Machine learning model-based training method, training system, quantum process chromatography method, control system, storage medium and electronic equipment

Abstract

The invention provides a training method, a training system, a quantum process chromatography method, a control system, a storage medium and electronic equipment based on a machine learning model. The training method comprises the following steps: acquiring a data set obtained by processing a to-be-measured sub-process, and processing the data set by the machine learning model to obtain a predicted value; inputting the measured value and the predicted value into a preset loss function, processing according to the loss function to obtain a gradient of a parameter of the machine learning model, updating the gradient on a manifold curve through gradient constraint processing, and reducing the loss function; and obtaining a change value of the loss function, judging whether the change value meets a preset convergence requirement, and if yes, completing training of the machine learning model. According to the gradient of the loss function and the machine learning model parameters, updating is carried out on the manifold curve, retraction processing is carried out on the gradient, efficient optimization of built-in physical constraints is achieved, it is ensured that the quantum process chromatography result always meets complete positive performance and trace preserving performance, and unreasonable results or results difficult to understand visually are avoided.

Description

Technical Field

[0001] This disclosure relates to the field of quantum process tomography, and more particularly to a training method, training system, quantum process tomography method, control system, storage medium, and electronic device based on a machine learning model. Background Technology

[0002] Quantum process tomography (QPT) is a key technique in quantum information processing used to characterize the evolution of quantum systems. It involves preparing a series of known input quantum states, passing these states through a subprocess to be measured, and then measuring the output states to collect sufficient statistical data. Using this data, a Choi matrix or other characterization of the quantum process can be reconstructed, thus providing a comprehensive understanding of the quantum process's properties.

[0003] Existing quantum process tomography methods are susceptible to significant accuracy issues due to noise in experimental data. Processing noisy data can easily introduce large errors, leading to inaccurate reconstructed quantum processes. Furthermore, the impact of noise on quantum process tomography is even more pronounced with low data volumes.

[0004] Secondly, in ensuring the physical consistency of the recovered process, existing quantum process tomography methods have difficulty ensuring that the obtained model satisfies the conditions of complete positivity and trace preservation when recovering quantum processes, resulting in unreasonable or difficult-to-understand results of the reconstructed quantum processes. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this disclosure proposes a training method, training system, quantum process tomography method, control system, storage medium, and electronic device based on a machine learning model.

[0006] To achieve the above objectives, this disclosure provides a training method based on a machine learning model, comprising:

[0007] S11. Obtain a dataset, which is input into a machine learning model to obtain predicted values, wherein the dataset is the measurement value obtained by measuring the quantum state through the subprocess to be measured;

[0008] S12. The measured value and the predicted value are input into a preset loss function. The gradient of the parameters of the machine learning model is obtained by processing according to the loss function. The gradient is updated on the manifold curve through gradient constraint processing, thereby reducing the loss function.

[0009] S13. Obtain the change value of the loss function, determine whether the change value meets the preset convergence requirement, if so, end the training, and use the machine learning model for the tomography of the subprocess to be measured.

[0010] If not, return to step S11 and retrieve the dataset again.

[0011] Optionally, the loss function consists of least squares error loss and L1 regularization loss.

[0012] Optionally, updating the gradient on the manifold curve through gradient constraint processing includes:

[0013] Initialize the operator matrix and process it to obtain the gradient of the machine learning model parameters;

[0014] In the tangent space of the manifold, a descent direction is determined, and the gradient is projected onto the tangent space to obtain a tangent vector, thereby updating the gradient.

[0015] Determine whether the gradient update satisfies the descent direction of the manifold constraint. If not, perform gradient shrinkage. If yes, complete the update.

[0016] Optionally, the gradient shrinking process includes:

[0017] The stacking matrix is ​​obtained by processing the update amount of the tangent space and the operator matrix.

[0018] The stacked matrix is ​​processed according to a preset learning rate, so that the gradient is updated along the descent direction that satisfies the manifold constraint.

