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 .
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 Amendment
(Submitted on 9/8/2025)
The examiner notes that applicant has not amended any of the previous claims 1, 8-10, 17 and 21-29
and added three new dependent claims 30-32. Applicant’s arguments with respect to claims 1, 8 and 17
have been considered but are moot because the new ground of rejection does not rely on any reference
applied in the prior rejection of record for any teaching or matter specifically challenged in the
argument.
In regard to 103 rejection
- The applicant submitted the arguments on 9/8/25 for the last FINAL REJECTION. The applicant argues on Page 11 the 103 obviousness based on the references cited in the last Office Action. The applicant specifically argues on Page 13 that the references do not teach generating the quantum noise using swapping of qubits.
Examiner’s Response
As stated before, applicant’s arguments with respect to claims 1, 8 and 17 are moot because the
new ground of rejection does not rely on any reference applied in the prior rejection of record for
any teaching or matter specifically challenged in the argument.
The examiner first notes that no decision was taken at the time of interview which was conducted on 8/15/2025.
After a very thorough review of the arguments of the applicant, the examiner submits that qubit swapping is a key operation in quantum computing and may be used to generate noise in the quantum circuit. First, the examiner states that after reviewing the specification the specification does not state generating unbiased noise using swapping of qubits or any context thereof. It perhaps known in the art that quantum noise is an umbrella term for any unwanted disturbance or interaction that affects a quantum system, leading to errors and decoherence. Swapping of qubits is a source of noise as caused intentionally using an external source coupled to entangle the qubits where a microwave pulse or any other electromagnetic sources meant to induce a multi-qubit interaction (like an unwanted SWAP or partial SWAP). In fact, dependent claims 22, 25 and 28 such an interaction using microwave pulses. Using this broad interpretation, the examiner submits that new reference “ Silva” teaches generating the quantum noise using swapping of qubits using a microwave pulse as a source for interaction and a new reference “Alam” teaches the reclassification with noise. The examiner has used new reference “Schuld” to teach the new claims 30-32.
In Conclusion, claims 1, 8, 17 and dependent claims 9-10, 21-22, and 24-32 are rejected under 35 USC 103 and as NON- FINAL REJECTION
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1, 8, 17, 23, 26 and 29 is rejected under 35 U.S.C. 103 as being unpatentable over
Farhi (hereinafter Farhi) US 2020/0342345 A1,
in view of Gerado A. Paz-Silva (hereinafter Silva) Multiqubit Spectroscopy of Gaussian Quantum Nose, arXiv:1609.01792v2 [quant-ph] 21 Sep 2016,
in view of Mahabubul Alam (hereinafter Alam) Addressing Temporal Variations in Qubit Quality Metrics for Parameterized Quantum Circuits, arXiv:1903.08684v1 [cs.ET] 20 Mar 2019 [Also available in IEEE Xplore].
In regard to Claim 1 (Previously Presented)
Farhi discloses:
- A method comprising: training, using a classical processor, a neural network for solving a classification problem;
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state.
- preparing, using a quantum processor, a quantum state based on the neural network and the classification problem;
in [0034]:
The system 100 uses supervised learning to learn parameters of the quantum gates 104 that can obtain a predicted classification l′(z) 114 of an input state 106. Sample states 108 with known classifications l(z) (also referred to herein as label functions) are selected from a sample data set S for use in the supervised learning and an input state 106 comprising the sample state 108 and one or more readout qubits 110 is prepared,
in [0093]:
at least one of the two qubits operated on by the two-qubit quantum gate is a readout qubit 110. Layers of quantum gates 104 of the same type may be alternated in the quantum computer. For example, the sequence of quantum gates may comprise alternating three layers ZX quantum gates with three layers of XX quantum gates. Each layer may comprise a plurality of quantum gates. Each layer may comprise two-qubit quantum gates operating between one or more of the readout qubits 110 and each of the other qubits in the plurality of qubits 102. For example, in a binary classifier, each layer may comprise n two-qubit quantum gates, each of which acts between the readout qubit 110 and a different one of the n qubits representing the state to be classified,
in [0113]:
In some embodiments, a state to be classified 108 is input into a classical artificial neural network 116. The output of the classical artificial neural network 116 can be used an input to the quantum computing system 100 in order to generate the input state 106 to be classified according the methods described above. An example of such an embodiment is shown in FIG. 5a,
in [0114]:
In some embodiments, the readout state from readout qubits 110 in the quantum computing system 100 is input into a classical artificial neural network 116. The classical artificial neural network can be trained to determine, using the readout state of the output state of the one or more readout qubits in the plurality of qubits, a predicted classification of the input state. An example of such an embodiment is shown in FIG. 5 b.
(BRI: Fig 5a and Fig 5B represents a hybrid classification network)
in [0047]:
the method comprises repeatedly preparing the plurality of qubits in the input state 106, applying the parameterized quantum gates 104 to the input state 106 and measuring the readout state of the one or more readout qubits.
in [0051]:
There are many examples of sample loss functions that can be used to compare the known classification with the predicted classification 114. As an example, for a binary classifier l(
Ψ
) that classifies an input state as either +1 or -1, and with a single readout qubit initially set to 1 in the computational basis,
in [0106]:
with a quantum neural network, input states may comprise classical data in a superposition. A single quantum state that is a superposition of computational basis states, each of which represents a single sample from a batch of samples, can be viewed as quantum encoding of the batch.
- classifying, using a quantum classifier based on the neural network, data set to generate a first set of classified data, wherein the classifying comprises classifying a data item of the data set resulting in a first classification result of the data item
in [0038]:
FIG. 2 shows a flow diagram of a method for training a classifier implemented on a quantum computer,
in [0035]:
By analogy with classical artificial neural networks, the trained quantum classifier can be described as a “quantum neural network”,
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state; determining, using a readout state of the one or more readout qubits in the output state, a predicted classification of the input state; comparing the predicted classification with the known classification; and updating one or more parameters of the parameterised quantum gates in dependence on the comparison of the predicted classification with the known classification.
in [0036]:
Systems and methods described herein can accept both classical quantum states as an input and classify them accordingly, in contrast with classical artificial neural networks, which can only take classical states as an input.
in [0037]:
quantum computers with good enough fidelity to run circuits with enough depth to perform tasks that cannot be simulated on classical computers are expected to be available. One approach to designing quantum algorithms to run on such devices is to let the architecture of the hardware determine which gate sets to use.
- classifying, using a quantum classifier based on the neural network, data set to generate a first set of classified data, wherein the classifying comprises classifying a data item of the data set resulting in a first classification result of the data item
in [0038]:
FIG. 2 shows a flow diagram of a method for training a classifier implemented on a quantum computer,
in [0035]:
By analogy with classical artificial neural networks, the trained quantum classifier can be described as a “quantum neural network”,
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state; determining, using a readout state of the one or more readout qubits in the output state, a predicted classification of the input state; comparing the predicted classification with the known classification; and updating one or more parameters of the parameterised quantum gates in dependence on the comparison of the predicted classification with the known classification.
in [0036]:
Systems and methods described herein can accept both classical quantum states as an input and classify them accordingly, in contrast with classical artificial neural networks, which can only take classical states as an input.
in [0037]:
quantum computers with good enough fidelity to run circuits with enough depth to perform tasks that cannot be simulated on classical computers are expected to be available. One approach to designing quantum algorithms to run on such devices is to let the architecture of the hardware determine which gate sets to use.
- determining, responsive to comparing the first classification result of the data item and the second classification result of the data item,
in [0054]:
In some embodiments, a gradient descent method is used
to compare the predicted classifier of the input state 106 with the known classifier of the
sample state 108 and update the parameters. FIG. 3 shows a flowchart of an example of a
method for updating the parameters using gradient descent,
in [0064]:
At operation 4.1 an unclassified input state is received. The unclassified input state comprises a plurality of qubits 102. The plurality of qubits 102 comprises n qubits representing a quantum state to be classified 108, and one or more readout qubits 110 in a known state. The quantum state is, in some embodiments, received from a routine running on a quantum or classical computer, and/or experimental equipment. Many other examples are possible. In some embodiments, the method encompasses preparing the input state 106 from a received quantum state to be classified 108.
- comparing the first sensitivity metric against a pre-established sensitivity criterion;
in [0050]:
The predicted classifier 114 can be compared to the known classifier using a metric. For example, a sample loss function (or loss function) can be used to compare the predicted classifier 114 to the known classifier. The sample loss function provides a “cost” for mismatching known and predicted classifications. The sample loss function, can, for example, be a function that has a minimum value when the predicted classifiers 114 match the known classifiers. In these examples, the aim of the training method can be to reduce the average sample loss over the training set to below a threshold value.
(BRI: threshold is the sensitivity criterion using the sample loss comparisons for predicted and known classifier)
- upon a determination that the first sensitivity metric does not meet the pre-established sensitivity criterion, updating a parameter of the neural network, and re-training, using the classical processor, the neural network comprising the updated parameter.
in [0061]:
With reference again to FIG. 2, if the threshold condition is not met, once one or more parameters have been updated the method returns to operation 2.2 and selects another training example (i.e. another sample state 108 with a known classification) and performs operations 2.3 to 2.8 with the updated quantum gate 104 parameters.
Farhi does not explicitly disclose:
- generating quantum noise in the quantum processor at least by swapping qubits in the quantum processor, the swapping qubits in the quantum processor causing the quantum noise to be unbiased with respect to the data set used to generate the first set of classified data:
However, Silva explicitly discloses:
- generating quantum noise in the quantum processor at least by swapping qubits in the quantum processor, the swapping qubits in the quantum processor causing the quantum noise to be unbiased with respect to the data set used to generate the first set of classified data:
in [ 1, Page 2]:
Characterization of discrete non-Gaussian phase noise has, likewise, been implemented in trapped ions [25], whereas general QNS protocols for reconstructing high-order spectra of non-Gaussian classical and quantum dephasing environments have been proposed in [14],
in [ Abstract, Page 1]:
We introduce multi-pulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources.
in [ 1, Page 2]:
noise may exhibit non-trivial spatial correlations, which may only become manifest in the coherence dynamics of multiple qubit probes at different locations. Let S`,`0 (ω) ≡ S + `,`0 (ω)+S − `,`0 (ω) denote the spectrum of the noise affecting a pair of qubits `, `0 , where the “classical” (+) and the “quantum” (−) components
in [ II C, Page 5]:
Statistical features of the noise are compactly described by the cumulants of the bath operators [36, 51, 52]. For the zero-mean Gaussian noise we consider1 , the only non-vanishing cumulants are the second-order cumulants
(BRI: a zero-mean Gaussian noise process is widely used in both classical and quantum contexts as a model for unbiased noise)
In [III B, Page 8]:
The dynamics of multiple qubits coupled to a quantum bath are considerably more rich than those of a single qubit. Notably, interaction with a quantum bath can generate quantum correlations and entangle the qubits, even in the absence of direct coupling between them,
While the steady state populations are always equal for a classical, spectrally symmetric bath, this is generally not true when the bath is quantum, as dictated by the requirement of detailed balance at equilibrium [51].
in [II B, Page 4]:
Beside interacting with the bath, the N qubits are subject to external control generated by a Hamiltonian
H
c
t
r
l
(
t
)
. We restrict ourselves to control that preserves the dephasing character of the noise in the interaction picture associated with
H
c
t
r
l
(
t
)
(aka the “toggling frame”).
in [II B, Page 5]:
The second form of dephasing-preserving control we consider are instantaneous swap gates between any pair of qubits. The gate SWAP`,`0 acts non-locally on qubits ` and ` 0 , effecting the transformation SWAP† `,`0 Z` SWAP`,`0 = Z` 0 . A sequence consisting of both instantaneous π-pulses and swap gates has a control propagator of the form
- determining, responsive to comparing the first classification result of the data item and the second classification result of the data item,
- reclassifying, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, and Silva.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise by swapping qubits using microwave pulses as a source.
One of ordinary skill would have motivation to combine Farhi , and Silva that can provide
analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control [Abstract, Page 1].
Farhi and Silva do not explicitly disclose:
- determining, responsive to comparing the first classification result of the data item and the second classification result of the data item, a first sensitivity metric of the quantum processor , the first sensitivity metric based on a proportion of actual positives that are correctly identified by the quantum classifier:
However, Alam discloses:
- determining, responsive to comparing the first classification result of the data item and the second classification result of the data item, a first sensitivity metric of the quantum processor , the first sensitivity metric based on a proportion of actual positives that are correctly identified by the quantum classifier:
In [Introduction , Page 1]:
due to temporal variations of the qubit quality metrics, we have received significantly different outcomes at different points of time as shown in Figure 1(c). The y-axis shows the fidelity of the measurements (which is the % of the correct output for 1024 samples at a time). For circuits such as circuit-centric binary quantum classifiers based on P QC (discussed in Section II), the final outcome is decided after analyzing the measurement distributions in a classical computer which can be completely wrong due to the temporal variations of the qubit quality metrics.
