DETAILED ACTION
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 .
Continued Examination Under 37 CFR 1.114
A request for continued examination under 37 CFR 1.114, including the fee set forth in 37 CFR 1.17(e), was filed in this application after final rejection. Since this application is eligible for continued examination under 37 CFR 1.114, and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114. Applicant's submission filed on 05/11/2026 has been entered.
Response to Arguments
Applicant's arguments filed 05/11/2026 have been fully considered but they are not persuasive.
Regarding applicant’s remarks directed to the rejection of claims under 35 USC § 103,
Alleged No teaching of a single parameterized two-qubit gate
In Remarks p. 9-10, Applicant contends:
“The rejection of independent claim 1 is improper at least because the combination of
Schuld in view of Huang and Rudolph does not teach or suggest "executing layers of BS gates of a quantum circuit, each BS gate being a single parameterized two-qubit gate," as recited in claim 1. The Office Action cites "where each Ue is either a single qubit or a two-qubit quantum gate" as teaching or suggesting this limitation of claim 1 ( quotation from Section 11.B of Schuld). However, this teaching of Schuld is silent on the number of parameters of the quantum gates.” Wherein Applicant notes that “Section II. B of Schuld requires the quantum gates to be defined by four parameters.”
The relevant claim limitations appear to be “executing layers of BS gates of a quantum circuit, each BS gate being a single parameterized two-qubit gate” in amended claim 1.
As noted in the previous Office Action, Schuld teaches (emphasis added):
Schuld teaches A method for training a layer of a neural network with an [orthogonal] weight matrix, the method comprising: executing layers of BS gates of a quantum circuit, each BS gate being a single parameterized two-qubit gate,
(Schuld, Section II B., “Given an encoded feature vector ϕ(x) which is now a ‘ket’ vector in the Hilbert space of a n qubit system, the model circuit maps this ket vector to another ket vector ϕ 0 = Uθϕ(x) by a unitary operation Uθ which is parametrised by a set of variables θ.
As described before, we decompose U into
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where each Ul is either a single qubit or a two-qubit quantum gate [each BS gate being a single parameterized two-qubit gate].”)
After careful consideration, the argument is considered unpersuasive as “a single parameterized two-qubit gate” is not a term of art and the specification does not disclose “a single parameterized two-qubit gate” as a parameterizable two-qubit gate with only one parameter. Rather, per para. [0046] of the specification of the instant application, it discloses the BS gate explicitly as a parameterizable two-qubit gate that may have one parameter “[0046] The quantum circuits proposed in this work that implement fully connected neural network layers with orthogonal weight matrices may use only one type of quantum gate: the Reconfigurable Beam Splitter (BS) gate. The BS gate is a parametrizable two-qubit gate. This two-qubit gate may be considered hardware efficient, and it may have one parameter: angle 0 E [0, 2wc].” Thus, the BRI of “a single parameterized two-qubit gate” is merely one BS gate or one parameterizable two-qubit gate (in light of the specification) wherein Schuld teaches Ul as a two-qubit quantum gate parameterized by a set of variables θ.
Alleged No teaching of the total number of parameters of the BS gates equals the number of degrees of freedom of the orthogonal weight matrix.
In Remarks p. 11, Applicant contends:
“Separately, independent claim 1 is amended herein to recite inter alia "the total number
of parameters of the BS gates equals the number of degrees of freedom of the orthogonal weight
matrix." The combination of Schuld in view of Huang and Rudolph also does not teach or suggest this.”
After careful consideration, the argument is considered unpersuasive as Applicant's arguments fail to comply with 37 CFR 1.111(b) because they amount to a general allegation that the claims define a patentable invention without specifically pointing out how the language of the claims patentably distinguishes them from the references.
Lastly, the remaining arguments are directed to newly amended limitations that were not previously examined by the examiner. Therefore, applicants arguments are rendered moot. The examiner refers to the rejection under 35 USC § 103 in the current office action for more details.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
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.
