitation, under its broadest reasonable interpretation, covers mathematical relationships, mathematical formulas or equations, or mathematical calculations but for the recitation of generic computer components, then it falls within the "Mathematical Concepts" grouping of abstract ideas. Here, steps of the claimed method are mathematical concepts. Specifically, the claim recites
“Daubechies-6 (D6) wavelet inverse transform . . . generate a first intermediate result, wherein the first part comprises data of (n-1)th dimension and data of nth dimension of the n-dimensional data . . . generating a second intermediate result corresponding to the first intermediate result and a first result corresponding to the second part, wherein the second part comprises data of 1st dimension to data of (n-2)th dimension of the n-dimensional data . . . generate a second result according to the second intermediate result . . . the n is a positive integer . . . Daubechies-6 (D6) wavelet inverse transform” (mathematical concepts – amounts to the recitation of a mathematical formula for D6 wavelet transform to transfer a state amplitude, see Pg. 7, Ln. 4-10,
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”; which is inversed to perform the inverse operation and the inverse matrix “may be decomposed into (I2 n−2 ⊗(B)−1) (Q2 n )−1·(Q2 n )−1·(I2 n−2 ⊗(A)−1)”, see Pg. 11, Ln. 2-3);
“to implement an inverse matrix of a 4 x 4 parameter matrix . . . another inverse matrix of another 4 x 4 parameter matrix” (mathematical concepts – amounts to the recitation of a specific elements in a formula for D6 wavelet transform, see generally Pg 8, Ln. 4-5,
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”, where the inverse matrices are used in the inverse formula); and
“to implement a dot product of inverse matrices of the two same 2n x 2n unitary matrices and the two same 2n x 2n unitary matrices” (mathematical concepts – amounts to the recitation of a mathematical operation on specific elements in a formula for D6 wavelet transform, see generally Pg. 8, Ln. 1,
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”, where the inverse matrix is used in the inverse formula);
“((VA1)−1⊗(VA2)−1)·M ·((Aa1)−1⊕(Aa2)−1)·M†·((UA1)−1⊗(UA2)−1) . . . ((VB1)−1⊗(VB2)−1)·M·((Bb1)−1⊕(Bb2)−1)·M†·((UB1)−1⊗(UB2)−1)” (mathematical concepts – amounts to the recitation of mathematical formulas);
“Aa1 is Ph(π)⋅ Rz(
π
2
)⋅ Ry(1.15909π) ⋅ Rz(
-
π
2
)” (mathematical concepts – amounts to the recitation of a formula for an element in a larger mathematical formula) (“Aa1” is used as a representative example for the elements contained on Pg. 16, Ln. 6-15, this analysis applies equally to elements “Aa2” through “VB2” which are similarly found to be mathematical concepts); and
“a matrix form of M is
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, a matrix form of the Mt is a conjugate transpose matrix of the matrix form of the M , the 2n x 2n unitary matrix is
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” (mathematical concepts – amounts to the recitation of a formula for an element in a larger mathematical formula).
Step 2A Prong 2: This judicial exception is not integrated into a practical application.
The claim recites the additional elements:
“a quantum circuit for . . . comprising . . . a (A)-1 quantum circuit . . . a (Q2n)-1⋅(Q2n)-1 quantum circuit . . . the (Q2n)-1⋅(Q2n)-1 quantum circuit coupled to the (A)-1 quantum circuit . . . the (Q2n)-1⋅(Q2n)-1 quantum circuit . . . an (B)-1 quantum circuit coupled to the (Q2n)-1⋅(Q2n)-1 quantum circuit . . . wherein the (A)-1 quantum circuit is configured to . . . and the (B)-1 quantum circuit is configured . . . the (Q2n)-1⋅(Q2n)-1 quantum circuit is configured . . . configured to transfer a state amplitude. . . the quantum circuit for . . . wherein the (A)-1 quantum circuit is implemented as . . . the (B)-1 quantum circuit is implemented as” (Field of use – recitation of quantum circuit components amounts to merely generally linking the use of well-defined mathematical concepts to a particular field of use) and
“configured to receive a first part of n-dimensional data . . . configured to receive a second part of the n-dimensional data . . . to receive the first intermediate result . . . to receive the second intermediate result . . . a set of the first result and the second result serves as an output” (Insignificant extra-solution activity – receiving and transmitting data across computer components by unspecified means is incidental to the claimed functionality of the wavelet transform operations).
Step 2B: The claim does not include additional elements considered individually and in combination that are sufficient to amount to significantly more than the judicial exception.