[0019] Optionally, the convergence requirements include:

[0020] If the change value meets a preset first standard value within a consecutive number of training iterations, it indicates convergence, or

[0021] If the number of training iterations is within a preset second standard value, and the change value does not meet the first standard value, then training ends, and the current minimum loss function is obtained.

[0022] It also includes a quantum process tomography method based on a machine learning model, comprising:

[0023] S21. Obtain the measurement dataset, wherein the dataset consists of measurement values ​​obtained by processing the quantum state through the subprocess to be measured;

[0024] S22. The dataset is input into a machine learning model for processing to obtain a prediction matrix;

[0025] S23. Process the results to obtain the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset threshold.

[0026] If so, the prediction matrix is ​​used to represent the subprocess to be measured, and the process ends;

[0027] If not, the gradient of the machine learning model parameters is updated using the loss function to obtain the updated machine learning model;

[0028] S24. The dataset is input into the updated machine learning model to obtain the updated prediction matrix and return to step S23.

[0029] Optionally, the dataset is input into the machine learning model to obtain a prediction matrix, including:

[0030] The machine learning model obtains the corresponding operators based on the dataset, and the operators are linearly combined and input into the matrix definition to obtain the prediction matrix.

[0031] It also includes a training system for a machine learning model, comprising:

[0032] The first data processing module acquires a dataset, which is a quantum state processed by a subprocess to be measured to obtain measurement values, and the dataset is input into a machine learning model to obtain prediction values.

[0033] The first model processing module establishes a machine learning model, receives the dataset and the predicted value sent by the first data processing module, and inputs the dataset and the predicted value into a preset loss function.

[0034] The training update module obtains the gradient of the parameters of the machine learning model based on the loss function, updates the gradient on the manifold curve through gradient constraint processing, reduces the loss function, obtains the change value of the loss function, and determines whether the change value meets the preset convergence requirement. If yes, the training ends and the machine learning model is used for the tomography of the subprocess to be measured. If not, the dataset is re-acquired.

[0035] It also includes a control system for quantum process tomography, comprising:

[0036] The second data processing module acquires the measured dataset;

[0037] The second model processing module receives the dataset sent by the second data processing module and inputs it into the machine learning model to obtain a prediction matrix;

[0038] The evaluation module processes the prediction matrix to obtain the fidelity between the prediction matrix and the preset ideal matrix, and determines whether it meets a preset threshold. If yes, the prediction matrix output by the machine learning model is used to characterize the quantum process characteristics; otherwise, the machine learning model updates its parameters through a loss function, and the dataset is input into the updated machine learning model to obtain an updated prediction matrix, until the fidelity between the obtained prediction matrix and the ideal matrix meets the preset threshold.

[0039] It also includes a computer-readable storage medium storing a computer program for running a training method, wherein the computer program causes a computer to perform the training method as described in any of the above-described technical solutions.

[0040] It also includes an electronic device, comprising:

[0041] One or more processors; memory; and

[0042] One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including a training method as described in any of the above technical solutions.

[0043] The above technical solution has the following beneficial effects:

[0044] 1. By using gradient constraint processing, the gradient of the loss function and the parameters of the machine learning model is updated on the manifold curve, and the gradient is shrunken. This achieves efficient optimization with built-in physical constraints, ensuring that the quantum process tomography results always meet the requirements of complete positive definiteness and trace preservation. This allows the machine learning model to always maintain the complete positive definiteness-trace preservation condition during training, avoiding unreasonable or difficult-to-understand results.

[0045] 2. The parameters of the machine learning model are updated according to the designed loss function. The change in the loss function is used to determine whether the machine learning model has completed training, so as to continuously monitor the convergence of the loss function and achieve high convergence accuracy.

