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 .
Response to Arguments
Applicant's arguments filed 12/02/2025 have been fully considered and they are partially persuasive.
Regarding applicant’s remarks directed to the rejection of claims under 35 USC § 103, the 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 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].”)
(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;
(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], a circumstance that plays a role for the convergence of the hybrid training method.”)
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,
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.”)
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.”)
In regards to claim 2,
Schuld and Huang 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 and Huang 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 and Huang 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 and Huang 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 and Huang 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 and Huang 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 and Huang 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 and Huang 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 and Huang 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
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). 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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/J.T.T./Examiner, Art Unit 2129
/MICHAEL J HUNTLEY/Supervisory Patent Examiner, Art Unit 2129