PNG
media_image1.png
206
220
media_image1.png
Greyscale
- reclassifying, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
In [II B, Page 2]: Classifier Basics
Binary classification is the task of classifying any input data into one of two possible groups. In supervised machine learning, this classification problem is solved by training a mathematical model (f(x, θ)) with a properly labeled input data-set {(
x
1
,
y
1
)
, (
x
2
,
y
2
)
,
.... ,
(
x
M
,
y
M
)
} where
x
i
is the feature vector (can be multi-dimensional) of the i th input data and
y
i
is the associated label. The mathematical model predicts the class of any input data based on its features (x) and the parameters (θ) of the model. The parameters (θ) are updated iteratively until the model predictions are satisfactory over the input data-set. In [6], a binary classification on quantum computers is proposed for classical data where a P QC serves as the mathematical model. A state-preparation routine is required to encode the classical data and feed it to the P QC. The output is captured from a target qubit. During the training phase of the P QC, the parameters are updated iteratively based on the given input data-set so that the probability of getting 1 through a measurement of the target qubit for one class is maximized (and 0 for the other class)
In [II E, Page 3]:
PNG
media_image2.png
546
607
media_image2.png
Greyscale
In [III, Page 3]:
Training of a model circuit (P QC, Figure 4(b)) for binary classification can follow three
disparate strategies as described below.
PNG
media_image3.png
127
595
media_image3.png
Greyscale
(b) Structure of a multi-layer circuit centric Quantum Classifier (4-Qubits)
In [III A, Page 4]: Existing Approaches
Two classes of P QC training proposals exist in the literature: i) Train the P QC in a hardware-in-the-loop fashion. Hereafter, we term this approach as app01. In this approach, the P QC is executed on a real quantum computer. For a certain input, the output is measured and then the measured output is post-processed in a classical computer. Statistical techniques such as, Kullback-Leibler (KL) divergence method is used to calculate the disparity between the target distribution and the measured distribution (hence the cost) to update the parameters with any classical optimization techniques such as stochastic gradient descent or particle swarm optimization etc. [11]–[13]. Then, the P QC is executed again with updated parameters and process iterates until measured output matches target output up to a certain threshold. While it may seem to be an ideal approach, the technique is plagued with certain impediments.
In [III A, Page 4]: Existing Approaches
we can define the following cost-function to iteratively update the parameters of the P QC (Figure 5(b)) to solve the binary classification problem (described for the hybrid approach) [6]:
PNG
media_image4.png
67
565
media_image4.png
Greyscale
where m is the batch-size,
y
i
is the label of the i th data in the batch (data are labeled as -1 and +1 for class A and class B respectively),
x
i
is the i th input, and ‘expectation(PQC(xi,θ):QT )’ is the expectation value of the target qubit (
Q
T
) for the i th input and current values of the θ. The target is to minimize the cost. Gradient descent technique is applied to achieve the optimization goal where the partial derivatives of the cost function (Equation 1) with respect to the circuit parameters are calculated using numerical differentiation [20].
In [III A, Page 4]: Existing Approaches
the simulation models an ideal (i.e., without noise) quantum computer whereas quantum computers are noisy (and noise behavior shows temporal variation).
In [III A, Page 4]: Existing Approaches
the parameter optimization without considering noise may not give optimal result during inferencing phase in the real noisy quantum computer
In [III B, Page 4]: Proposed Approach: Classical Training with Noise Effects
To deal with the noisy hardware related dependency of the trained P QC, we propose to update the parameters where the expectation values are calculated with modeled noise behavior of a target hardware with our noisy quantum hardware simulation framework
In [III B, Page 4]:
To address the stochastic behavior of the noise sources as evident from Figure 2, we use the average value of the qubit quality metrics collected over a significant amount of time (43 days) to optimize the P QC parameters.
In [IV B, Page 5]:
2) Evaluation Method: Although parameterized quantum circuits can minimize the effects of noise, it cannot suppress it altogether. Therefore, the expectation values cannot be optimized to exactly -1/+1 values for all the inputs during the P QC training period which indicates that a measurement is not guaranteed to result in the desired class output (0/1) for a certain input.
In [IV B, Page 5]:
The ratio between the correct and incorrect outputs is also a representation of the fidelity of the circuit.
(BRI: Fidelity is the sensitivity)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Siva and Alam.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
One of ordinary skill would have motivation to combine Farhi , Silva and Alam that can provide a training methodology in a classical environments to improve the fidelity of the trained quantum circuit ([Abstract, Page 1])
In regard to Claim 8 (Previously Presented)
Farhi discloses:
- A computer usable program product comprising a computer-readable storage medium, and program instructions stored on the storage medium, the stored program instructions comprising:
in [0017, [0171], [0176], [0177]:
- program instructions to train, using a classical processor, a neural network for solving a classification problem;
Program instructions
In [0118]:
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state.
- program instructions to prepare, using a quantum processor, a quantum state based on the neural network and the classification problem;
in [0034]:
The system 100 uses supervised learning to learn parameters of the quantum gates 104 that can obtain a predicted classification l′(z) 114 of an input state 106. Sample states 108 with known classifications l(z) (also referred to herein as label functions) are selected from a sample data set S for use in the supervised learning and an input state 106 comprising the sample state 108 and one or more readout qubits 110 is prepared,
in [0093]:
at least one of the two qubits operated on by the two-qubit quantum gate is a readout qubit 110. Layers of quantum gates 104 of the same type may be alternated in the quantum computer. For example, the sequence of quantum gates may comprise alternating three layers ZX quantum gates with three layers of XX quantum gates. Each layer may comprise a plurality of quantum gates. Each layer may comprise two-qubit quantum gates operating between one or more of the readout qubits 110 and each of the other qubits in the plurality of qubits 102. For example, in a binary classifier, each layer may comprise n two-qubit quantum gates, each of which acts between the readout qubit 110 and a different one of the n qubits representing the state to be classified,
in [0113]:
In some embodiments, a state to be classified 108 is input into a classical artificial neural network 116. The output of the classical artificial neural network 116 can be used an input to the quantum computing system 100 in order to generate the input state 106 to be classified according the methods described above. An example of such an embodiment is shown in FIG. 5a,
in [0114]:
In some embodiments, the readout state from readout qubits 110 in the quantum computing system 100 is input into a classical artificial neural network 116. The classical artificial neural network can be trained to determine, using the readout state of the output state of the one or more readout qubits in the plurality of qubits, a predicted classification of the input state. An example of such an embodiment is shown in FIG. 5 b.
(BRI: Fig 5a and Fig 5B represents a hybrid classification network)
in [0047]:
the method comprises repeatedly preparing the plurality of qubits in the input state 106, applying the parameterized quantum gates 104 to the input state 106 and measuring the readout state of the one or more readout qubits.
in [0051]:
There are many examples of sample loss functions that can be used to compare the known classification with the predicted classification 114. As an example, for a binary classifier l(
Ψ
) that classifies an input state as either +1 or -1, and with a single readout qubit initially set to 1 in the computational basis,
in [0106]:
with a quantum neural network, input states may comprise classical data in a superposition. A single quantum state that is a superposition of computational basis states, each of which represents a single sample from a batch of samples, can be viewed as quantum encoding of the batch.
- program instructions to classify, using a quantum classifier based on the neural network, a data set to generate a first set of classified data, wherein the classifying comprises classifying a data item of the data set resulting in a first classification result of the data item
in [0038]:
FIG. 2 shows a flow diagram of a method for training a classifier implemented on a quantum computer,
in [0035]:
By analogy with classical artificial neural networks, the trained quantum classifier can be described as a “quantum neural network”,
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state; determining, using a readout state of the one or more readout qubits in the output state, a predicted classification of the input state; comparing the predicted classification with the known classification; and updating one or more parameters of the parameterised quantum gates in dependence on the comparison of the predicted classification with the known classification.
in [0036]:
Systems and methods described herein can accept both classical quantum states as an input and classify them accordingly, in contrast with classical artificial neural networks, which can only take classical states as an input.
in [0037]:
quantum computers with good enough fidelity to run circuits with enough depth to perform tasks that cannot be simulated on classical computers are expected to be available. One approach to designing quantum algorithms to run on such devices is to let the architecture of the hardware determine which gate sets to use.
- program instructions to [ Note: for unbiased noise induction]
in [0141]:
several example embodiments for programming and/or operating a quantum computing device,
in [0003] :
a form of robust principal component analysis is disclosed that can tolerate noise intentionally introduced to a quantum training set.
- program instructions to determine, responsive to comparing the first classification result of the data item and the second classification result of the data item, a first sensitivity metric of the quantum processor
in [0054]:
In some embodiments, a gradient descent method is used
to compare the predicted classifier of the input state 106 with the known classifier of the
sample state 108 and update the parameters. FIG. 3 shows a flowchart of an example of a
method for updating the parameters using gradient descent,
in [0064]:
At operation 4.1 an unclassified input state is received. The unclassified input state comprises a plurality of qubits 102. The plurality of qubits 102 comprises n qubits representing a quantum state to be classified 108, and one or more readout qubits 110 in a known state. The quantum state is, in some embodiments, received from a routine running on a quantum or classical computer, and/or experimental equipment. Many other examples are possible. In some embodiments, the method encompasses preparing the input state 106 from a received quantum state to be classified 108.
a first sensitivity metric of the quantum processor
in [0098] :
The binary classifier used in the example described below corresponds to whether an expected value of a Hamiltonian
H
^
with a state is positive or negative. This is equivalent to determining whether some Such a classifier can be useful when finding minimum energy states of system governed by a particular Hamiltonian,
in [0055]:
At operation 3.1, a sample loss is estimated. To estimate the sample loss, repeated measurements of the one or more readout qubits 110 in the output state 112 are made, and the sample loss is calculated from results of the measurements. Copies of the initial state 106 are repeatedly prepared and acted on by the quantum gates 104 to produce copies of the output state 112, and the readout qubits 110 for each copy of the output state 112 are measured. To achieve an estimate of the sample loss to within
δ
of the true sample loss at 99% probability, at least 2/
δ
.sub.2 measurements of the readout state are made.
- program instructions to compare the first sensitivity metric against a pre-established sensitivity criterion
(in [0050] The predicted classifier 114 can be compared to the known classifier using a metric. For example, a sample loss function (or loss function) can be used to compare the predicted classifier 114 to the known classifier. The sample loss function provides a “cost” for mismatching known and predicted classifications. The sample loss function, can, for example, be a function that has a minimum value when the predicted classifiers 114 match the known classifiers. In these examples, the aim of the training method can be to reduce the average sample loss over the training set to below a threshold value.
(BRI: threshold is the sensitivity criterion using the sample loss comparisons for predicted and known classifier)
- and upon a determination that the first sensitivity metric does not meet the sensitivity criterion, update a parameter of the neural network, and re-train, using the classical processor, the neural network comprising the updated parameter.
in [0061]:
With reference again to FIG. 2, if the threshold condition is not met, once one or more parameters have been updated the method returns to operation 2.2 and selects another training example (i.e. another sample state 108 with a known classification) and performs operations 2.3 to 2.8 with the updated quantum gate 104 parameters,
Farhi does not explicitly disclose:
- generate quantum noise in the quantum processor at least by swapping qubits in the quantum processor, the swapping qubits in the quantum processor causing the quantum noise to be unbiased with respect to the data set used to generate the first set of classified data:
- program instructions to reclassify, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
However, Silva discloses:
- generate quantum noise in the quantum processor at least by swapping qubits in the quantum processor, the swapping qubits in the quantum processor causing the quantum noise to be unbiased with respect to the data set used to generate the first set of classified data:
in [ 1, Page 2]:
Characterization of discrete non-Gaussian phase noise has, likewise, been implemented in trapped ions [25], whereas general QNS protocols for reconstructing high-order spectra of non-Gaussian classical and quantum dephasing environments have been proposed in [14]
in [ Abstract, Page 1]:
We introduce multi-pulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources.
in [ 1, Page 2]:
noise may exhibit non-trivial spatial correlations, which may only become manifest in the coherence dynamics of multiple qubit probes at different locations. Let S`,`0 (ω) ≡ S + `,`0 (ω)+S − `,`0 (ω) denote the spectrum of the noise affecting a pair of qubits `, `0 , where the “classical” (+) and the “quantum” (−) components
in [ II C, Page 5]:
Statistical features of the noise are compactly described by the cumulants of the bath operators [36, 51, 52]. For the zero-mean Gaussian noise we consider1 , the only non-vanishing cumulants are the second-order cumulants
(BRI: a zero-mean Gaussian noise process is widely used in both classical and quantum contexts as a model for unbiased noise)
In [III B, Page 8]:
The dynamics of multiple qubits coupled to a quantum bath are considerably more rich than those of a single qubit. Notably, interaction with a quantum bath can generate quantum correlations and entangle the qubits, even in the absence of direct coupling between them,
In [III A, Page 8]:
While the steady state populations are always equal for a classical, spectrally symmetric bath, this is generally not true when the bath is quantum, as dictated by the requirement of detailed balance at equilibrium [51].
in [II B, Page 4]:
Beside interacting with the bath, the N qubits are subject to external control generated by a Hamiltonian
H
c
t
r
l
(
t
)
. We restrict ourselves to control that preserves the dephasing character of the noise in the interaction picture associated with
H
c
t
r
l
(
t
)
(aka the “toggling frame”).
in [II B, Page 5]:
The second form of dephasing-preserving control we consider are instantaneous swap gates between any pair of qubits. The gate SWAP`,`0 acts non-locally on qubits ` and ` 0 , effecting the transformation SWAP† `,`0 Z` SWAP`,`0 = Z` 0 . A sequence consisting of both instantaneous π-pulses and swap gates has a control propagator of the form
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, and Silva.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise by swapping qubits using microwave pulses as a source.
One of ordinary skill would have motivation to combine Farhi , and Silva that can provide
analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control [Abstract, Page 1].