Claim(s) 1-4, 7-12, and 15-20 are rejected under 35 U.S.C. 103 as being unpatentable over Schuld, Maria, et al. "Circuit-centric quantum classifiers." arXiv preprint arXiv:1804.00633 (2018). (“Schuld”) in view of Huang, Lei, et al. "Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks." arXiv preprint arXiv:1709.06079 (2017). (“Huang”) in further view of Rudolph, Terry, and Lov Grover. "A 2 rebit gate universal for quantum computing." arXiv preprint quant-ph/0210187 (2002). (“Rudolph”).
In regards to claim 1,
Schuld teaches A method for training a layer of a neural network with an [orthogonal] weight matrix, the method comprising: executing layers of BS gates of a quantum circuit, each BS gate being a single parameterized two-qubit gate,
(Schuld, Section II B., “Given an encoded feature vector ϕ(x) which is now a ‘ket’ vector in the Hilbert space of a n qubit system, the model circuit maps this ket vector to another ket vector ϕ 0 = Uθϕ(x) by a unitary operation Uθ which is parametrised by a set of variables θ.
As described before, we decompose U into
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where each Ul is either a single qubit or a two-qubit quantum gate [each BS gate being a single parameterized two-qubit gate; wherein the single gate is parameterized by a set of variables θ].”)
(Schuld, Section II C., “As a product of elementary gates, the model circuit Ux can be understood as a sequence of linear layers of a neural network with the same number of units in each “hidden layer”. This perspective facilitates the comparison of the circuit-centric quantum classifier with widely studied neural network models, and visualises the connectivity power of (controlled) single qubit gates. The position of the qubit (as well as the control) determine the architecture of each layer, i.e. which units are connected and which “weights” are tied in a “gate-layer” [executing layers of BS gates of a quantum circuit].”)
Schuld teaches wherein weights of the [orthogonal] weight matrix are based on values of parameters of the BS gates; and the total number of parameters of the BS gates equals the number of degrees of freedom of the orthogonal weight matrix;
(Schuld, Section II. C., “Note that although we speak of linear layers here, the weights (i.e., the entries of the weight matrix representing a gate) have a nonlinear dependency on the model parameters θ [wherein weights of the [orthogonal] weight matrix are based on values of parameters of the BS gates… and the total number of parameters of the BS gates ie model parameters θ equals the number of degrees of freedom ie number of parameters that may vary independently of the orthogonal weight matrix; wherein as the weights representing a gate of the weight matrix are dependent on the model parameters θ, the model parameters θ are interpreted to be the degrees of freedom of the weight matrix], a circumstance that plays a role for the convergence of the hybrid training method.”; see Schuld Section II B. for more information on the parameters)
Schuld teaches determining gradients of a cost function C with respect to parameters of the BS gates of the quantum circuit;
(Schuld, Section IV. B., “The derivative [determining gradients of a cost function C with respect to parameters of the BS gates of the quantum circuit] of the objective function with respect to a model parameter ν = b, µ (where µ ∈ θ is a circuit parameter) for a single data sample {(x m, ym)} is calculated as
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”)
Schuld teaches and updating values of parameters of the BS gates of the quantum circuit based on the gradients of the cost function C, wherein updating values of the parameters of the BS gates of the quantum circuit based on gradients of the cost function comprises: updating a value of a parameter
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of a BS gate of the quantum circuit based on the value of the parameter
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and
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wherein
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is the gradient of the cost function C with respect to the parameter
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.
(Schuld, Section IV. A., “We choose a standard least-squares objective to evaluate the cost of a parameter configuration θ and a bias b given a training set, D = {(x 1 , y1 ), ...,(xM, yM)},
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here π is the continuous output of the model defined in Equation (7)…
Gradient descent updates each parameter µ [updating values of parameters of the BS gates of the quantum circuit based on the gradients of the cost function C] from the set of circuit parameters θ via
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[ wherein updating values of the parameters of the BS gates of the quantum circuit based on gradients of the cost function comprises: updating a value of a parameter
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of a BS gate of the quantum circuit based on the value of the parameter
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and
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wherein
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is the gradient of the cost function C with respect to the parameter
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.]”)