[0046] 3. The trained machine learning model is used to generate a prediction matrix. By processing the matrix to obtain the fidelity between the prediction matrix and the ideal matrix, it can not only accurately describe the quantum process to be measured, but also provide intuitive information about the quantum process, thus avoiding unreasonable results. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of this disclosure or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 Here is a flowchart of the training method proposed in this disclosure;

[0049] Figure 2 This is a flowchart of gradient updates on the manifold curve in this disclosure;

[0050] Figure 3 This is a flowchart of gradient shrinkage processing in this disclosure;

[0051] Figure 4 This is a flowchart of the quantum process tomography method proposed in this disclosure;

[0052] Figure 5 This is a schematic diagram of the structural principle of the training system proposed in this disclosure;

[0053] Figure 6 This is a schematic diagram of the control system proposed in this disclosure;

[0054] Figure 7 This is a schematic diagram of gradient constraint processing in this disclosure;

[0055] Figure 8 This is a schematic diagram of the ideal matrix in this disclosure;

[0056] Figure 9 This is a schematic diagram of the prediction matrix in this disclosure;

[0057] Figure 10 This is a training variation diagram of the loss function in this disclosure.

[0058] Legend:

[0059] 1. First data processing module; 2. First model processing module; 3. Training and update module; 4. Second data processing module; 5. Second model processing module; 6. Evaluation module. Detailed Implementation

[0060] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this disclosure.

[0061] Currently, existing quantum process tomography methods generally employ approaches such as Neural Network Quantum State Tomography (NNQST) and Variational Quantum Process Tomography (VQPT). NNQST utilizes a neural network model to learn the parameterized representation of quantum states from experimental data, thereby recovering the information of the quantum states. This method can effectively handle high-dimensional quantum states and, in some cases, achieve high accuracy with relatively little data. VQPT achieves efficient learning of quantum processes by combining classical optimization algorithms with quantum circuit simulation. VQPT runs a specifically designed circuit on a quantum computer and iteratively updates the circuit parameters using optimization algorithms on a classical computer, ultimately obtaining a model that approximates the target quantum process. This method is applicable not only to continuous variable (CV) and discrete variable (DV) quantum systems but also maintains good performance under noisy conditions.

[0062] While the aforementioned methods have achieved some success, they still face limitations in efficiency and scalability when dealing with large-scale quantum systems. Furthermore, there is room for improvement in ensuring the physical consistency of the recovered process (such as complete positivity and trace preservation).

[0063] To address the aforementioned issues, this disclosure provides a training method based on a machine learning model, achieved by learning the Kraus operator for quantum processes. According to Kraus's theorem, the Kraus operator can represent any perfectly positive definite linear mapping, and the number of Kraus terms can be flexibly adjusted to accommodate various low-rank reconstructions. Quantum process estimation is viewed as a learning task performed using batches of measurement data, similar to the training of neural networks. By constructing a method that ensures perfect positive definiteness and employing efficient gradient descent to implement orthogonal normalization constraints, the trace preservation condition is always satisfied during optimization. Through gradient descent optimization techniques, combined with Kraus operator representation and optimization on the Stiefel manifold, quantum processes can be efficiently and accurately recovered from measurement data, successfully overcoming the problems of high resource consumption, noise sensitivity, insufficient physical consistency guarantees, and poor interpretability faced by existing quantum process tomography methods.

[0064] In some embodiments of this disclosure, reference is made to Figure 1 This disclosure provides a training method based on a machine learning model, comprising:

[0065] S11. Obtain the dataset, input the dataset into the machine learning model to obtain the predicted value, wherein the dataset is the measurement value obtained by measuring the quantum state through the subprocess to be measured;

[0066] S12. Input the measured and predicted values ​​into the preset loss function. The gradient of the parameters of the machine learning model is obtained by processing the loss function. The gradient is updated on the manifold curve through gradient constraint processing, thereby reducing the loss function.

[0067] S13. Obtain the change value of the loss function and determine whether the change value meets the preset convergence requirement. If so, end the training and use the machine learning model for the tomography of the subprocess to be measured.