Farhi and Silva does not explicitly disclose:
- reclassifying, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
However, Alam discloses:
- reclassifying, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
In [II B, Page 2]: Classifier Basics
Binary classification is the task of classifying any input data into one of two possible groups. In supervised machine learning, this classification problem is solved by training a mathematical model (f(x, θ)) with a properly labeled input data-set {(
x
1
,
y
1
)
, (
x
2
,
y
2
)
,
.... ,
(
x
M
,
y
M
)
} where
x
i
is the feature vector (can be multi-dimensional) of the i th input data and
y
i
is the associated label. The mathematical model predicts the class of any input data based on its features (x) and the parameters (θ) of the model. The parameters (θ) are updated iteratively until the model predictions are satisfactory over the input data-set. In [6], a binary classification on quantum computers is proposed for classical data where a P QC serves as the mathematical model. A state-preparation routine is required to encode the classical data and feed it to the P QC. The output is captured from a target qubit. During the training phase of the P QC, the parameters are updated iteratively based on the given input data-set so that the probability of getting 1 through a measurement of the target qubit for one class is maximized (and 0 for the other class)
In [II E, Page 3]:
PNG
media_image2.png
546
607
media_image2.png
Greyscale
In [III, Page 3]:
Training of a model circuit (P QC, Figure 4(b)) for binary classification can follow three
disparate strategies as described below.
PNG
media_image3.png
127
595
media_image3.png
Greyscale
(b) Structure of a multi-layer circuit centric Quantum Classifier (4-Qubits)
In [III A, Page 4]: Existing Approaches
Two classes of P QC training proposals exist in the literature: i) Train the P QC in a hardware-in-the-loop fashion. Hereafter, we term this approach as app01. In this approach, the P QC is executed on a real quantum computer. For a certain input, the output is measured and then the measured output is post-processed in a classical computer. Statistical techniques such as, Kullback-Leibler (KL) divergence method is used to calculate the disparity between the target distribution and the measured distribution (hence the cost) to update the parameters with any classical optimization techniques such as stochastic gradient descent or particle swarm optimization etc. [11]–[13]. Then, the P QC is executed again with updated parameters and process iterates until measured output matches target output up to a certain threshold. While it may seem to be an ideal approach, the technique is plagued with certain impediments.
In [III A, Page 4]: Existing Approaches
we can define the following cost-function to iteratively update the parameters of the P QC (Figure 5(b)) to solve the binary classification problem (described for the hybrid approach) [6]:
PNG
media_image4.png
67
565
media_image4.png
Greyscale
where m is the batch-size,
y
i
is the label of the i th data in the batch (data are labeled as -1 and +1 for class A and class B respectively),
x
i
is the i th input, and ‘expectation(PQC(xi,θ):QT )’ is the expectation value of the target qubit (
Q
T
) for the i th input and current values of the θ. The target is to minimize the cost. Gradient descent technique is applied to achieve the optimization goal where the partial derivatives of the cost function (Equation 1) with respect to the circuit parameters are calculated using numerical differentiation [20].
In [III A, Page 4]: Existing Approaches
the simulation models an ideal (i.e., without noise) quantum computer whereas quantum computers are noisy (and noise behavior shows temporal variation).
In [III A, Page 4]: Existing Approaches
the parameter optimization without considering noise may not give optimal result during inferencing phase in the real noisy quantum computer
In [III B, Page 4]: Proposed Approach: Classical Training with Noise Effects
To deal with the noisy hardware related dependency of the trained P QC, we propose to update the parameters where the expectation values are calculated with modeled noise behavior of a target hardware with our noisy quantum hardware simulation framework
In [III B, Page 4]:
To address the stochastic behavior of the noise sources as evident from Figure 2, we use the average value of the qubit quality metrics collected over a significant amount of time (43 days) to optimize the P QC parameters.
In [IV B, Page 5]:
2) Evaluation Method: Although parameterized quantum circuits can minimize the effects of noise, it cannot suppress it altogether. Therefore, the expectation values cannot be optimized to exactly -1/+1 values for all the inputs during the P QC training period which indicates that a measurement is not guaranteed to result in the desired class output (0/1) for a certain input.
In [IV B, Page 5]:
The ratio between the correct and incorrect outputs is also a representation of the fidelity of the circuit.
(BRI: Fidelity is the sensitivity)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva and Alam.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
One of ordinary skill would have motivation to combine Farhi , Silva and Alam that can provide a training methodology in a classical environments to improve the fidelity of the trained quantum circuit ([Abstract, Page 1])
In regard to Claim 17 ( Previously Presented)
Farhi discloses:
- A computer system comprising a quantum processor, a computer- readable memory, and a computer-readable storage medium, and program instructions stored on the storage medium for execution by the classical processor and the quantum processor via the memory, the stored program instructions comprising:
in [0017, [0171], [0176], [0177]:
- program instructions to train, using a classical processor, a neural network for solving a classification problem;
Program instructions
In [0118]:
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state.
- program instructions to prepare, using a quantum processor, a quantum state based on the neural network and the classification problem;
in [0034]:
The system 100 uses supervised learning to learn parameters of the quantum gates 104 that can obtain a predicted classification l′(z) 114 of an input state 106. Sample states 108 with known classifications l(z) (also referred to herein as label functions) are selected from a sample data set S for use in the supervised learning and an input state 106 comprising the sample state 108 and one or more readout qubits 110 is prepared,
in [0093]:
at least one of the two qubits operated on by the two-qubit quantum gate is a readout qubit 110. Layers of quantum gates 104 of the same type may be alternated in the quantum computer. For example, the sequence of quantum gates may comprise alternating three layers ZX quantum gates with three layers of XX quantum gates. Each layer may comprise a plurality of quantum gates. Each layer may comprise two-qubit quantum gates operating between one or more of the readout qubits 110 and each of the other qubits in the plurality of qubits 102. For example, in a binary classifier, each layer may comprise n two-qubit quantum gates, each of which acts between the readout qubit 110 and a different one of the n qubits representing the state to be classified,
in [0113]:
In some embodiments, a state to be classified 108 is input into a classical artificial neural network 116. The output of the classical artificial neural network 116 can be used an input to the quantum computing system 100 in order to generate the input state 106 to be classified according the methods described above. An example of such an embodiment is shown in FIG. 5a,
in [0114]:
In some embodiments, the readout state from readout qubits 110 in the quantum computing system 100 is input into a classical artificial neural network 116. The classical artificial neural network can be trained to determine, using the readout state of the output state of the one or more readout qubits in the plurality of qubits, a predicted classification of the input state. An example of such an embodiment is shown in FIG. 5 b.
(BRI: Fig 5a and Fig 5B represents a hybrid classification network)
in [0047 ]:
the method comprises repeatedly preparing the plurality of qubits in the input state 106, applying the parameterized quantum gates 104 to the input state 106 and measuring the readout state of the one or more readout qubits.
in [0051]:
There are many examples of sample loss functions that can be used to compare the known classification with the predicted classification 114. As an example, for a binary classifier l(
Ψ
) that classifies an input state as either +1 or -1, and with a single readout qubit initially set to 1 in the computational basis,
(in [0106] with a quantum neural network, input states may comprise classical data in a superposition. A single quantum state that is a superposition of computational basis states, each of which represents a single sample from a batch of samples, can be viewed as quantum encoding of the batch.
- program instructions to classify, using a quantum classifier based on the neural network, a data set to generate a first set of classified data, wherein the classifying comprises classifying a data item of the data set resulting in a first classification result of the data item
in [0038]:
FIG. 2 shows a flow diagram of a method for training a classifier implemented on a quantum computer,
in [0035] :
By analogy with classical artificial neural networks, the trained quantum classifier can be described as a “quantum neural network”,
in [0005]:
a method for training a classifier implemented on a quantum computer, the method comprising: preparing a plurality of qubits in an input state with a known classification, said plurality of qubits comprising one or more readout qubits; applying one or more parameterised quantum gates to the plurality of qubits to transform the input state to an output state; determining, using a readout state of the one or more readout qubits in the output state, a predicted classification of the input state; comparing the predicted classification with the known classification; and updating one or more parameters of the parameterised quantum gates in dependence on the comparison of the predicted classification with the known classification.
in [0036]:
Systems and methods described herein can accept both classical quantum states as an input and classify them accordingly, in contrast with classical artificial neural networks, which can only take classical states as an input.
in [0037]:
quantum computers with good enough fidelity to run circuits with enough depth to perform tasks that cannot be simulated on classical computers are expected to be available. One approach to designing quantum algorithms to run on such devices is to let the architecture of the hardware determine which gate sets to use.
- program instructions to [ Note: for unbiased noise induction]
in [0141]:
several example embodiments for programming and/or operating a quantum computing device,
in [0003] :
a form of robust principal component analysis is disclosed that can tolerate noise intentionally introduced to a quantum training set.
- program instructions to determine, responsive to comparing the first classification result of the data item and the second classification result of the data item, a first sensitivity metric of the quantum processor
in [0054]:
In some embodiments, a gradient descent method is used
to compare the predicted classifier of the input state 106 with the known classifier of the
sample state 108 and update the parameters. FIG. 3 shows a flowchart of an example of a
method for updating the parameters using gradient descent,
in [0064]:
At operation 4.1 an unclassified input state is received. The unclassified input state comprises a plurality of qubits 102. The plurality of qubits 102 comprises n qubits representing a quantum state to be classified 108, and one or more readout qubits 110 in a known state. The quantum state is, in some embodiments, received from a routine running on a quantum or classical computer, and/or experimental equipment. Many other examples are possible. In some embodiments, the method encompasses preparing the input state 106 from a received quantum state to be classified 108.
a first sensitivity metric of the quantum processor
in [0098]:
The binary classifier used in the example described below corresponds to whether an expected value of a Hamiltonian
H
^
with a state is positive or negative. This is equivalent to determining whether some Such a classifier can be useful when finding minimum energy states of system governed by a particular Hamiltonian,
in [0055]:
At operation 3.1, a sample loss is estimated. To estimate the sample loss, repeated measurements of the one or more readout qubits 110 in the output state 112 are made, and the sample loss is calculated from results of the measurements. Copies of the initial state 106 are repeatedly prepared and acted on by the quantum gates 104 to produce copies of the output state 112, and the readout qubits 110 for each copy of the output state 112 are measured. To achieve an estimate of the sample loss to within
δ
of the true sample loss at 99% probability, at least 2/
δ
.sub.2 measurements of the readout state are made.
(BRI: the estimate of the sample loss to be within the true sample loss relates to sensitivity and the first sensitivity is within the context of plurality of classification)
- program instructions to compare the first sensitivity metric against a pre-established sensitivity criterion
in [0050]:
The predicted classifier 114 can be compared to the known classifier using a metric. For example, a sample loss function (or loss function) can be used to compare the predicted classifier 114 to the known classifier. The sample loss function provides a “cost” for mismatching known and predicted classifications. The sample loss function, can, for example, be a function that has a minimum value when the predicted classifiers 114 match the known classifiers. In these examples, the aim of the training method can be to reduce the average sample loss over the training set to below a threshold value.
(BRI: threshold is the sensitivity criterion using the sample loss comparisons for predicted and known classifier)
- and upon a determination that the first sensitivity metric does not meet the sensitivity criterion, update a parameter of the neural network, and re-train, using the classical processor, the neural network comprising the updated parameter.
in [0061]:
With reference again to FIG. 2, if the threshold condition is not met, once one or more parameters have been updated the method returns to operation 2.2 and selects another training example (i.e. another sample state 108 with a known classification) and performs operations 2.3 to 2.8 with the updated quantum gate 104 parameters.
Farhi discloses:
- program instructions to
In [0118]:
- generate quantum noise in the quantum processor at least by swapping qubits in the quantum processor, the swapping qubits in the quantum processor causing the quantum noise to be unbiased with respect to the data set used to generate the first set of classified data:
However, Silva discloses:
- generate quantum noise in the quantum processor at least by swapping qubits in the quantum processor, the swapping qubits in the quantum processor causing the quantum noise to be unbiased with respect to the data set used to generate the first set of classified data:
in [ 1, Page 2]:
Characterization of discrete non-Gaussian phase noise has, likewise, been implemented in trapped ions [25], whereas general QNS protocols for reconstructing high-order spectra of non-Gaussian classical and quantum dephasing environments have been proposed in
in [ Abstract, Page 1]:
We introduce multi-pulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources.
in [ 1, Page 2]:
noise may exhibit non-trivial spatial correlations, which may only become manifest in the coherence dynamics of multiple qubit probes at different locations. Let S`,`0 (ω) ≡ S + `,`0 (ω)+S − `,`0 (ω) denote the spectrum of the noise affecting a pair of qubits `, `0 , where the “classical” (+) and the “quantum” (−) components
in [ II C, Page 5]:
Statistical features of the noise are compactly described by the cumulants of the bath operators [36, 51, 52]. For the zero-mean Gaussian noise we consider1 , the only non-vanishing cumulants are the second-order cumulants
(BRI: a zero-mean Gaussian noise process is widely used in both classical and quantum contexts as a model for unbiased noise)
In [III B, Page 8]:
The dynamics of multiple qubits coupled to a quantum bath are considerably more rich than those of a single qubit. Notably, interaction with a quantum bath can generate quantum correlations and entangle the qubits, even in the absence of direct coupling between them,
In [III A, Page 8]:
While the steady state populations are always equal for a classical, spectrally symmetric bath, this is generally not true when the bath is quantum, as dictated by the requirement of detailed balance at equilibrium [51].
in [II B, Page 4]:
Beside interacting with the bath, the N qubits are subject to external control generated by a Hamiltonian
H
c
t
r
l
(
t
)
. We restrict ourselves to control that preserves the dephasing character of the noise in the interaction picture associated with
H
c
t
r
l
(
t
)
(aka the “toggling frame”).
in [II B, Page 5]:
The second form of dephasing-preserving control we consider are instantaneous swap gates between any pair of qubits. The gate SWAP`,`0 acts non-locally on qubits ` and ` 0 , effecting the transformation SWAP† `,`0 Z` SWAP`,`0 = Z` 0 . A sequence consisting of both instantaneous π-pulses and swap gates has a control propagator of the form
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, and Silva.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise by swapping qubits using microwave pulses as a source.