However, Schuld does not explicitly teach an orthogonal weight matrix; updated values of the parameters preserving the orthogonality of the orthogonal weight matrix, each BS gate only has real amplitudes
Huang teaches an orthogonal weight matrix; updated values of the parameters preserving the orthogonality of the orthogonal weight matrix,
(Huang, Abstact, “We also propose a novel orthogonal weight normalization [an orthogonal weight matrix] method to solve OMDSM. Particularly, it constructs orthogonal transformation over proxy parameters to ensure the weight matrix is orthogonal [updated values of the parameters preserving the orthogonality of the orthogonal weight matrix] and back-propagates gradient information through the transformation during training.”)
Rudolph teaches each BS gate only has real amplitudes
(Rudolph, pg. 1 col. 1 para. 3-4, “The ability to perform a CNOT and arbitrary single qubit gates allows one to evolve an n qubit state to any point in the Hilbert space, i.e. it allows the construction of arbitrary unitary transforms. However it has been shown within the Quantum Turing Machine model that universal quantum computing can be performed using only real amplitudes [each BS gate only has real amplitudes] [4].
The Quantum Turing Machine model is not particularly intuitive for either thinking about construction of a practical quantum computer, nor for design of quantum algorithms. The purpose of this note is to point out how any quantum computation can be simply translated into a quantum circuit in which all quantum states and gates are real.”)
Schuld is considered to be analogous to the claimed invention because they are in the same field of quantum neural networks. Huang is considered to be analogous to the claimed invention because they are in the same field of orthogonal neural networks. Therefore, it would have been obvious to someone of ordinary skill in the art before the effective filing date of the claimed invention to have modified Schuld to incorporate the teachings of Huang in order to provide a method of orthogonal weight normalization as doing so stabilizes the network activations and regularize FNNs.(Huang, Abstract, “Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to orthogonal rectangular matrix and formulating this problem in feedforward Neural Networks (FNNs) as Optimization over Multiple Dependent Stiefel Manifolds (OMDSM). We show that the rectangular orthogonal matrix can stabilize the distribution of network activations and regularize FNNs. We also propose a novel orthogonal weight normalization method to solve OMDSM. Particularly, it constructs orthogonal transformation over proxy parameters to ensure the weight matrix is orthogonal and back-propagates gradient information through the transformation during training. To guarantee stability, we minimize the distortions between proxy parameters and canonical weights over all tractable orthogonal transformations. In addition, we design an orthogonal linear module (OLM) to learn orthogonal filter banks in practice, which can be used as an alternative to standard linear module. Extensive experiments demonstrate that by simply substituting OLM for standard linear module without revising any experimental protocols, our method largely improves the performance of the state-of-the-art networks, including Inception and residual networks on CIFAR and ImageNet datasets. In particular, we have reduced the test error of wide residual network on CIFAR-100 from 20.04% to 18.61% with such simple substitution. Our code is available online for result reproduction.”)
Schuld is considered to be analogous to the claimed invention because they are in the same field of quantum neural networks. Rudolph is considered analogous to the claimed invention because they are reasonably pertinent to the problem the inventor faced of efficiently performing quantum computations. Therefore, it would have been obvious to someone of ordinary skill in the art before the effective filing date of the claimed invention to have modified Schuld to incorporate the teachings of Rudolph in order to substitute the quantum computations with complex amplitude gates of Schuld with a method of universal quantum computing that can be efficiently performed using states with only real amplitudes and simplify the quantum computations. (Rudolph, Abstract, “We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact 2-rebit) gate which is universal for quantum computing, although it cannot be used to perform arbitrary unitary transformations.”)
In regards to claim 2,
Schuld in view of Huang and Rudolph teaches The method of claim 1,
Schuld teaches wherein determining gradients of the cost function comprises determining gradients of the cost function with respect to the parameter of each BS gate of the quantum circuit.