[0068] If not, return to step S11 and retrieve the dataset again.

[0069] Specifically, obtaining the input quantum state ρ i This allows the quantum state to generate the corresponding output state ρ′ through the measured subprocess P. i =P(ρ i Each output state uses a set of preset measurement operators M. j Perform multiple measurements, average the results of each measurement, and obtain an estimate d of the expected value of the output state with respect to different measurement operators. ij To simulate statistical fluctuations in actual measurements, each expected value is estimated by d. ij The measurements include random noise sampled from a Gaussian distribution G(0, ∈) with zero mean and standard deviation ∈ ∈, ensuring the accuracy and reliability of the data collection. By taking multiple sets of measurements and inputting them into a machine learning model, corresponding predicted values ​​can be obtained.

[0070] The measured and predicted values ​​are input into a preset loss function to quantify the difference between the measured and predicted values, obtaining the gradient of the loss function relative to the machine learning model parameters. Gradient constraint processing is used to update the gradient on the manifold curve, reducing the loss function. The parameters of the machine learning model are updated accordingly, and the change value of the loss function is obtained. Based on the change value, it is determined whether the loss function meets the convergence requirement. If it does, the training of the machine learning model is completed, and the machine learning model is used for quantum process tomography. If it does not meet the requirement, a new dataset is obtained to update the gradient of the loss function and the machine learning model parameters.

[0071] Furthermore, existing methods use Choi matrix representation because it makes it easier to handle positive definite trace preservation (CPTP) constraints, and the problem can be formulated in linear form.

[0072] This disclosure provides the flexibility to select the rank to be used in the process, thereby achieving a low-rank approximation without constructing a complete Choi matrix. The complexity of the machine learning model is balanced with physical plausibility by controlling r. The specific principle is as follows:

[0073] The equivalence of the Choi matrix rank to the number of Kraus operators: According to quantum information theory, the Choi matrix rank *r* of a quantum process is given by the minimum number of Kraus operators required to represent that process. The maximum Choi matrix rank is *r = n*. 2 (where n is the number of qubits), but in reality, the Choi matrix of a quantum process can have a low rank r << n. 2 (For unitary processes, r = 1).

[0074] When r > 1, it corresponds to a mixed-state process or a noisy channel. In this case, the number of Kraus operators reflects the complexity of the process (e.g., the number of noise modes). Therefore, by adjusting r, quantum processes under different physical scenarios can be adapted. By dynamically adjusting the number of Kraus operators, measurements with different noise levels can be accommodated, improving overall robustness and reliability.

[0075] Based on the universally low-rank property of quantum processes, this embodiment is applicable to the efficient characterization of various quantum systems. It can not only accurately describe the subprocess to be measured, but also provide intuitive information about the physical mechanism of the subprocess to be measured.

[0076] In some embodiments of this disclosure, the loss function consists of least squares error loss and L1 regularization loss.

[0077] Specifically, to accurately reconstruct the measurand P, a loss function L is constructed to quantify the difference between the measured and predicted values. By adjusting the parameters of the machine learning model to minimize the loss function L, the estimation of the measurand P can be progressively optimized, ultimately achieving high-precision quantum process reconstruction. The loss function L combines least squares error loss and L1 regularization loss.

[0078]

[0079] in, It is a kN×N stacked operator matrix, representing the measurement of a quantum process by stacking k Kraus operators, where N is the qubit dimension and K is the operator matrix. It is the L1 norm, α is the regularization strength, α≥0, optional, α=10 -3 , The least squares error loss represents the predicted value of the machine learning model. It measures the difference between the predicted value and the measured value, ensuring that the machine learning model can accurately fit the measured value. The L1 regularization loss is the L1 norm multiplied by a small weighting coefficient α = 10. -3 This is used to prevent machine learning models from overfitting by penalizing larger weight values ​​to promote sparsity in machine learning models.