One of ordinary skill would have motivation to combine Farhi , and Silva that can provide
analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control [Abstract, Page 1].
Farhi and Silva do not explicitly disclose:
- reclassify, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
However, Alam discloses:
- reclassify, using the quantum classifier, the data set with the generated noise to generate a second set of classified data, wherein the reclassifying comprises reclassifying the data item with the generated noise resulting in a second classification result of the data item;
In [II B, Page 2]: Classifier Basics
Binary classification is the task of classifying any input data into one of two possible groups. In supervised machine learning, this classification problem is solved by training a mathematical model (f(x, θ)) with a properly labeled input data-set {(
x
1
,
y
1
)
, (
x
2
,
y
2
)
,
.... ,
(
x
M
,
y
M
)
} where
x
i
is the feature vector (can be multi-dimensional) of the i th input data and
y
i
is the associated label. The mathematical model predicts the class of any input data based on its features (x) and the parameters (θ) of the model. The parameters (θ) are updated iteratively until the model predictions are satisfactory over the input data-set. In [6], a binary classification on quantum computers is proposed for classical data where a P QC serves as the mathematical model. A state-preparation routine is required to encode the classical data and feed it to the P QC. The output is captured from a target qubit. During the training phase of the P QC, the parameters are updated iteratively based on the given input data-set so that the probability of getting 1 through a measurement of the target qubit for one class is maximized (and 0 for the other class)
In [II E, Page 3]:
PNG
media_image2.png
546
607
media_image2.png
Greyscale
In [III, Page 3]:
Training of a model circuit (P QC, Figure 4(b)) for binary classification can follow three
disparate strategies as described below.
PNG
media_image3.png
127
595
media_image3.png
Greyscale
(b) Structure of a multi-layer circuit centric Quantum Classifier (4-Qubits)
In [III A, Page 4]: Existing Approaches
Two classes of P QC training proposals exist in the literature: i) Train the P QC in a hardware-in-the-loop fashion. Hereafter, we term this approach as app01. In this approach, the P QC is executed on a real quantum computer. For a certain input, the output is measured and then the measured output is post-processed in a classical computer. Statistical techniques such as, Kullback-Leibler (KL) divergence method is used to calculate the disparity between the target distribution and the measured distribution (hence the cost) to update the parameters with any classical optimization techniques such as stochastic gradient descent or particle swarm optimization etc. [11]–[13]. Then, the P QC is executed again with updated parameters and process iterates until measured output matches target output up to a certain threshold. While it may seem to be an ideal approach, the technique is plagued with certain impediments.
In [III A, Page 4]: Existing Approaches
we can define the following cost-function to iteratively update the parameters of the P QC (Figure 5(b)) to solve the binary classification problem (described for the hybrid approach) [6]:
PNG
media_image4.png
67
565
media_image4.png
Greyscale
where m is the batch-size,
y
i
is the label of the i th data in the batch (data are labeled as -1 and +1 for class A and class B respectively),
x
i
is the i th input, and ‘expectation(PQC(xi,θ):QT )’ is the expectation value of the target qubit (
Q
T
) for the i th input and current values of the θ. The target is to minimize the cost. Gradient descent technique is applied to achieve the optimization goal where the partial derivatives of the cost function (Equation 1) with respect to the circuit parameters are calculated using numerical differentiation [20].
In [III A, Page 4]: Existing Approaches
the simulation models an ideal (i.e., without noise) quantum computer whereas quantum computers are noisy (and noise behavior shows temporal variation).
In [III A, Page 4]: Existing Approaches
the parameter optimization without considering noise may not give optimal result during inferencing phase in the real noisy quantum computer
In [III B, Page 4]: Proposed Approach: Classical Training with Noise Effects
To deal with the noisy hardware related dependency of the trained P QC, we propose to update the parameters where the expectation values are calculated with modeled noise behavior of a target hardware with our noisy quantum hardware simulation framework
In [III B, Page 4]:
To address the stochastic behavior of the noise sources as evident from Figure 2, we use the average value of the qubit quality metrics collected over a significant amount of time (43 days) to optimize the P QC parameters.
In [IV B, Page 5]:
2) Evaluation Method: Although parameterized quantum circuits can minimize the effects of noise, it cannot suppress it altogether. Therefore, the expectation values cannot be optimized to exactly -1/+1 values for all the inputs during the P QC training period which indicates that a measurement is not guaranteed to result in the desired class output (0/1) for a certain input.
In [IV B, Page 5]:
The ratio between the correct and incorrect outputs is also a representation of the fidelity of the circuit.
(BRI: Fidelity is the sensitivity)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva and Alam.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
One of ordinary skill would have motivation to combine Farhi , Silva and Alam that can provide a training methodology in a classical environments to improve the fidelity of the trained quantum circuit ([Abstract, Page 1])
In regard to Claim 23 :( Previously Presented)
Farhi do not explicitly disclose:
- tune the noise generated by the quantum processor.
However, Silva discloses:
- tune the noise generated by the quantum processor.
In [1A, Page 2]:
Central to QNS protocols is the idea that, by suitably tailoring the external control, and hence the FFs describing the ensuing modulation in the frequency domain, one may engineer a frequency comb which makes it possible to “deconvolve” the effect of the noise and sample a desired spectrum at a set of control-dependent harmonic frequencies
In [1A, Page 2]:
the search for QNS protocols able to characterize arbitrary, quantum and classical, noise sources simultaneously influencing multiple qubits
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, and Silva.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise by swapping qubits using microwave pulses as a source.
One of ordinary skill would have motivation to combine Farhi , and Silva that can provide
analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control [Abstract, Page 1].
In regard to Claim 26 :( Previously Presented)
Farhi discloses:
- program instructions
In [0018]:
Farhi do not explicitly disclose:
- tune the noise generated by the quantum processor.
However, Silva discloses:
- tune the noise generated by the quantum processor.
In [1A, Page 2]:
Central to QNS protocols is the idea that, by suitably tailoring the external control, and hence the FFs describing the ensuing modulation in the frequency domain, one may engineer a frequency comb which makes it possible to “deconvolve” the effect of the noise and sample a desired spectrum at a set of control-dependent harmonic frequencies
In [1A, Page 2]:
the search for QNS protocols able to characterize arbitrary, quantum and classical, noise sources simultaneously influencing multiple qubits
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, and Silva.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise by swapping qubits using microwave pulses as a source.
One of ordinary skill would have motivation to combine Farhi , and Silva that can provide
analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control [Abstract, Page 1].
In regard to Claim 29 :( Previously Presented)
Farhi discloses:
- program instructions
In [0018]:
Farhi do not explicitly disclose:
- tune the noise generated by the quantum processor.
However, Silva discloses:
- tune the noise generated by the quantum processor.
In [1A, Page 2]:
Central to QNS protocols is the idea that, by suitably tailoring the external control, and hence the FFs describing the ensuing modulation in the frequency domain, one may engineer a frequency comb which makes it possible to “deconvolve” the effect of the noise and sample a desired spectrum at a set of control-dependent harmonic frequencies
In [1A, Page 2]:
the search for QNS protocols able to characterize arbitrary, quantum and classical, noise sources simultaneously influencing multiple qubits
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, and Silva.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise by swapping qubits using microwave pulses as a source.
One of ordinary skill would have motivation to combine Farhi , and Silva that can provide
analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control [Abstract, Page 1].
Claims 9-10 are rejected under 35 U.S.C. 103 as being unpatentable over
in view of Farhi (hereinafter Farhi) US 2020/0342345 A1,
in view of Gerado A. Paz-Silva (hereinafter Silva) Multiqubit Spectroscopy of Gaussian Quantum Nose, arXiv:1609.01792v2 [quant-ph] 21 Sep 2016,
in view of Mahabubul Alam (hereinafter Alam) Addressing Temporal Variations in Qubit Quality Metrics for Parameterized Quantum Circuits, arXiv:1903.08684v1 [cs.ET] 20 Mar 2019 [Also available in IEEE Xplore].
further in view of Wiebe (hereinafter Wiebe) 2018/0349605 A1.
In regard to Claim 9 (Previously Presented)
Farhi, Silva and Alam do not explicitly disclose:
- the program instructions are stored in a computer readable storage medium in a data processing system, and wherein the computer usable code is transferred over a network from a remote data processing system.
However, Wiebe discloses:
- the program instructions are stored in a computer readable storage medium in a data processing system, and wherein the computer usable code is transferred over a network from a remote data processing system.
in [0141]:
several example embodiments for programming and/or operating a quantum computing device,
in [0156]:
At 1310, a quantum computing device is programmed to implement quantum circuits that perform a machine learning technique,
in [0178]:
the computing device 1020 is configured to communicate with a computing device 1030 (e.g., a remote server, such as a server in a cloud computing environment) via a network 1012.
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Wiebe.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding an unbiased noise using swapping qubits of the quantum component .
Alam teaches reclassifying the data item with the generated noise.
Wiebe teaches usable code transfer.
One of ordinary skill would have motivation to combine Farhi , Silva, Alam and Wiebe to provide the ability of the classification by adding noise and improve the quality of the classifier (Wiebe [0095]).
In regard to Claim 10 (Previously Presented)
Farhi, Silva and Alam do not explicitly disclose:
- the computer usable code is downloaded over a network to a remote data processing system for use in a computer readable storage medium associated with the remote data processing system.
However, Wiebe discloses:
- the computer usable code is downloaded over a network to a remote data processing system for use in a computer readable storage medium associated with the remote data processing system.
in [0178]:
the computing device 1020 is configured to communicate with a computing device 1030 (e.g., a remote server, such as a server in a cloud computing environment) via a network 1012,
in [0184]:
the remote computer 1200 can store the high-level description and/or machine learning instructions in the memory or storage devices 1262 and transmit the high-level description and/or instructions to the computing environment 1200 for compilation and use with the quantum pro-cessor(s).
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Wiebe.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding unbiased noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Wiebe teaches downloading a usable code.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Wiebe to provide the ability of the classification by adding noise and improve the quality of the classifier (Wiebe [0095]).
Claims 21-22, and 24-28 are rejected under 35 U.S.C. 103 as being unpatentable over
in view of Farhi (hereinafter Farhi) US 2020/0342345 A1,
in view of Gerado A. Paz-Silva (hereinafter Silva) Multiqubit Spectroscopy of Gaussian Quantum Nose, arXiv:1609.01792v2 [quant-ph] 21 Sep 2016,
in view of Mahabubul Alam (hereinafter Alam) Addressing Temporal Variations in Qubit Quality Metrics for Parameterized Quantum Circuits, arXiv:1903.08684v1 [cs.ET] 20 Mar 2019 [Also available in IEEE Xplore].
further in view of Zeng (hereinafter Zeng) US 10325218 B1.
In regard to Claim 21 ( Previously Presented)
Farhi discloses:
- determining, responsive to comparing the second classification result of the data item and the third classification result of the data item
in [0054]:
In some embodiments, a gradient descent method is used
to compare the predicted classifier of the input state 106 with the known classifier of the
sample state 108 and update the parameters. FIG. 3 shows a flowchart of an example of a
method for updating the parameters using gradient descent,
in [0064]:
At operation 4.1 an unclassified input state is received. The unclassified input state comprises a plurality of qubits 102. The plurality of qubits 102 comprises n qubits representing a quantum state to be classified 108, and one or more readout qubits 110 in a known state. The quantum state is, in some embodiments, received from a routine running on a quantum or classical computer, and/or experimental equipment. Many other examples are possible. In some embodiments, the method encompasses preparing the input state 106 from a received quantum state to be classified 108.
(BRI: the third classification in context with plurality of qubits for quantum state classification-
- a second sensitivity metric of the quantum processor
in [0098]:
The binary classifier used in the example described below corresponds to whether an expected value of a Hamiltonian
H
^
with a state is positive or negative. This is equivalent to determining whether some Such a classifier can be useful when finding minimum energy states of system governed by a particular Hamiltonian,
in [0055]:
At operation 3.1, a sample loss is estimated. To estimate the sample loss, repeated measurements of the one or more readout qubits 110 in the output state 112 are made, and the sample loss is calculated from results of the measurements. Copies of the initial state 106 are repeatedly prepared and acted on by the quantum gates 104 to produce copies of the output state 112, and the readout qubits 110 for each copy of the output state 112 are measured. To achieve an estimate of the sample loss to within
δ
of the true sample loss at 99% probability, at least 2/
δ
.sub.2 measurements of the readout state are made.
(BRI: the estimate of the sample loss to be within the true sample loss relates to sensitivity and the second sensitivity is within the context of plurality of classification)
- and comparing the second sensitivity metric against the pre-established sensitivity criterion,
in [0050]:
The predicted classifier 114 can be compared to the known classifier using a metric. For example, a sample loss function (or loss function) can be used to compare the predicted classifier 114 to the known classifier. The sample loss function provides a “cost” for mismatching known and predicted classifications. The sample loss function, can, for example, be a function that has a minimum value when the predicted classifiers 114 match the known classifiers. In these examples, the aim of the training method can be to reduce the average sample loss over the training set to below a threshold value.