(Schuld, Section IV. B., “The derivative [wherein determining gradients of the cost function comprises determining gradients of the cost function with respect to the parameter of each BS gate of the quantum circuit] of the objective function with respect to a model parameter ν = b, µ (where µ ∈ θ is a circuit parameter) for a single data sample {(x m, ym)} is calculated as
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”)
In regards to claim 3,
Schuld in view of Huang and Rudolph teaches The method of claim 1,
Schuld teaches wherein executing layers of BS gates of the quantum circuit comprises: measuring a resulting quantum state
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after each layer
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of the quantum circuit is executed.
(Schuld, Section II C., “After executing the quantum circuit Uθϕ(x) in Step 2 [measuring a resulting quantum state
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after each layer
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of the quantum circuit is executed], the measurement of the first qubit (Step 3) results in state 1 with probability[32]
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To resolve these statistics we have to run the entire circuit S times and measure the first qubit. We estimate p(q0 = 1) from these samples s1, ..., sS. This is a Bernoulli parameter estimation problem which we discuss in Section IV E.
The classical postprocessing (Step 4) consists of adding a learnable bias term b to produce the continuous output of the model,
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”)
In regards to claim 4,
Schuld in view of Huang and Rudolph teaches The method of claim 3,
Schuld teaches further comprising determining errors
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for layers
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of the quantum circuit.
(Schuld, Section IV E.2., “The continuous output of the circuit-centric quantum classifier was based on the probability of measuring the first qubit in state 1. To resolve this number, we have to repeat the entire algorithm multiple times. Each measurement samples from the Bernoulli distribution p(q0 = 1) = ν, and we want to estimate ν from the S samples q 1 1 , ..., qS 1 . The number of samples needed to estimate ν at error
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with probability > 2/3 scales as O(Var(σz)/
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2 )), where Var(σz) is the variance of the sigma-z operator that we measure with respect to the final quantum state [12, 34]. If amplitude estimation is used then the number of repetitions of circuit centric classifier falls into O(1/
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) at a price of increasing the circuit depth by a factor of O(1/
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).”)
In regards to claim 7,
Schuld in view of Huang and Rudolph teaches The method of claim 1, wherein updating the value of the parameter
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of the BS gate of the quantum circuit based on the value of the parameter
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and
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comprises: updating a value of a parameter
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of a BS gate of the quantum circuit according to
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where
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is the learning rate.
(Schuld, Section IV. A., “We choose a standard least-squares objective to evaluate the cost of a parameter configuration θ and a bias b given a training set, D = {(x 1 , y1 ), ...,(xM, yM)},
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here π is the continuous output of the model defined in Equation (7)…
Gradient descent updates each parameter µ from the set of circuit parameters θ via
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[updating a value of a parameter
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of a BS gate of the quantum circuit according to
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where
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is the learning rate]”)
In regards to claim 8,
Schuld in view of Huang and Rudolph teaches The method of claim 1,
Schuld teaches wherein a quantum computing system executes the layers of the BS gates of the quantum circuit.
(Schuld, Section IV E.1., “Each of these gates has to be decomposed into the elementary constant gate set used in the physical implementation of the quantum computer.”)
Claims 9 and 17 are rejected on the same rational under 35 U.S.C. 103 as claim 1.
Claims 10 and 18 are rejected on the same rational under 35 U.S.C. 103 as claim 2.
Claims 11 and 19 are rejected on the same rational under 35 U.S.C. 103 as claim 3.
Claims 12 and 20 are rejected on the same rational under 35 U.S.C. 103 as claim 4.
Claim 15 is rejected on the same rational under 35 U.S.C. 103 as claim 7.
Claim 16 is rejected on the same rational under 35 U.S.C. 103 as claim 8.