[0080] In some embodiments of this disclosure, reference is made to Figure 2 Updating the gradient on the manifold curve through gradient constraint processing includes:

[0081] S121. Initialize the operator matrix and process the gradients of the machine learning model parameters;

[0082] S122. Determine a descent direction in the tangent space of the manifold, project the gradient onto the tangent space to obtain the tangent vector, and update the gradient.

[0083] S123. Determine whether the gradient update satisfies the descent direction of the manifold constraint. If not, perform gradient shrinkage. If yes, complete the update.

[0084] To minimize the loss function, optionally, through the negative conjugate gradient. Update stacked operator matrix This can be achieved. However, simple gradient descent may lead to results that violate the trace preservation constraint, which is equivalent to the orthogonality condition satisfied by the Kraus operator. To address the issue of violating trace preservation constraints, existing methods typically involve adding a penalty term, such as adding a penalty term to the loss function. To reduce this bias, existing methods cannot strictly guarantee the orthogonality condition.

[0085] Reference Figure 7 Instead of using existing methods, this disclosure processes the gradient of the parameters according to the Stiefel manifold.

[0086] Specifically, the orthogonality condition of the Kraus operator defines the Stiefel manifold. During optimization, gradient constraints and shrinkage can be used to ensure that the optimization process never deviates from this manifold.

[0087] Initialize the operator matrix and process the gradients of the obtained machine learning model parameters. Through the tangent space of the manifold A descent direction is determined. The gradient is projected onto the tangent space to obtain the tangent vector. The gradient is updated along any curve on the manifold, at the operator matrix K, where the tangent space T of the Stiefel manifold is...K S t (k, N) 2 ) is defined as all that satisfy The set of tangent vector matrices V ensures that the descent direction conforms to the manifold constraint.

[0088] During gradient updates, the gradient is normalized using the L2 norm, i.e.:

[0089]

[0090] To avoid the learning rate being too large and causing the update step size to get out of control, it is determined whether the gradient update satisfies the descent direction of the manifold constraint. If not, the gradient is shrunk; if so, the gradient update is completed.

[0091] Furthermore, the initial operator matrices need to be normalized to ensure they are fully positive definite trace-preserving (CPTP), achieved by randomly generating an N matrix. 2 ×N 2 A unitary matrix Ur, corresponding to a pure-state quantum process such as an ideal quantum gate, satisfies complete positive definiteness. Normalization is performed to accommodate the rank of the Kraus operator: if the number of Kraus operators is pre-defined as r, the first r columns of the unitary matrix Ur are selected to form an N2×r matrix, and then normalization is performed: each column of the unitary matrix Ur is divided by... The initial Kraus operator matrix is ​​obtained:

[0092] In some embodiments of this disclosure, reference is made to Figure 3 Gradient shrinking includes:

[0093] S1231. Obtain the stacking matrix by processing the update amount of the tangent space and the operator matrix;

[0094] S1232. The stacking matrix is ​​processed according to the preset learning rate, so that the gradient is updated along the descent direction that satisfies the manifold constraint.

[0095] Specifically, the gradient updates in Euclidean space are mapped onto the manifold through a shrinking process to minimize the loss function while preserving the manifold constraints. A stacking matrix is ​​obtained based on the update amount of the tangent space and the operator matrix. This stacking matrix is ​​used to construct the tangent space basis. The shrinking formula can be derived from the stacking matrix as follows:

[0096]

[0097] In this context, the stacking matrices are denoted by Q = [G, K] and N = [K, -G]. Q represents the horizontal stacking of the tangent space update quantity G with the operator matrix K, and N represents the horizontal stacking of the operator matrix K with the negative tangent space update quantity -G. Q and K are used to construct different basis vectors of the manifold tangent space. A is a constant factor used to ensure the correctness of the update direction, and η is the learning rate, which adopts an exponential decay strategy, set to 0.1, and decays by a factor of 0.999 in each training iteration. Calculate the current stacking operator matrix The projection in the orthogonal complement space is used to identify components that violate the trace preservation constraint. By using inverse matrix operations to suppress components that deviate from the manifold in the update direction, gradient updates are made along the tangent space direction.