The claim recites the additional elements:
“a quantum circuit for . . . comprising . . . a (A)-1 quantum circuit . . . a (Q2n)-1⋅(Q2n)-1 quantum circuit . . . the (Q2n)-1⋅(Q2n)-1 quantum circuit coupled to the (A)-1 quantum circuit . . . the (Q2n)-1⋅(Q2n)-1 quantum circuit . . . an (B)-1 quantum circuit coupled to the (Q2n)-1⋅(Q2n)-1 quantum circuit . . . wherein the (A)-1 quantum circuit is configured to . . . and the (B)-1 quantum circuit is configured . . . the (Q2n)-1⋅(Q2n)-1 quantum circuit is configured . . . configured to transfer a state amplitude. . . the quantum circuit for . . . wherein the (A)-1 quantum circuit is implemented as . . . the (B)-1 quantum circuit is implemented as” (Field of use – recitation of quantum circuit components do not impose meaningful limitations on the use of the mathematical concepts because it merely refers to a pre-existing coupling structure for quantum circuit decomposition used in quantum wavelet transform mathematical operations, see generally Mayo Collaborative Servs. v. Prometheus Labs. Inc., 566 U.S. 66, 78, 101 USPQ2d 1961, 1968 (2012)) and
“configured to receive a first part of n-dimensional data . . . configured to receive a second part of the n-dimensional data . . . to receive the first intermediate result . . . to receive the second intermediate result . . . a set of the first result and the second result serves as an output” (receiving and transmitting data across computer components is well‐understood, routine, and conventional, see buySAFE, Inc. v. Google, Inc., 765 F.3d 1350, 1355, 112 USPQ2d 1093, 1096 (Fed. Cir. 2014); Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334, 115 USPQ2d 1681, 1701 (Fed. Cir. 2015); OIP Techs., 788 F.3d at 1363, 115 USPQ2d at 1092-93; which is recited here with a high level of generality, and remains insignificant extra-solution activity even upon reconsideration).
For the reasons above, Claim 3 is rejected as being directed to an abstract idea without significantly more.
Regarding Claim 5:
Step 1: Claim 5 is a process claim. Therefore, Claims 5-6 are directed to a statutory category of eligible subject matter.
Step 2A Prong 1: If a claim limitation, under its broadest reasonable interpretation, covers mathematical relationships, mathematical formulas or equations, or mathematical calculations but for the recitation of generic computer components, then it falls within the "Mathematical Concepts" grouping of abstract ideas. Here, steps of the claimed method are mathematical concepts. Specifically, the claim recites
“Daubechies-6 (D6) wavelet transform . . . decomposing a matrix D2n (6) of Daubechies-6 (D6) wavelet into (I2 n−2 ⊗A)·Q2 n ·Q2 n ·(I2 n−2 ⊗B); decomposing a parameter matrix A into (UA1⊗UA2)·M·(Aa1⊕Aa2)·M†·(VA1⊗VA2), and decomposing a parameter matrix B into (UB1⊗UB2)·M·(Bb1⊕Bb2)·M†·(VB1⊗VB2) . . . for Daubechies-6 (D6) wavelet transform . . . based on (I2 n−2 ⊗A)·Q2 n ·Q2 n ·(I2 n−2 ⊗B), (UA1⊗UA2)·M·(Aa1⊕Aa2)·M†·(VA1⊗VA2) and (UB1⊗UB2)·M·(Bb1⊕Bb2)·M†·(VB1⊗VB2)” (mathematical concepts – amounts to performing mathematical operations to decomposing a matrix into subcomponents correspond to mathematical formulas, see Pg. 7, Ln. 4-10,
“
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”; which “may be further decomposed into: (I2 n−2 ⊗A)·Q2 n ·Q2 n ·(I2 n−2 ⊗B) . . . the aforementioned formula”, see Pg. 7, Ln. 11-16; Pg 8, Ln. 4-5,
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”);
“wherein the Q2 n is a 2n×2n unitary matrix” (mathematical concepts – amounts to the recitation of a specific element in a formula for D6 wavelet transform, see Pg. 8, Ln. 1,
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”);
“the matrix M is
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, the Mt is a conjugate transpose matrix of the M (mathematical concepts – amounts to the recitation of a formula for elements in a larger mathematical formula); and
“Aa1 is Ph(π)⋅ Rz(
π
2
)⋅ Ry(1.15909π)⋅Rz(
-
π
2
)” (mathematical concepts – amounts to the recitation of a formula for an element in a larger mathematical formula) (“Aa1” is used as a representative example for the elements contained on Pg. 17, Ln.9-18, this analysis applies equally to elements “Aa2” through “VB2” which are similarly found to be mathematical concepts).