(BRI: threshold is the sensitivity criterion using the sample loss comparisons for predicted and known classifier)
- upon a determination that the second sensitivity metric does not meet the sensitivity criterion, updating the parameter of the neural network, and re-training, using the classical processor, the neural network comprising the updated parameter.
in [0061]:
with reference again to FIG. 2, if the threshold condition is not met, once one or more parameters have been updated the method returns to operation 2.2 and selects another training example (i.e. another sample state 108 with a known classification) and performs operations 2.3 to 2.8 with the updated quantum gate 104 parameters.
Farhi and Silva do not explicitly disclose:
- reclassifying, using the quantum classifier, the data set with the additional generated noise to generate a third set of classified data, wherein the reclassifying comprises reclassifying the data item with the additional generated noise resulting in a third classification result of the data item;
However, Alam discloses:
- reclassifying, using the quantum classifier, the data set with the additional generated noise to generate a third set of classified data, wherein the reclassifying comprises reclassifying the data item with the additional generated noise resulting in a third classification result of the data item;
In [II B, Page 2]: Classifier Basics
Binary classification is the task of classifying any input data into one of two possible groups. In supervised machine learning, this classification problem is solved by training a mathematical model (f(x, θ)) with a properly labeled input data-set {(x1,y1), (x2,y2), .... , (xM,yM)} where xi is the feature vector (can be multi-dimensional) of the i 0 th input data and yi is the associated label. The mathematical model predicts the class of any input data based on its features (x) and the parameters (θ) of the model. The parameters (θ) are updated iteratively until the model predictions are satisfactory over the input data-set. In [6], a binary classification on quantum computers is proposed for classical data where a P QC serves as the mathematical model. A state-preparation routine is required to encode the classical data and feed it to the P QC. The output is captured from a target qubit. During the training phase of the P QC, the parameters are updated iteratively based on the given input data-set so that the probability of getting 1 through a measurement of the target qubit for one class is maximized (and 0 for the other class)
In [II E, Page 3]:
PNG
media_image2.png
546
607
media_image2.png
Greyscale
In [III, Page 3]:
Training of a model circuit (P QC, Figure 4(b)) for binary classification can follow three
disparate strategies as described below.
PNG
media_image3.png
127
595
media_image3.png
Greyscale
(b) Structure of a multi-layer circuit centric Quantum Classifier (4-Qubits)
In [III A, Page 4]: Existing Approaches
Two classes of P QC training proposals exist in the literature: i) Train the P QC in a hardware-in-the-loop fashion. Hereafter, we term this approach as app01. In this approach, the P QC is executed on a real quantum computer. For a certain input, the output is measured and then the measured output is post-processed in a classical computer. Statistical techniques such as, Kullback-Leibler (KL) divergence method is used to calculate the disparity between the target distribution and the measured distribution (hence the cost) to update the parameters with any classical optimization techniques such as stochastic gradient descent or particle swarm optimization etc. [11]–[13]. Then, the P QC is executed again with updated parameters and process iterates until measured output matches target output up to a certain threshold. While it may seem to be an ideal approach, the technique is plagued with certain impediments.
In [III A, Page 4]: Existing Approaches
we can define the following cost-function to iteratively update the parameters of the P QC (Figure 5(b)) to solve the binary classification problem (described for the hybrid approach) [6]:
PNG
media_image4.png
67
565
media_image4.png
Greyscale
where m is the batch-size,
y
i
is the label of the i th data in the batch (data are labeled as -1 and +1 for class A and class B respectively),
x
i
is the i th input, and ‘expectation(PQC(xi,θ):QT )’ is the expectation value of the target qubit (
Q
T
) for the i th input and current values of the θ. The target is to minimize the cost. Gradient descent technique is applied to achieve the optimization goal where the partial derivatives of the cost function (Equation 1) with respect to the circuit parameters are calculated using numerical differentiation [20].
In [III A, Page 4]: Existing Approaches
the simulation models an ideal (i.e., without noise) quantum computer whereas quantum computers are noisy (and noise behavior shows temporal variation).
In [III A, Page 4]: Existing Approaches
the parameter optimization without considering noise may not give optimal result during inferencing phase in the real noisy quantum computer
In [III B, Page 4]: Proposed Approach: Classical Training with Noise Effects
To deal with the noisy hardware related dependency of the trained P QC, we propose to update the parameters where the expectation values are calculated with modeled noise behavior of a target hardware with our noisy quantum hardware simulation framework
In [III B, Page 4]:
To address the stochastic behavior of the noise sources as evident from Figure 2, we use the average value of the qubit quality metrics collected over a significant amount of time (43 days) to optimize the P QC parameters.
In [IV B, Page 5]:
2) Evaluation Method: Although parameterized quantum circuits can minimize the effects of noise, it cannot suppress it altogether. Therefore, the expectation values cannot be optimized to exactly -1/+1 values for all the inputs during the P QC training period which indicates that a measurement is not guaranteed to result in the desired class output (0/1) for a certain input.
In [IV B, Page 5]:
The ratio between the correct and incorrect outputs is also a representation of the fidelity of the circuit.
(BRI: Fidelity is the sensitivity)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva and Alam.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
One of ordinary skill would have motivation to combine Farhi , Silva and Alam that can provide a training methodology in a classical environments to improve the fidelity of the trained quantum circuit ([Abstract, Page 1])
In regard to Claim 22 (Previously Presented)
Farhi, Silva and Alam do not explicitly disclose:
- program instructions to alter an amplitude of a microwave pulse in the quantum processor and lengthening pulses in the quantum processor.
However, Zeng discloses:
- program instructions to alter an amplitude of a microwave pulse in the quantum processor and lengthening pulses in the quantum processor.
In [Col 2, lines 32-44]:
In [Col 2, lines 7-15]:
In some instances, a quantum logic circuit can be optimized (or otherwise improved) for execution on small and noisy quantum processor chips. For instance, a classical simulator may emulate the noise profile of the quantum processor chip hardware during the construction of the quantum logic circuit, and, if the quantum logic circuits are run on the quantum processor chip hardware, their performance can account for the actual noise profile of the quantum processor chip hardware.
in [Col 8, lines 17-20]:
The optimization algorithm can be executed by an optimization engine or machine learning engine that is programmed to optimize (e.g., minimize) the objective function,
in [Col 6, lines 22-24]:
The process 150 can construct the quantum process by analyzing and modifying variable parameters of the quantum process,
in [Col 6, lines 30-35]:
The variable parameters of the quantum process can include classical control parameters for the quantum processor, such as, for example, the duration, frequency, shape, or amplitude of a microwave pulse, a laser pulse, a tuning pulse
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding unbiased noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches microwave pulse.
One of ordinary skill would have motivation to combine Farhi, Silva, and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
In regard to Claim 24 ( Previously Presented)
Farhi discloses:
- a program instructions to determine, responsive to comparing the second classification result of the data item and the third classification result of the data item, a second sensitivity metric of the quantum processor;
program instructions
In [0118]:
(Note: teaches program instructions)
in [0054]:
In some embodiments, a gradient descent method is used
to compare the predicted classifier of the input state 106 with the known classifier of the
sample state 108 and update the parameters. FIG. 3 shows a flowchart of an example of a
method for updating the parameters using gradient descent,
in [0064]:
At operation 4.1 an unclassified input state is received. The unclassified input state comprises a plurality of qubits 102. The plurality of qubits 102 comprises n qubits representing a quantum state to be classified 108, and one or more readout qubits 110 in a known state. The quantum state is, in some embodiments, received from a routine running on a quantum or classical computer, and/or experimental equipment. Many other examples are possible. In some embodiments, the method encompasses preparing the input state 106 from a received quantum state to be classified 108.
- a second sensitivity metric of the quantum processor
in [0098]:
The binary classifier used in the example described below corresponds to whether an expected value of a Hamiltonian
H
^
with a state is positive or negative. This is equivalent to determining whether some Such a classifier can be useful when finding minimum energy states of system governed by a particular Hamiltonian,
in [0055]:
At operation 3.1, a sample loss is estimated. To estimate the sample loss, repeated measurements of the one or more readout qubits 110 in the output state 112 are made, and the sample loss is calculated from results of the measurements. Copies of the initial state 106 are repeatedly prepared and acted on by the quantum gates 104 to produce copies of the output state 112, and the readout qubits 110 for each copy of the output state 112 are measured. To achieve an estimate of the sample loss to within
δ
of the true sample loss at 99% probability, at least 2/
δ
.sub.2 measurements of the readout state are made.
(BRI: the estimate of the sample loss to be within the true sample loss relates to sensitivity and the second sensitivity is within the context of plurality of classification)
- and comparing the second sensitivity metric against the pre-established sensitivity criterion,
in [0050] :
The predicted classifier 114 can be compared to the known classifier using a metric. For example, a sample loss function (or loss function) can be used to compare the predicted classifier 114 to the known classifier. The sample loss function provides a “cost” for mismatching known and predicted classifications. The sample loss function, can, for example, be a function that has a minimum value when the predicted classifiers 114 match the known classifiers. In these examples, the aim of the training method can be to reduce the average sample loss over the training set to below a threshold value.
(BRI: threshold is the sensitivity criterion using the sample loss comparisons for predicted and known classifier)
- and upon a determination that the second sensitivity metric does not meet the sensitivity criterion, updating the parameter of the neural network, and re-training, using the classical processor, the neural network comprising the updated parameter.
in [0061] :
With reference again to FIG. 2, if the threshold condition is not met, once one or more parameters have been updated the method returns to operation 2.2 and selects another training example (i.e. another sample state 108 with a known classification) and performs operations 2.3 to 2.8 with the updated quantum gate 104 parameters.
Farhi and Silva do not explicitly disclose:
- reclassify, using the quantum classifier, the data set with the additional generated noise to generate a third set of classified data, wherein the reclassifying comprises reclassifying the data item with the additional generated noise resulting in a third classification result of the data item;
However, Alam discloses:
- reclassify, using the quantum classifier, the data set with the additional generated noise to generate a third set of classified data, wherein the reclassifying comprises reclassifying the data item with the additional generated noise resulting in a third classification result of the data item;
In [II B, Page 2]: Classifier Basics
Binary classification is the task of classifying any input data into one of two possible groups. In supervised machine learning, this classification problem is solved by training a mathematical model (f(x, θ)) with a properly labeled input data-set {(x1,y1), (x2,y2), .... , (xM,yM)} where xi is the feature vector (can be multi-dimensional) of the i 0 th input data and yi is the associated label. The mathematical model predicts the class of any input data based on its features (x) and the parameters (θ) of the model. The parameters (θ) are updated iteratively until the model predictions are satisfactory over the input data-set. In [6], a binary classification on quantum computers is proposed for classical data where a P QC serves as the mathematical model. A state-preparation routine is required to encode the classical data and feed it to the P QC. The output is captured from a target qubit. During the training phase of the P QC, the parameters are updated iteratively based on the given input data-set so that the probability of getting 1 through a measurement of the target qubit for one class is maximized (and 0 for the other class)
In [II E, Page 3]:
PNG
media_image2.png
546
607
media_image2.png
Greyscale
In [III, Page 3]:
Training of a model circuit (P QC, Figure 4(b)) for binary classification can follow three
disparate strategies as described below.
PNG
media_image3.png
127
595
media_image3.png
Greyscale
(b) Structure of a multi-layer circuit centric Quantum Classifier (4-Qubits)
In [III A, Page 4]: Existing Approaches
Two classes of P QC training proposals exist in the literature: i) Train the P QC in a hardware-in-the-loop fashion. Hereafter, we term this approach as app01. In this approach, the P QC is executed on a real quantum computer. For a certain input, the output is measured and then the measured output is post-processed in a classical computer. Statistical techniques such as, Kullback-Leibler (KL) divergence method is used to calculate the disparity between the target distribution and the measured distribution (hence the cost) to update the parameters with any classical optimization techniques such as stochastic gradient descent or particle swarm optimization etc. [11]–[13]. Then, the P QC is executed again with updated parameters and process iterates until measured output matches target output up to a certain threshold. While it may seem to be an ideal approach, the technique is plagued with certain impediments.
In [III A, Page 4]: Existing Approaches
we can define the following cost-function to iteratively update the parameters of the P QC (Figure 5(b)) to solve the binary classification problem (described for the hybrid approach) [6]:
PNG
media_image4.png
67
565
media_image4.png
Greyscale
where m is the batch-size,
y
i
is the label of the i th data in the batch (data are labeled as -1 and +1 for class A and class B respectively),
x
i
is the i th input, and ‘expectation(PQC(xi,θ):QT )’ is the expectation value of the target qubit (
Q
T
) for the i th input and current values of the θ. The target is to minimize the cost. Gradient descent technique is applied to achieve the optimization goal where the partial derivatives of the cost function (Equation 1) with respect to the circuit parameters are calculated using numerical differentiation [20].
In [III A, Page 4]: Existing Approaches
the simulation models an ideal (i.e., without noise) quantum computer whereas quantum computers are noisy (and noise behavior shows temporal variation).
In [III A, Page 4]: Existing Approaches
the parameter optimization without considering noise may not give optimal result during inferencing phase in the real noisy quantum computer
In [III B, Page 4]: Proposed Approach: Classical Training with Noise Effects
To deal with the noisy hardware related dependency of the trained P QC, we propose to update the parameters where the expectation values are calculated with modeled noise behavior of a target hardware with our noisy quantum hardware simulation framework
In [III B, Page 4]:
To address the stochastic behavior of the noise sources as evident from Figure 2, we use the average value of the qubit quality metrics collected over a significant amount of time (43 days) to optimize the P QC parameters.