[0098] This formula uses matrix inversion and multiplication to transform the gradient into an update direction on the manifold, allowing for iterative gradient updates. make sure satisfy Implement minimizing the loss function At the same time, maintain On the Stiefel manifold.

[0099] In some embodiments of this disclosure, the convergence requirements include:

[0100] If the change value satisfies a preset first standard value over a consecutive number of training iterations, then convergence is indicated, or

[0101] If the number of training iterations is within the preset second standard value, and the change value does not meet the first standard value, then training ends and the current minimum loss function is obtained.

[0102] Specifically, the convergence of the machine learning model is determined by the change in the loss function. The convergence is defined as follows: if the change in the loss function is less than a first criterion value within 100 consecutive training iterations, then the comprehensive loss function has converged. Optionally, the first criterion value is 10. -6 Alternatively, if the number of training iterations is within the second standard value and the change is not less than the first standard value, then training ends. Optionally, the second standard value is 10. 4 The number of training sessions reached 10. 4 However, it was still not less than 10 times the first standard value. -6 When the minimum loss function is reached, training ends and the current minimum loss function is obtained. The value of the loss function after each training iteration is continuously recorded (refer to...). Figure 10 This is to facilitate monitoring the convergence of the loss function during training.

[0103] In some embodiments of this disclosure, reference is made to Figure 4 It also includes a quantum process tomography method based on a machine learning model, comprising:

[0104] S21. Obtain the measurement dataset, wherein the dataset consists of the measurement values ​​obtained by processing the quantum state through the subprocess to be measured;

[0105] S22. The dataset is input into the machine learning model for processing to obtain the prediction matrix;

[0106] S23. Process the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset threshold.

[0107] If so, the prediction matrix is ​​used to represent the subprocess to be measured, and the process ends;

[0108] If not, the gradient of the machine learning model parameters is updated by the loss function to obtain the updated machine learning model;

[0109] S24. Input the dataset into the updated machine learning model to obtain the updated prediction matrix and return to step S23.

[0110] Specifically, a set of real Kraus operators is generated to simulate quantum processes, and a Choi matrix is ​​constructed based on the Kraus operators as a pre-defined ideal matrix (see...). Figure 8 The trained machine learning model is used for quantum process tomography to obtain a measurement dataset. This dataset is then input into the machine learning model, and the corresponding operators are obtained based on the dataset. The dataset is then transformed into a prediction matrix based on the operators (see [reference]). Figure 9 The process obtains the fidelity between the predicted matrix and the ideal matrix. The preset threshold can be set to 98%. When the fidelity is greater than 98%, it is considered that the predicted matrix can accurately reflect the subprocess to be measured. If it is not greater than the threshold, the gradient of the machine learning model parameters is updated. Under the gradient constraint processing, the updated parameters of the machine learning model are obtained, and the predicted matrix is ​​regenerated.

[0111] Table 1 presents three sets of examples, demonstrating the convergence and accuracy of the prediction matrix at different quantum system scales:

[0112]

[0113]

[0114] Table 1

[0115] In benchmark tests of random processes with 3 qubits, a high fidelity of 99.87% can be achieved, which is significantly better than existing maximum likelihood estimation and Bayesian estimation quantum process tomography techniques. Furthermore, because it can reconstruct the measured subprocess with fewer random measurements, it is not only applicable to 3-qubit systems but can also be extended to larger-scale quantum systems, such as at least 5 qubits, maintaining a high fidelity of 98.2%.

[0116] In some embodiments of this disclosure, the data set is input into a machine learning model to obtain a prediction matrix, including:

[0117] The machine learning model obtains the corresponding operators based on the dataset. After linear combination of the operators, the matrix is ​​input into the matrix definition to obtain the prediction matrix.