Step 2A Prong 2: This judicial exception is not integrated into a practical application.
The claim recites the additional elements:
“A manufacturing method of a quantum circuit for . . . comprising . . . constituting the quantum circuit . . . by a plurality of basic 1-bit logic gates, a controlled-NOT gate and a controlled-U gate . . . configured to transfer a state amplitude” (Field of use – recitation of quantum circuit components amounts to merely generally linking the use of well-defined mathematical concepts to a particular field of use).
Step 2B: The claim does not include additional elements considered individually and in combination that are sufficient to amount to significantly more than the judicial exception.
The claim recites the additional elements:
“A manufacturing method of a quantum circuit for . . . comprising . . . constituting the quantum circuit . . . by a plurality of basic 1-bit logic gates, a controlled-NOT gate and a controlled-U gate . . . configured to transfer a state amplitude” (Field of use – recitation of quantum circuit components do not impose meaningful limitations on the use of the mathematical concepts because it merely refers to a pre-existing circuit structure used in quantum wavelet transform mathematical operations, see generally Mayo Collaborative Servs. v. Prometheus Labs. Inc., 566 U.S. 66, 78, 101 USPQ2d 1961, 1968 (2012)).
For the reasons above, Claim 5 is rejected as being directed to an abstract idea without significantly more. This rejection applies equally to dependent Claim 6. The additional limitations of the dependent claim are addressed below.
Regarding Claim 6:
Step 2A Prong 1: See the rejection of Claim 5 above, which Claim depends on. Here, the claim recites additional elements that are mathematical concepts:
“wherein the 2n x 2n unitary matrix is
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” (mathematical concepts – amounts to the recitation of a formula for an element in a larger mathematical formula).
Step 2A Prong 2 & Step 2B: There are no elements left for consideration, considered individually and in combination, of implementation within a practical application or for consideration of significantly more.
Accordingly, Claim 6 is rejected as being directed to an abstract idea without significantly more.
Allowable Subject Matter
No prior art rejections are made for Claims 1, 3, and 5-6. However, claims 1, 3, and 5-6 are still rejected under 101 – abstract ideas and claim 3 is still rejected under 35 112(b) – indefinite.
As discussed in the July 8th, 2025 Office Action, the subject matter of claims 2, 4, and 5-6, as presented in the May 6th, 2022 version of the claims, were found to be distinct from the prior art. Specifically, Fijany et al. (hereinafter Fijany) (“Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits”), Krol et al. (hereinafter Krol) (“Efficient decomposition of unitary matrices in quantum circuit compilers”), and Vatan et al. (hereinafter Vatan) (“Optimal Quantum Circuits for General Two-Qubit Gates”) were found to disclose teachings relevant to the subject matter of claims 2, 4, and 5-6. For example, Vatan in combination with Fijany teach the “(UAl ⊗ UA2) ⋅ M ⋅ (Aai ⊕ Aa2) ⋅ Mt⋅ (VA1 ⊗ VA2)” circuit decomposition (Vatan, Pg. 3, Col. 1, Para. 3-4, “every U ∈ U(4) can be written as U = (A1 ⊗ A2)・N(α, β, ỿ)・(A3 ⊗ A4) . . . N(α, β, ỿ) = M・ D・M∗”; where the direct sum component is taught be Fijany, see Fijany, Pg. 19, Fig. 2). Additionally, Krol teaches the “Ph([value])⋅ Rz([value])⋅ Ry([value])⋅Rz([value])” gate decomposition (Pg. 4, Col. 1, Equation 11). Furthermore, Fijany teaches a similar element to “Q2n” (Pg. 11, Equation 33) and Vatan teaches a similar element to “M” (Pg. 2, Col. 1, Para. 7). However, these elements are not identical and none of these references teach the specific values used in the phase-shift and rotation gates.
Accordingly, given that the claims have been amended such that all of the pending claims contain these limitations, Claims 1, 3, and 5-6 are allowable over the prior art, pending the resolution of the 35 USC § 101 rejections and 35 USC § 112(b) rejections discussed above.
Examiner’s Remarks
Claims 1, 3, and 5 include symbols such as “⊗” and “Ph”. While the definitions of these symbols would be known to a person of ordinary skill in the art and are defined in the specification, examiner recommends amending the claims to define each symbol in order to conform with best practices.
Response to Arguments
Applicant's arguments filed on November 10th, 2025 have been fully considered. Each argument is addressed in detail below.
I. Applicant argues the objections to the specification should be withdrawn (Applicant’s Remarks, 11/10/2025, Pg. 11, Section “Objection to Specification”).