In [IV B, Page 5]:
2) Evaluation Method: Although parameterized quantum circuits can minimize the effects of noise, it cannot suppress it altogether. Therefore, the expectation values cannot be optimized to exactly -1/+1 values for all the inputs during the P QC training period which indicates that a measurement is not guaranteed to result in the desired class output (0/1) for a certain input.
In [IV B, Page 5]:
The ratio between the correct and incorrect outputs is also a representation of the fidelity of the circuit.
(BRI: Fidelity is the sensitivity)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva and Alam.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches quantum noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
One of ordinary skill would have motivation to combine Farhi , Silva and Alam that can provide a training methodology in a classical environments to improve the fidelity of the trained quantum circuit ([Abstract, Page 1])
Farhi, Silva and Alam do not explicitly disclose:
- generate additional noise in the quantum processor;
However, Zeng discloses:
- generate additional noise in the quantum processor;
In [Col 2, lines 7-15]:
In some instances, a quantum logic circuit can be optimized (or otherwise improved) for execution on small and noisy quantum processor chips. For instance, a classical simulator may emulate the noise profile of the quantum processor chip hardware during the construction of the quantum logic circuit, and, if the quantum logic circuits are run on the quantum processor chip hardware, their performance can account for the actual noise profile of the quantum processor chip hardware.
in [Col 6, lines 22-24]:
The process 150 can construct the quantum process by analyzing and modifying variable parameters of the quantum process,
in [Col 6, lines 30-35]:
The variable parameters of the quantum process can include classical control parameters for the quantum processor, such as, for example, the duration, frequency, shape, or amplitude of a microwave pulse, a laser pulse, a tuning pulse
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding unbiased noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches microwave pulse.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
In regard to Claim 25 (Previously Presented)
Farhi, Silva, and Alam do not explicitly disclose:
- program instructions to alter an amplitude of a microwave pulse in the quantum processor and lengthening pulses in the quantum processor.
However, Zeng discloses:
- program instructions to alter an amplitude of a microwave pulse in the quantum processor and lengthening pulses in the quantum processor.
In [Col 2, lines 32-44]:
In [Col 2, lines 7-15]:
In some instances, a quantum logic circuit can be optimized (or otherwise improved) for execution on small and noisy quantum processor chips. For instance, a classical simulator may emulate the noise profile of the quantum processor chip hardware during the construction of the quantum logic circuit, and, if the quantum logic circuits are run on the quantum processor chip hardware, their performance can account for the actual noise profile of the quantum processor chip hardware.
in [Col 8, lines 17-20]:
The optimization algorithm can be executed by an optimization engine or machine learning engine that is programmed to optimize (e.g., minimize) the objective function,
in [Col 6, lines 22-24]:
The process 150 can construct the quantum process by analyzing and modifying variable parameters of the quantum process,
in [Col 6, lines 30-35]:
The variable parameters of the quantum process can include classical control parameters for the quantum processor, such as, for example, the duration, frequency, shape, or amplitude of a microwave pulse, a laser pulse, a tuning pulse
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding unbiased noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches microwave pulse.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
In regard to Claim 27 ( Previously Presented)
Farhi discloses:
- a program instructions to determine, responsive to comparing the second classification result of the data item and the third classification result of the data item, a second sensitivity metric of the quantum processor;
program instructions
In [0118]:
(Note: teaches program instructions)
in [0054]:
In some embodiments, a gradient descent method is used
to compare the predicted classifier of the input state 106 with the known classifier of the
sample state 108 and update the parameters. FIG. 3 shows a flowchart of an example of a
method for updating the parameters using gradient descent,
in [0064]:
At operation 4.1 an unclassified input state is received. The unclassified input state comprises a plurality of qubits 102. The plurality of qubits 102 comprises n qubits representing a quantum state to be classified 108, and one or more readout qubits 110 in a known state. The quantum state is, in some embodiments, received from a routine running on a quantum or classical computer, and/or experimental equipment. Many other examples are possible. In some embodiments, the method encompasses preparing the input state 106 from a received quantum state to be classified 108.
- a second sensitivity metric of the quantum processor
in [0098]:
The binary classifier used in the example described below corresponds to whether an expected value of a Hamiltonian
H
^
with a state is positive or negative. This is equivalent to determining whether some Such a classifier can be useful when finding minimum energy states of system governed by a particular Hamiltonian,
in [0055]:
At operation 3.1, a sample loss is estimated. To estimate the sample loss, repeated measurements of the one or more readout qubits 110 in the output state 112 are made, and the sample loss is calculated from results of the measurements. Copies of the initial state 106 are repeatedly prepared and acted on by the quantum gates 104 to produce copies of the output state 112, and the readout qubits 110 for each copy of the output state 112 are measured. To achieve an estimate of the sample loss to within
δ
of the true sample loss at 99% probability, at least 2/
δ
.sub.2 measurements of the readout state are made.
(BRI: the estimate of the sample loss to be within the true sample loss relates to sensitivity and the second sensitivity is within the context of plurality of classification)
- and comparing the second sensitivity metric against the pre-established sensitivity criterion,
in [0050] :
The predicted classifier 114 can be compared to the known classifier using a metric. For example, a sample loss function (or loss function) can be used to compare the predicted classifier 114 to the known classifier. The sample loss function provides a “cost” for mismatching known and predicted classifications. The sample loss function, can, for example, be a function that has a minimum value when the predicted classifiers 114 match the known classifiers. In these examples, the aim of the training method can be to reduce the average sample loss over the training set to below a threshold value.
(BRI: threshold is the sensitivity criterion using the sample loss comparisons for predicted and known classifier)
- and upon a determination that the second sensitivity metric does not meet the sensitivity criterion, updating the parameter of the neural network, and re-training, using the classical processor, the neural network comprising the updated parameter.
in [0061] :
With reference again to FIG. 2, if the threshold condition is not met, once one or more parameters have been updated the method returns to operation 2.2 and selects another training example (i.e. another sample state 108 with a known classification) and performs operations 2.3 to 2.8 with the updated quantum gate 104 parameters.
Farhi and Silva do not explicitly disclose:
- reclassify, using the quantum classifier, the data set with the additional generated noise to generate a third set of classified data, wherein the reclassifying comprises reclassifying the data item with the additional generated noise resulting in a third classification result of the data item;
However, Alam discloses:
- reclassify, using the quantum classifier, the data set with the additional generated noise to generate a third set of classified data, wherein the reclassifying comprises reclassifying the data item with the additional generated noise resulting in a third classification result of the data item;
In [II B, Page 2]: Classifier Basics
Binary classification is the task of classifying any input data into one of two possible groups. In supervised machine learning, this classification problem is solved by training a mathematical model (f(x, θ)) with a properly labeled input data-set {(x1,y1), (x2,y2), .... , (xM,yM)} where xi is the feature vector (can be multi-dimensional) of the i 0 th input data and yi is the associated label. The mathematical model predicts the class of any input data based on its features (x) and the parameters (θ) of the model. The parameters (θ) are updated iteratively until the model predictions are satisfactory over the input data-set. In [6], a binary classification on quantum computers is proposed for classical data where a P QC serves as the mathematical model. A state-preparation routine is required to encode the classical data and feed it to the P QC. The output is captured from a target qubit. During the training phase of the P QC, the parameters are updated iteratively based on the given input data-set so that the probability of getting 1 through a measurement of the target qubit for one class is maximized (and 0 for the other class)
In [II E, Page 3]:
PNG
media_image2.png
546
607
media_image2.png
Greyscale
In [III, Page 3]:
Training of a model circuit (P QC, Figure 4(b)) for binary classification can follow three
disparate strategies as described below.
PNG
media_image3.png
127
595
media_image3.png
Greyscale
(b) Structure of a multi-layer circuit centric Quantum Classifier (4-Qubits)
In [III A, Page 4]: Existing Approaches
Two classes of P QC training proposals exist in the literature: i) Train the P QC in a hardware-in-the-loop fashion. Hereafter, we term this approach as app01. In this approach, the P QC is executed on a real quantum computer. For a certain input, the output is measured and then the measured output is post-processed in a classical computer. Statistical techniques such as, Kullback-Leibler (KL) divergence method is used to calculate the disparity between the target distribution and the measured distribution (hence the cost) to update the parameters with any classical optimization techniques such as stochastic gradient descent or particle swarm optimization etc. [11]–[13]. Then, the P QC is executed again with updated parameters and process iterates until measured output matches target output up to a certain threshold. While it may seem to be an ideal approach, the technique is plagued with certain impediments.
In [III A, Page 4]: Existing Approaches
we can define the following cost-function to iteratively update the parameters of the P QC (Figure 5(b)) to solve the binary classification problem (described for the hybrid approach) [6]:
PNG
media_image4.png
67
565
media_image4.png
Greyscale
where m is the batch-size,
y
i
is the label of the i th data in the batch (data are labeled as -1 and +1 for class A and class B respectively),
x
i
is the i th input, and ‘expectation(PQC(xi,θ):QT )’ is the expectation value of the target qubit (
Q
T
) for the i th input and current values of the θ. The target is to minimize the cost. Gradient descent technique is applied to achieve the optimization goal where the partial derivatives of the cost function (Equation 1) with respect to the circuit parameters are calculated using numerical differentiation [20].
In [III A, Page 4]: Existing Approaches
the simulation models an ideal (i.e., without noise) quantum computer whereas quantum computers are noisy (and noise behavior shows temporal variation).
In [III A, Page 4]: Existing Approaches
the parameter optimization without considering noise may not give optimal result during inferencing phase in the real noisy quantum computer
In [III B, Page 4]: Proposed Approach: Classical Training with Noise Effects
To deal with the noisy hardware related dependency of the trained P QC, we propose to update the parameters where the expectation values are calculated with modeled noise behavior of a target hardware with our noisy quantum hardware simulation framework
In [III B, Page 4]:
To address the stochastic behavior of the noise sources as evident from Figure 2, we use the average value of the qubit quality metrics collected over a significant amount of time (43 days) to optimize the P QC parameters.
In [IV B, Page 5]:
2) Evaluation Method: Although parameterized quantum circuits can minimize the effects of noise, it cannot suppress it altogether. Therefore, the expectation values cannot be optimized to exactly -1/+1 values for all the inputs during the P QC training period which indicates that a measurement is not guaranteed to result in the desired class output (0/1) for a certain input.
In [IV B, Page 5]:
The ratio between the correct and incorrect outputs is also a representation of the fidelity of the circuit.
(BRI: Fidelity is the sensitivity)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva and Alam.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
One of ordinary skill would have motivation to combine Farhi , Silva and Alam that can provide a training methodology in a classical environments to improve the fidelity of the trained quantum circuit ([Abstract, Page 1])
Farhi, Silva and Alam do not explicitly disclose:
- generate additional noise in the quantum processor;
However, Zeng discloses:
- generate additional noise in the quantum processor;
In [Col 2, lines 7-15]:
In some instances, a quantum logic circuit can be optimized (or otherwise improved) for execution on small and noisy quantum processor chips. For instance, a classical simulator may emulate the noise profile of the quantum processor chip hardware during the construction of the quantum logic circuit, and, if the quantum logic circuits are run on the quantum processor chip hardware, their performance can account for the actual noise profile of the quantum processor chip hardware.
in [Col 6, lines 22-24]:
The process 150 can construct the quantum process by analyzing and modifying variable parameters of the quantum process,
in [Col 6, lines 30-35]:
The variable parameters of the quantum process can include classical control parameters for the quantum processor, such as, for example, the duration, frequency, shape, or amplitude of a microwave pulse, a laser pulse, a tuning pulse
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding unbiased noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches microwave pulse.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
In regard to Claim 28 ( Previously Presented)
Farhi, Silva and Alam do not explicitly disclose:
- generating the additional noise comprises at least one of altering an amplitude of a microwave pulse in the quantum processor and lengthening pulses in the quantum processor.
However, Zeng discloses:
- at least one of altering an amplitude of a microwave pulse in the quantum processor and lengthening pulses in the quantum processor.
In [Col 2, lines 7-15]:
In some instances, a quantum logic circuit can be optimized (or otherwise improved) for execution on small and noisy quantum processor chips. For instance, a classical simulator may emulate the noise profile of the quantum processor chip hardware during the construction of the quantum logic circuit, and, if the quantum logic circuits are run on the quantum processor chip hardware, their performance can account for the actual noise profile of the quantum processor chip hardware.
in [Col 6, lines 22-24]:
The process 150 can construct the quantum process by analyzing and modifying variable parameters of the quantum process,
in [Col 6, lines 30-35]:
The variable parameters of the quantum process can include classical control parameters for the quantum processor, such as, for example, the duration, frequency, shape, or amplitude of a microwave pulse, a laser pulse, a tuning pulse
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding unbiased noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches microwave pulse.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
Claim 30 is rejected under 35 U.S.C. 103 as being unpatentable over
in view of Farhi (hereinafter Farhi) US 2020/0342345 A1,
in view of Gerado A. Paz-Silva (hereinafter Silva) Multiqubit Spectroscopy of Gaussian Quantum Nose, arXiv:1609.01792v2 [quant-ph] 21 Sep 2016,
in view of Mahabubul Alam (hereinafter Alam) Addressing Temporal Variations in Qubit Quality Metrics for Parameterized Quantum Circuits, arXiv:1903.08684v1 [cs.ET] 20 Mar 2019 [Also available in IEEE Xplore].
further in view of Maria Schuld (hereinafter Schuld) Quantum ensembles of quantum classifiers, Scientific Reports, Feb 2018.