Claim(s) 5-6 and 13-14 are rejected under 35 U.S.C. 103 as being unpatentable over Schuld in view of Huang and Rudolph in further view of Michael A. Nielsen, “Chapter 2 How the backpropagation algorithm works”, Neural Networks and Deep Learning, Determination Press, 2015 (Last update: Thu Dec 26 15:26:33 2019)
In regards to claim 5,
Schuld in view of Huang and Rudolph teaches The method of claim 4,
Nielsen teaches wherein determining errors
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for layers
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of the quantum circuit comprises determining errors for each layer of the quantum circuit in reverse order according to:
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where
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is the transpose of
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, where
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is the error for layer
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of the quantum circuit and
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is a matrix representation of BS gates in layer
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of the quantum circuit.
(Nielsen, (BP2), “An equation for the error δl in terms of the error in the next layer, δl+1: In particular
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where (wl+1)T is the transpose of the weight matrix wl+1 for the (l+1)th layer.”)
Nielsen is considered to be analogous to the claimed invention because they are reasonably pertinent to the problem the inventor faced (understanding the math behind gradient descent and backpropagation). Therefore, it would have been obvious to someone of ordinary skill in the art before the effective filing date of the claimed invention to have modified Schuld in view of Huang and Rudolph to incorporate the teachings of Nielsen in order to provide backpropagation and better understand the mathematics behind backpropagation (Nielsen, paragraph 3-4, “This chapter is more mathematically involved than the rest of the book. If you're not crazy about mathematics you may be tempted to skip the chapter, and to treat backpropagation as a black box whose details you're willing to ignore. Why take the time to study those details?
The reason, of course, is understanding. At the heart of backpropagation is an expression for the partial derivative ∂C/∂w of the cost function C with respect to any weight w (or bias b) in the network. The expression tells us how quickly the cost changes when we change the weights and biases. And while the expression is somewhat complex, it also has a beauty to it, with each element having a natural, intuitive interpretation. And so backpropagation isn't just a fast algorithm for learning. It actually gives us detailed insights into how changing the weights and biases changes the overall behaviour of the network. That's well worth studying in detail.”)
In regards to claim 6,
Schuld in view of Huang and Rudolph teaches The method of claim 5,
Schuld teaches wherein the gradient of the cost function C with respect to a parameter
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of a BS gate acting on qubits i and i + 1 is defined by:
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(Schuld, Section II B., “To make the single qubit gates trainable we need to formulate them in terms of parameters that can be learnt. The way the parametrisation is defined can have a significant impact on training, since it defines the shape of the cost function [wherein the gradient of the cost function C with respect to a parameter
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of a BS gate]. A single qubit gate G is a 2 × 2 unitary, which can always be written [30] as
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”)
(Schuld, Section III C., “To show an example, consider a Hilbert space of dimension 2n with n = 2 qubits |q0q1> [acting on qubits i and i + 1]. A single qubit unitary G applied to q0 would have the following matrix representation
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Claim 13 is rejected on the same rational under 35 U.S.C. 103 as claim 5.
Claim 14 is rejected on the same rational under 35 U.S.C. 103 as claim 6.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
NPL: Perdomo, Oscar. "Schmidt representation of 3-qubits with real amplitudes." arXiv preprint arXiv:2012.14031 (2020).
(Perdomo, Section 1., “There is not doubt that to deal with real numbers and orthogonal matrices is easier (at least, computationally less expensive) than to deal with complex numbers and unitary matrices. We need only one real parameter to describe an orthogonal 2 by 2 matrix, while we need 4 real parameters (three if we take unitary matrices with determinant one) to describe a 2 by 2 unitary matrix….This can be useful, for example, if we are training a quantum circuit ([3], [5], [9]) to achieve a particular entanglement, there is not need to consider unitary matrices, it is enough to consider real 2-qubits states and Ry gates…One of the goals of this paper is to show that for any real state |φ1⟩ there is a real state |φ2⟩ = Ry(θ2)⊗Ry(θ1)⊗Ry(θ0)|φ1⟩ of the form λ1|000⟩+λ2|011⟩+λ3|101⟩+ λ4|110⟩ + λ5|111⟩ with Pλ2 i = 1. Recall that
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”)
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/J.T.T./Examiner, Art Unit 2129
/MICHAEL J HUNTLEY/Supervisory Patent Examiner, Art Unit 2129
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