Applicant’s amendments have overcome each and every objection to the specification previously set forth in the July 8, 2025 Office Action. As a result, these objections to the specification have been withdrawn.
II. Applicant argues the objections to the claims should be withdrawn (Applicant’s Remarks, 11/10/2025, Pg. 11, Section “Claim Objections”).
Applicant’s amendments to the claims have overcome most, but not all, of the claim objections previously set forth in the July 8, 2025 Office Action. Specifically, regarding the objections to claims 1 and 3 for the minor informality of the recitation of “n is positive integer” instead of “n is a positive integer” (Claim 1, Ln. 16), only claim 3 was amended to correct this issue. As a result, this objection is maintained in regard to claim 1.
Whereas Applicant’s amendments have overcome every other objection to the claims previously set forth in the July 8, 2025 Office Action. As a result, these objections to the claims have been withdrawn.
III. Applicant argues the rejections to the claims, under 35 U.S.C. § 112, should be withdrawn (Applicant’s Remarks, 11/10/2025, Pg. 11-12, Section “Rejections Under 35 U.S.C. § 112”).
Applicant’s amendments to the claims have overcome most, but not all, of the rejections to the claims, under 35 U.S.C. § 112, previously set forth in the July 8, 2025 Office Action. Specifically, regarding the rejections to claims 1 and 3 for the indefiniteness created by the lack of antecedent basis for “the two same 2n x 2n unitary matrices . . . and the two same 2n x 2n unitary matrices” (Claim 3, ln. 18-19), only claim 1 was amended to correct this issue. As a result, this rejection is maintained in regard to claim 3.
Whereas Applicant’s amendments have overcome every other rejection to the claims, under 35 U.S.C. § 112, previously set forth in the July 8, 2025 Office Action. As a result, these rejections to the claims have been withdrawn.
IV. Applicant argues the rejections to the claims, under 35 U.S.C. § 101, should be withdrawn (Applicant’s Remarks, 11/10/2025, Pg. 12-13, Section “Rejections Under 35 U.S.C. § 101”).
First, Applicant argues the claims and the specification expressly define A and B quantum circuits in terms of specific unitary decompositions and gate-level implementations with explicit gate primitives and parameter values. As a result, applicant argues the claim limitations require a specific hardware implementation. Therefore, Applicant argues the claims integrate the judicial expression into a practical application (Step 2A, Prong 2).
In support of this position, Applicant argues the specification teaches the concrete realization of the D6 transform and its inverse using only 1-bit logic gates, the controlled-NOT gate, and the controlled-U gate, which results in tangible hardware with advantages of reduced overall circuit volume via a dimensional reduction and enabled higher-resolution quantum circuits suitable for high-information-complexity applications. Additionally, Applicant argues the claims require construction of quantum circuits with particular gate compositions, coupling relationships, and parameterized unitary decompositions, which integrate the mathematical concepts into a concrete quantum hardware architecture.
According to MPEP 2106.04(d), “After determining that a claim recites a judicial exception in Step 2A Prong One, examiners should evaluate whether the claim as a whole integrates the recited judicial exception into a practical application . . . Examiners evaluate integration into a practical application by: (1) identifying whether there are any additional elements recited in the claim beyond the judicial exception(s); and (2) evaluating those additional elements individually and in combination to determine whether they integrate the exception into a practical application . . . the way in which the additional elements use or interact with the exception may integrate it into a practical application. Accordingly, the additional limitations should not be evaluated in a vacuum, completely separate from the recited judicial exception. Instead, the analysis should take into consideration all the claim limitations and how those limitations interact and impact each other when evaluating whether the exception is integrated into a practical application . . . One way to demonstrate such integration is when the claimed invention improves the functioning of a computer or improves another technology or technical field”.
Additionally, also according to MPEP 2106.04(d), “Limitations the courts have found indicative that an additional element (or combination of elements) may have integrated the exception into a practical application include: . . . An improvement in the functioning of a computer, or an improvement to other technology or technical field . . . [and] Implementing a judicial exception with, or using a judicial exception in conjunction with, a particular machine . . . The courts have also identified limitations that did not integrate a judicial exception into a practical application: . . . Merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea . . . [and] Generally linking the use of a judicial exception to a particular technological environment or field of use”.
Furthermore, according to MPEP 2106.05(f), “Another consideration when determining whether a claim integrates a judicial exception into a practical application in Step 2A Prong Two . . . [is that] A claim having broad applicability across many fields of endeavor may not provide meaningful limitations that integrate a judicial exception into a practical application”.