In regard to Claim 30 (New)
Farhi, Silva and Alam do not explicitly disclose:
- wherein the quantum classifier comprises a quantum support vector machine (QSVM), wherein the classifying the data set to generate the first set of classified data is performed by the QSVM producing a discrete classification of the data set by the quantum processor;
- wherein the determining the first sensitivity metric is performed by a sensitivity analysis component, and wherein the method further comprises:
- wherein determining, by the sensitivity analysis component, an overall sensitivity of the quantum processor, the overall sensitivity comprising a number of differentiations between an original class and a new class of a data item of a set of data items;
- determining, by the sensitivity analysis component, whether any original classes of a set of original classes differs from any corresponding new classes of a set of new classes;
- and repeating the method until a determination by the sensitivity analysis component that none of the original classes differs from any of the new classes of the set of data items.
However, Schuld discloses:
- wherein the quantum classifier comprises a quantum support vector machine (QSVM), wherein the classifying the data set to generate the first set of classified data is performed by the QSVM producing a discrete classification of the data set by the quantum processor;
In [Abstract, Page 1]:
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer.
In [Introduction, Page 1]:
In machine learning, a classifier can be understood as a mathematical model or computer algorithm that takes input vectors of features and assigns them to classes or ‘labels’.
In [Results, Page 4]:
The quantum ensemble. Consider a quantum routine [Symbol font/0x41] which ‘computes’ a model function
PNG
media_image5.png
45
423
media_image5.png
Greyscale
which we will call a quantum classifier in the following. The last qubit |f (x; θ)〉 encodes class f (x; θ)= −1 in state |0〉 and class 1 in state |1〉. Note that it is not important whether the registers |x〉, |θ〉 encode the classical vectors x, θ in the amplitudes or qubits of the quantum state. If encoding classical information into the binary sequence of computational basis states (i.e. x=2→010→|010〉), every function f (x; θ) a classical computer can compute efficiently could in principle be translated into a quantum circuit [Symbol font/0x41]. This means that every classifier leads to an efficient quantum classifier (possibly with large polynomial overhead). An example for a quantum perceptron classifier can be found in ref.18, while feed-forward neural networks have been considered in19. With this definition of a quantum classifier, [Symbol font/0x41] can be implemented in parallel to a superposition of parameter states.
In [Introduction, Page 1]:
Exponentially large ensembles do not only have the potential to increase the predictive power of single quantum classifiers, they also offer an interesting perspective on how to circumvent the training problem in quantum machine learning. Training in the quantum regime relies on methods that range from sampling from quantum states4 to quantum matrix inversion2
(BRI: quantum machine learning, particularly with Quantum Support Vector Machines (QSVMs), classical data (such as vectors or data that can be represented as a matrix) is indeed encoded into the quantum states of qubits. This quantum state, represented by a "qubit string" (a sequence of qubits), serves as the training vector within the quantum classifier
- wherein the determining the first sensitivity metric is performed by a sensitivity analysis component, and wherein the method further comprises:
wherein determining, by the sensitivity analysis component, an overall sensitivity of the quantum processor, the overall sensitivity comprising a number of differentiations between an original class and a new class of a data item of a set of data items;
In [Analytical investigation of the accuracy-weighted ensemble, Page 7]:
In order to explore the accuracy-weighted ensemble classifier further, we conduct some analytical and numerical investigations for the remainder of the article. It is convenient to assume that we know the probability distribution p (x, y) from which the data is picked (that is either the ‘true’ probability distribution with which data is generated, or the approximate distribution inferred by some data mining technique). Furthermore, we consider the continuous limit ∑→∫. Each parameter θ defines decision regions in the input space,
R
-
1
θ
for class -1 and
R
1
θ
for class 1 (i.e. regions of inputs that are mapped to the respective classes). The accuracy can then be expressed as
PNG
media_image6.png
80
977
media_image6.png
Greyscale
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
We consider a minimal toy example for a classifier, namely a perceptron model on a one-dimensional input space, f (x; w,
w
0
)=sgn (wx+w0) with x, w,
w
0
∈
R
. While one parameter would be sufficient to mark the position of the point-like ‘decision boundary’, a second one is required to define its orientation. One can simplify the model even further by letting the bias
w
0
define the position of the decision boundary and introducing a binary ‘orientation’ parameter o ∈{−1, 1} (as illustrated in Fig. 6)
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution. This might be a desired behaviour in some contexts
(BRI: the accuracy is the weight)
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
Our goal is to compute the expectation value
PNG
media_image7.png
57
1255
media_image7.png
Greyscale
of which the sign function evaluates the desired prediction
y
~
.
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
The simplicity of the core model allows us to have a look into the structure of the expectation value. Figure 9 shows the components of the integrand in Eq. (11) for the expectation value, namely the accuracy, the core model function as well as their product.
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
Example 1 shows the same variances σ+ =σ−, while Example 2 plots different variances. The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
- determining, by the sensitivity analysis component, whether any original classes of a set of original classes differs from any corresponding new classes of a set of new classes;
In [Analytical investigation of the accuracy-weighted ensemble, Page 7]:
Each parameter θ defines decision regions in the input space,
R
-
1
θ
for class -1 and
R
1
θ
for class 1 (i.e. regions of inputs that are mapped to the respective classes).
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
Example 1 shows the same variances σ+ =σ−, while Example 2 plots different variances. The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution
In [Choosing the weights proportional to the accuracy, Page 6]:.
PNG
media_image8.png
511
1291
media_image8.png
Greyscale
(BRI: It may be interpreted that regions of class "-1" are original classes while class "1" can be a new class defined by the model's decision boundary, or a second original class. A decision boundary is the dividing line or surface that separates regions of the feature space into different predicted classes. In a binary classification (two-class) problem, the model learns this boundary to distinguish between the classes)
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
Figure 7 plots the expectation value for different inputs x[Symbol font/0xB0] for the case of two Gaussians with σ− =σ+ =0.5, and μ− = −1, μ+ =1. The decision boundary is at the point where the expectation value changes from a negative to a positive value, [Symbol font/0x45][ (f x; , w o)] 0 ˆ 0 = . One can see that for this simple case, the decision boundary will be in between the two means, which we would naturally expect. This is an important finding, since it implies that the accuracy-weighted ensemble classifier works - arguably only for a very simple model and dataset
(BRI: a decision boundary will typically be located between the means of two classes, and its exact position represents the line or surface where the model's prediction transitions from one class to another. The boundary is learned by the model to separate the feature space into distinct regions for each class )
- and repeating the method until a determination by the sensitivity analysis component that none of the original classes differs from any of the new classes of the set of data items.
[Background and Related Results, Page 2]).
The coefficients
w
θ
weigh the decision f (
x
~
; θ) { ∈ −1, 1} of each model in the ensemble [Symbol font/0x45] specified by θ, while the sign function assigns class 1 to the new input if the weighed sum is positive and −1 otherwise. It is important
In [Background and Related Results, Page 3]:
finite number representation and limit the parameters to a certain interval to get the discrete sum
PNG
media_image9.png
88
841
media_image9.png
Greyscale
In [Choosing the weights proportional to the accuracy, Page 5]:
Now load the new input into the first δ qubits of the data register, apply the routine [Symbol font/0x41] once more and uncompute (and disregard) the data register to obtain
PNG
media_image10.png
87
535
media_image10.png
Greyscale
The measurement statistics of the last qubit now contain the desired value. More precisely, the expectation value of
PNG
media_image11.png
36
217
media_image11.png
Greyscale
PNG
media_image12.png
67
796
media_image12.png
Greyscale
and corresponds to the classifier in Eq. (3). Repeated measurements reveal this expectation value to the desired precision
(BRI: the mapping may suggest that if the decision boundary between classes is indistinct even with the use of repeated measurements to improve precision, it may be an indication that the classes are not statistically different or are heavily overlapped)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Schuld.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component.
Alam teaches reclassifying the data item with the generated noise.
Schuld teaches ensemble quantum classifier.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Schuld to increase the performance of the ensemble decision (Schuld [Background and Related Results, Page 3]).
Claims 31-32 are rejected under 35 U.S.C. 103 as being unpatentable over
in view of Farhi (hereinafter Farhi) US 2020/0342345 A1,
i in view of Gerado A. Paz-Silva (hereinafter Silva) Multiqubit Spectroscopy of Gaussian Quantum Nose, arXiv:1609.01792v2 [quant-ph] 21 Sep 2016,
in view of Mahabubul Alam (hereinafter Alam) Addressing Temporal Variations in Qubit Quality Metrics for Parameterized Quantum Circuits, arXiv:1903.08684v1 [cs.ET] 20 Mar 2019 [Also available in IEEE Xplore].
further in view of Zeng (hereinafter Zeng) US 10325218 B1,
further in view of Maria Schuld (hereinafter Schuld) Quantum ensembles of quantum classifiers, Scientific Reports, Feb 2018.
In regard to Claim 31 (New)
Farhi, Silva and Alam do not explicitly disclose:
- wherein the program instructions
- program instructions to determine
- program instructions to determine
- program instructions to repeat
- repeat the program instructions until
However, Zeng discloses:
- wherein the program instructions
In [Col 4, lines 1-5]
- program instructions to determine
In [Col 4, lines 1-5]
- program instructions to determine,
In [Col 4, lines 1-5]
- program instructions to repeat
In [Col 5, lines 11-44]
- repeat the program instructions until
In [Col 5, lines 11-44]
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier and sensitivity metric.
Silva teaches adding noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches program instructions and repeating the method.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
Farhi, Silva, Alam and Zeng do not explicitly disclose:
- wherein the quantum classifier comprises a quantum support vector machine (QSVM), wherein the program instructions to classify the data set to generate the first set of classified data are performed by the QSVM producing a discrete classification of the data set by the quantum processor;
- to determine the first sensitivity metric are performed by a sensitivity analysis component, and wherein the method further comprises
- by the sensitivity analysis component, an overall sensitivity of the quantum processor, the overall sensitivity comprising a number of differentiations between an original class and a new class of a data item of a set of data items
- by the sensitivity analysis component, whether any original classes of a set of original classes differs from any corresponding new classes of a set of new classes;
- a determination by the sensitivity analysis component that none of the original classes differs from any of the new classes of the set of data items.
However, Schuld discloses:
- wherein the quantum classifier comprises a quantum support vector machine (QSVM), wherein the program instructions to classify the data set to generate the first set of classified data are performed by the QSVM producing a discrete classification of the data set by the quantum processor;
In [Abstract, Page 1]:
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer.
In [Introduction, Page 1]:
In machine learning, a classifier can be understood as a mathematical model or computer algorithm that takes input vectors of features and assigns them to classes or ‘labels’.
In [Results, Page 4]:
The quantum ensemble. Consider a quantum routine [Symbol font/0x41] which ‘computes’ a model function
PNG
media_image5.png
45
423
media_image5.png
Greyscale
which we will call a quantum classifier in the following. The last qubit |f (x; θ)〉 encodes class f (x; θ)= −1 in state |0〉 and class 1 in state |1〉. Note that it is not important whether the registers |x〉, |θ〉 encode the classical vectors x, θ in the amplitudes or qubits of the quantum state. If encoding classical information into the binary sequence of computational basis states (i.e. x=2→010→|010〉), every function f (x; θ) a classical computer can compute efficiently could in principle be translated into a quantum circuit [Symbol font/0x41]. This means that every classifier leads to an efficient quantum classifier (possibly with large polynomial overhead). An example for a quantum perceptron classifier can be found in ref.18, while feed-forward neural networks have been considered in19. With this definition of a quantum classifier, [Symbol font/0x41] can be implemented in parallel to a superposition of parameter states.
In [Introduction, Page 1]:
Exponentially large ensembles do not only have the potential to increase the predictive power of single quantum classifiers, they also offer an interesting perspective on how to circumvent the training problem in quantum machine learning. Training in the quantum regime relies on methods that range from sampling from quantum states4 to quantum matrix inversion2
(BRI: quantum machine learning, particularly with Quantum Support Vector Machines (QSVMs), classical data (such as vectors or data that can be represented as a matrix) is indeed encoded into the quantum states of qubits. This quantum state, represented by a "qubit string" (a sequence of qubits), serves as the training vector within the quantum classifier
- to determine the first sensitivity metric are performed by a sensitivity analysis component, and wherein the method further comprises
by the sensitivity analysis component, an overall sensitivity of the quantum processor, the overall sensitivity comprising a number of differentiations between an original class and a new class of a data item of a set of data items
In [Analytical investigation of the accuracy-weighted ensemble, Page 7]:
In order to explore the accuracy-weighted ensemble classifier further, we conduct some analytical and numerical investigations for the remainder of the article. It is convenient to assume that we know the probability distribution p (x, y) from which the data is picked (that is either the ‘true’ probability distribution with which data is generated, or the approximate distribution inferred by some data mining technique). Furthermore, we consider the continuous limit ∑→∫. Each parameter θ defines decision regions in the input space,
R
-
1
θ
for class -1 and
R
1
θ
for class 1 (i.e. regions of inputs that are mapped to the respective classes). The accuracy can then be expressed as
PNG
media_image6.png
80
977
media_image6.png
Greyscale
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
We consider a minimal toy example for a classifier, namely a perceptron model on a one-dimensional input space, f (x; w,
w
0
)=sgn (wx+w0) with x, w,
w
0
∈
R
. While one parameter would be sufficient to mark the position of the point-like ‘decision boundary’, a second one is required to define its orientation. One can simplify the model even further by letting the bias
w
0
define the position of the decision boundary and introducing a binary ‘orientation’ parameter o ∈{−1, 1} (as illustrated in Fig. 6)
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
The plots show that for equal variances, the accuracy is a symmetric function centered between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution. This might be a desired behaviour in some contexts
(BRI: the accuracy is the weight)
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
Our goal is to compute the expectation value
PNG
media_image7.png
57
1255
media_image7.png
Greyscale
of which the sign function evaluates the desired prediction
y
~
.