Here, as discussed in detail above, the independent claims recite steps for performance of a D6 wavelet transform that are mathematical concepts. Furthermore, while Applicant argues the claims recite specific unitary decompositions and gate-level implementations with explicit gate primitives and parameter values, the claim limitations, as currently formulated in the, do not require specific hardware implementations because the limitations recite algorithmic steps for performing mathematical concepts that are discussed without regard for a concrete quantum hardware architecture (see section “Claim Rejections - 35 USC § 101” above for a detailed overview of each claim limitation).
This is further evidenced by the specification, where the claimed subject matter is similarly discussed algorithmically and without regard for a concrete quantum hardware architecture (see for example Para. [0009] - [0011], where the quantum circuit is described in regard to its performance of algorithmic steps for a D6 wavelet transform, without discussion of a specific required hardware architecture). As a result, the additional elements of the claims amount to recitations that merely link the mathematical concepts to the field of use of quantum circuits or, alternatively, recitations of generic quantum computing components to apply the algorithmic steps of a D6 wavelet transform. Therefore, when considered individually and in light of the claim as a whole, these additional elements do not require a specific hardware implementation.
Additionally, the asserted technological improvements of dimensional reduction of computations and enablement of higher resolution information complexity have broad applicability across computational domains. Whereas the recitations of generic quantum computing components and a quantum circuit field of use do not sufficiently limit the mathematical concepts used to effectuate these technological improvements within a practical application.
As a result, the argument is not persuasive.
Additionally, Applicant asserts the claims amount to an inventive concept that is significantly more than the judicial exception (Step 2B). Specifically, Applicant argues the inventive concept is the specific decomposition, parametrization, and coupling that maps the D6 wavelet transform to a realizable gate network, enables a dimensional-reduction implementation that lowers circuit volume, and produces higher-resolution quantum circuits tailored for practical high-complexity tasks. As a result, Applicant asserts the limitations are not mere instructions to apply a formula on generic hardware nor generic field-of-use statements. Instead, Applicant asserts the limitations impose concrete structural and functional constraints on how the transform is implemented in hardware.
According to MPEP 2106.05, “an inventive concept is furnished by an element or combination of elements that is recited in the claim in addition to (beyond) the judicial exception, and is sufficient to ensure that the claim as a whole amounts to significantly more than the judicial exception itself . . . Limitations that the courts have found to qualify as significantly more when recited in a claim with a judicial exception include: . . . Improvements to the functioning of a computer . . . [and] applying the judicial exception with, or by use of, a particular machine . . . that is arranged in a particular way to optimize . . . the machine . . . Limitations that the courts have found not to be enough to qualify as significantly more when recited in a claim with a judicial exception include . . . [a]dding the words apply it (or an equivalent) with the judicial exception, or mere instructions to implement an abstract idea on a computer . . . [and g]enerally linking the use of the judicial exception to a particular technological environment or field of use” (internal quotation marks omitted).
Here, as discussed in detail above, the claim, as currently formulated, recites limitations amounting to algorithmic steps for performing mathematical concepts that are discussed without regard for a concrete quantum hardware architecture. Whereas, as also discussed above, the remaining additional elements of the claims amount to recitations that merely link the mathematical concepts to the field of use of quantum circuits or, alternatively, recitations of generic quantum computing components to apply the algorithmic steps of a D6 wavelet transform, neither of which constitute a technological improvement nor do they require a specific hardware implementation.
Upon reconsideration of whether the additional elements, individually and within the claim as a whole, amount to an inventive concept that is significantly more than the judicial exception, the above reasoning and subsequent determinations remain the same. Specifically, as discussed above, the claims as currently formulated recite algorithmic steps for performing mathematical concepts with broad technological benefits. Whereas the additional elements do not require specific hardware implementations because they amount to generic recitations of quantum computing equipment for use of the judicial exception within the field of use of quantum circuits.
As a result, the argument is not persuasive.
V. Applicant argues the rejections to the claims, under 35 U.S.C. § 103, should be withdrawn (Applicant’s Remarks, 11/10/2025, Pg. 13, Section “Rejections Under 35 U.S.C. § 103”).
As discussed in detail above, Applicant’s amendments have overcome each and every claim rejection, under 35 U.S.C. § 103, previously set forth in the July 8, 2025 Office Action. As a result, these rejections to the claims have been withdrawn.
Conclusion
THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
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/MATTHEW BRYCE GOLAN/Examiner, Art Unit 2123
/ALEXEY SHMATOV/Supervisory Patent Examiner, Art Unit 2123