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
The simplicity of the core model allows us to have a look into the structure of the expectation value. Figure 9 shows the components of the integrand in Eq. (11) for the expectation value, namely the accuracy, the core model function as well as their product.
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
Example 1 shows the same variances σ+ =σ−, while Example 2 plots different variances. The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution
- by the sensitivity analysis component, whether any original classes of a set of original classes differs from any corresponding new classes of a set of new classes;
In [Analytical investigation of the accuracy-weighted ensemble, Page 7]:
Each parameter θ defines decision regions in the input space,
R
-
1
θ
for class -1 and
R
1
θ
for class 1 (i.e. regions of inputs that are mapped to the respective classes).
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
Example 1 shows the same variances σ+ =σ−, while Example 2 plots different variances. The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution
In [Choosing the weights proportional to the accuracy, Page 6]:.
PNG
media_image8.png
511
1291
media_image8.png
Greyscale
(BRI: It may be interpreted that regions of class "-1" are original classes while class "1" can be a new class defined by the model's decision boundary, or a second original class. A decision boundary is the dividing line or surface that separates regions of the feature space into different predicted classes. In a binary classification (two-class) problem, the model learns this boundary to distinguish between the classes)
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
Figure 7 plots the expectation value for different inputs x[Symbol font/0xB0] for the case of two Gaussians with σ− =σ+ =0.5, and μ− = −1, μ+ =1. The decision boundary is at the point where the expectation value changes from a negative to a positive value, [Symbol font/0x45][ (f x; , w o)] 0 ˆ 0 = . One can see that for this simple case, the decision boundary will be in between the two means, which we would naturally expect. This is an important finding, since it implies that the accuracy-weighted ensemble classifier works - arguably only for a very simple model and dataset
(BRI: a decision boundary will typically be located between the means of two classes, and its exact position represents the line or surface where the model's prediction transitions from one class to another. The boundary is learned by the model to separate the feature space into distinct regions for each class )
- a determination by the sensitivity analysis component that none of the original classes differs from any of the new classes of the set of data items.
[Background and Related Results, Page 2]).
The coefficients
w
θ
weigh the decision f (
x
~
; θ) { ∈ −1, 1} of each model in the ensemble [Symbol font/0x45] specified by θ, while the sign function assigns class 1 to the new input if the weighed sum is positive and −1 otherwise. It is important
In [Background and Related Results, Page 3]:
finite number representation and limit the parameters to a certain interval to get the discrete sum
PNG
media_image9.png
88
841
media_image9.png
Greyscale
In [Choosing the weights proportional to the accuracy, Page 5]:
Now load the new input into the first δ qubits of the data register, apply the routine [Symbol font/0x41] once more and uncompute (and disregard) the data register to obtain
PNG
media_image10.png
87
535
media_image10.png
Greyscale
The measurement statistics of the last qubit now contain the desired value. More precisely, the expectation value of
PNG
media_image11.png
36
217
media_image11.png
Greyscale
PNG
media_image12.png
67
796
media_image12.png
Greyscale
and corresponds to the classifier in Eq. (3). Repeated measurements reveal this expectation value to the desired precision
(BRI: the mapping may suggest that if the decision boundary between classes is indistinct even with the use of repeated measurements to improve precision, it may be an indication that the classes are not statistically different or are heavily overlapped)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva , Alam, Zeng and Schuld.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches program instructions and repeating the method.
Schuld teaches ensemble quantum classifier.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam, Zeng and Schuld to increase the performance of the ensemble decision (Schuld [Background and Related Results, Page 3]).
In regard to Claim 32 (New)
Farhi, Silva and Alam do not explicitly disclose:
- program instructions to
- and program instructions to repeat the program instructions until a
However, Zeng discloses:
- program instructions
In [Col 4, lines 1-5]
- and program instructions to repeat the program instructions until
In [Col 5, lines 11-44]
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam and Zeng.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches adding noise using swapping qubits of the quantum component
Alam teaches reclassifying the data item with the generated noise.
Zeng teaches program instructions.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam and Zeng to minimize the objective function (Zeng [Col 10, lines 61-67]).
Farhi, Silva, Alam, and Zeng do not explicitly disclose:
- wherein the quantum classifier comprises a quantum support vector machine (QSVM), wherein the program instructions to classify the data set to generate the first set of classified data are performed by the QSVM producing a discrete classification of the data set by the quantum processor;
- determine the first sensitivity metric are performed by a sensitivity analysis component, and wherein the program instructions further comprise:
- determine, by the sensitivity analysis component, an overall sensitivity of the quantum processor, the overall sensitivity comprising a number of differentiations between an original class and a new class of a data item of a set of data items;
- determine, by the sensitivity analysis component, whether any original classes of a set of original classes differs from any corresponding new classes of a set of new classes;
- until a determination by the sensitivity analysis component that none of the original classes differs from any of the new classes of the set of data items.
However, Schuld discloses:
- wherein the quantum classifier comprises a quantum support vector machine (QSVM), wherein the program instructions to classify the data set to generate the first set of classified data are performed by the QSVM producing a discrete classification of the data set by the quantum processor;
In [Abstract, Page 1]:
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer.
In [Introduction, Page 1]:
In machine learning, a classifier can be understood as a mathematical model or computer algorithm that takes input vectors of features and assigns them to classes or ‘labels’.
In [Results, Page 4]:
The quantum ensemble. Consider a quantum routine [Symbol font/0x41] which ‘computes’ a model function
PNG
media_image5.png
45
423
media_image5.png
Greyscale
which we will call a quantum classifier in the following. The last qubit |f (x; θ)〉 encodes class f (x; θ)= −1 in state |0〉 and class 1 in state |1〉. Note that it is not important whether the registers |x〉, |θ〉 encode the classical vectors x, θ in the amplitudes or qubits of the quantum state. If encoding classical information into the binary sequence of computational basis states (i.e. x=2→010→|010〉), every function f (x; θ) a classical computer can compute efficiently could in principle be translated into a quantum circuit [Symbol font/0x41]. This means that every classifier leads to an efficient quantum classifier (possibly with large polynomial overhead). An example for a quantum perceptron classifier can be found in ref.18, while feed-forward neural networks have been considered in19. With this definition of a quantum classifier, [Symbol font/0x41] can be implemented in parallel to a superposition of parameter states.
In [Introduction, Page 1]:
Exponentially large ensembles do not only have the potential to increase the predictive power of single quantum classifiers, they also offer an interesting perspective on how to circumvent the training problem in quantum machine learning. Training in the quantum regime relies on methods that range from sampling from quantum states4 to quantum matrix inversion2
(BRI: quantum machine learning, particularly with Quantum Support Vector Machines (QSVMs), classical data (such as vectors or data that can be represented as a matrix) is indeed encoded into the quantum states of qubits. This quantum state, represented by a "qubit string" (a sequence of qubits), serves as the training vector within the quantum classifier
- determine the first sensitivity metric are performed by a sensitivity analysis component, and wherein the program instructions further comprise:
determine, by the sensitivity analysis component, an overall sensitivity of the quantum processor, the overall sensitivity comprising a number of differentiations between an original class and a new class of a data item of a set of data items;
In [Analytical investigation of the accuracy-weighted ensemble, Page 7]:
In order to explore the accuracy-weighted ensemble classifier further, we conduct some analytical and numerical investigations for the remainder of the article. It is convenient to assume that we know the probability distribution p (x, y) from which the data is picked (that is either the ‘true’ probability distribution with which data is generated, or the approximate distribution inferred by some data mining technique). Furthermore, we consider the continuous limit ∑→∫. Each parameter θ defines decision regions in the input space,
R
-
1
θ
for class -1 and
R
1
θ
for class 1 (i.e. regions of inputs that are mapped to the respective classes). The accuracy can then be expressed as
PNG
media_image6.png
80
977
media_image6.png
Greyscale
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
We consider a minimal toy example for a classifier, namely a perceptron model on a one-dimensional input space, f (x; w,
w
0
)=sgn (wx+w0) with x, w,
w
0
∈
R
. While one parameter would be sufficient to mark the position of the point-like ‘decision boundary’, a second one is required to define its orientation. One can simplify the model even further by letting the bias
w
0
define the position of the decision boundary and introducing a binary ‘orientation’ parameter o ∈{−1, 1} (as illustrated in Fig. 6)
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution. This might be a desired behaviour in some contexts
(BRI: the accuracy is the weight)
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
Our goal is to compute the expectation value
PNG
media_image7.png
57
1255
media_image7.png
Greyscale
of which the sign function evaluates the desired prediction
y
~
.
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
The simplicity of the core model allows us to have a look into the structure of the expectation value. Figure 9 shows the components of the integrand in Eq. (11) for the expectation value, namely the accuracy, the core model function as well as their product.
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
Example 1 shows the same variances σ+ =σ−, while Example 2 plots different variances. The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution
- determine, by the sensitivity analysis component, whether any original classes of a set of original classes differs from any corresponding new classes of a set of new classes;
In [Analytical investigation of the accuracy-weighted ensemble, Page 7]:
Each parameter θ defines decision regions in the input space,
R
-
1
θ
for class -1 and
R
1
θ
for class 1 (i.e. regions of inputs that are mapped to the respective classes).
In [Analytical investigation of the accuracy-weighted ensemble, Page 9]:
Example 1 shows the same variances σ+ =σ−, while Example 2 plots different variances. The plots show that for equal variances, the accuracy is a symmetric function centred between the two means, while for different variances, the function is highly asymmetric. In case the two distributions are sufficiently close to each other, this has a sensitive impact on the position of the decision boundary, which will be shifted towards the flatter distribution
In [Choosing the weights proportional to the accuracy, Page 6]:.
PNG
media_image8.png
511
1291
media_image8.png
Greyscale
(BRI: It may be interpreted that regions of class "-1" are original classes while class "1" can be a new class defined by the model's decision boundary, or a second original class. A decision boundary is the dividing line or surface that separates regions of the feature space into different predicted classes. In a binary classification (two-class) problem, the model learns this boundary to distinguish between the classes)
In [Analytical investigation of the accuracy-weighted ensemble, Page 8]:
Figure 7 plots the expectation value for different inputs x[Symbol font/0xB0] for the case of two Gaussians with σ− =σ+ =0.5, and μ− = −1, μ+ =1. The decision boundary is at the point where the expectation value changes from a negative to a positive value, [Symbol font/0x45][ (f x; , w o)] 0 ˆ 0 = . One can see that for this simple case, the decision boundary will be in between the two means, which we would naturally expect. This is an important finding, since it implies that the accuracy-weighted ensemble classifier works - arguably only for a very simple model and dataset
(BRI: a decision boundary will typically be located between the means of two classes, and its exact position represents the line or surface where the model's prediction transitions from one class to another. The boundary is learned by the model to separate the feature space into distinct regions for each class )
- a determination by the sensitivity analysis component that none of the original classes differs from any of the new classes of the set of data items.
[Background and Related Results, Page 2]).
The coefficients
w
θ
weigh the decision f (
x
~
; θ) { ∈ −1, 1} of each model in the ensemble [Symbol font/0x45] specified by θ, while the sign function assigns class 1 to the new input if the weighed sum is positive and −1 otherwise. It is important
In [Background and Related Results, Page 3]:
finite number representation and limit the parameters to a certain interval to get the discrete sum
PNG
media_image9.png
88
841
media_image9.png
Greyscale
In [Choosing the weights proportional to the accuracy, Page 5]:
Now load the new input into the first δ qubits of the data register, apply the routine [Symbol font/0x41] once more and uncompute (and disregard) the data register to obtain
PNG
media_image10.png
87
535
media_image10.png
Greyscale
The measurement statistics of the last qubit now contain the desired value. More precisely, the expectation value of
PNG
media_image11.png
36
217
media_image11.png
Greyscale
PNG
media_image12.png
67
796
media_image12.png
Greyscale
and corresponds to the classifier in Eq. (3). Repeated measurements reveal this expectation value to the desired precision
(BRI: the mapping may suggest that if the decision boundary between classes is indistinct even with the use of repeated measurements to improve precision, it may be an indication that the classes are not statistically different or are heavily overlapped)
It would have obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Farhi, Silva, Alam, Zeng and Schuld.
Farhi teaches classification using a hybrid classical and quantum classifier.
Silva teaches generating quantum noise.
Alam reclassifying the data item with the generated noise.
Zeng teaches program instructions and repeating the method.
Schuld teaches ensemble quantum classifier.
One of ordinary skill would have motivation to combine Farhi, Silva, Alam, Zeng and Schuld to increase the performance of the ensemble decision (Schuld [Background and Related Results, Page 3]).
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to TIRUMALE KRISHNASWAMY RAMESH whose telephone number is (571)272-4605. The examiner can normally be reached by phone.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Li B Zhen can be reached on phone (571-272-3768). The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/TIRUMALE K RAMESH/Examiner, Art Unit 2121
/James D. Rutten/Primary Examiner, Art Unit 2121