[0118] Specifically, the parameters of the trained machine learning model are transformed into Kraus operators, based on quantum information theory. The isomorphic transformation to a Choi matrix involves the following steps and mathematical principles:

[0119] Linear combination representation of the Kraus operator: The Kraus representation of the subprocess to be measured is: in, r is the rank of the Choi matrix (the minimum number of Kraus operators required), K l It is an N×N dimensional matrix.

[0120] Substituting the Krauss representation into the definition of the Choi matrix, we get:

[0121]

[0122] in: The matrix * denotes the direct product (Kronecker product); * denotes complex conjugate; and T denotes transpose. This indicates the conjugate transpose.

[0123] yes Maximum entanglement in dimensionality, where N is the dimension of the quantum system, such as N=2. n , where n is the number of qubits.

[0124] In some embodiments of this disclosure, reference is made to Figure 5 It also includes a training system for a machine learning model, comprising:

[0125] First data processing module 1 acquires a dataset, wherein the dataset consists of quantum states processed by a subprocess to be measured to obtain measured values, and the dataset is input into a machine learning model to obtain predicted values.

[0126] First model processing module 2 establishes a machine learning model, receives the dataset and the predicted value sent by the first data processing module, and inputs the dataset and the predicted value into a preset loss function;

[0127] Training update module 3 obtains the gradient of the parameters of the machine learning model based on the loss function, updates the gradient on the manifold curve through gradient constraint processing, reduces the loss function, obtains the change value of the loss function, and determines whether the change value meets the preset convergence requirement. If yes, training ends and the machine learning model is used for the tomography of the subprocess to be measured. If not, the dataset is re-acquired.

[0128] Specifically, the first data processing module 1 obtains the corresponding dataset and predicted value based on the known quantum state and through the measured subprocess and machine learning model, respectively.

[0129] The first model processing module 2 establishes a machine learning model, receives the dataset and predicted values ​​sent by the first data processing module 1, and inputs them into a preset loss function to perform gradient updates of the machine learning model parameters.

[0130] Training and update module 3 updates the gradient on the manifold curve through gradient constraint processing. It determines a descent direction in the tangent space of the manifold, so that the machine learning model parameters move along any curve on the manifold. It also suppresses the components in the update direction that deviate from the manifold through shrinkage processing, and gradually reduces the value of the loss function. It judges whether the change value of the loss function meets the preset convergence requirements. If yes, the training of the machine learning model is completed. If not, it re-acquires quantum states for training until the change value meets the preset convergence requirements.

[0131] In some embodiments of this disclosure, reference is made to Figure 6 It also includes a control system for quantum process tomography, comprising:

[0132] The second data processing module 4 acquires the measured dataset;

[0133] The second model processing module 5 receives the dataset sent by the second data processing module 4 and inputs it into the machine learning model to obtain the prediction matrix.

[0134] Evaluation module 6 processes the prediction matrix to obtain the fidelity between the prediction matrix and the preset ideal matrix, and determines whether it meets the preset threshold. If it does, the prediction matrix is ​​used to represent the sub-process to be measured, and the process ends. If not, the gradient of the machine learning model parameters is updated through the loss function to obtain an updated machine learning model. The dataset is input into the updated machine learning model to obtain an updated prediction matrix, until the fidelity meets the preset threshold.

[0135] Specifically, the second data module 4 receives the measured dataset for quantum process tomography. The second model processing module 5 receives the dataset and inputs it into the trained machine learning model to obtain a prediction matrix. The evaluation module 6 receives the prediction matrix sent by the second model processing module 5 and processes it according to a preset ideal matrix to obtain a fidelity, which represents the similarity between the prediction matrix and the ideal matrix. If the fidelity meets a preset threshold, it means that the prediction matrix can accurately represent the measured subprocess, and the quantum process tomography ends. If it does not meet the threshold, the dataset is reacquired, the machine learning model is updated, the dataset is input into the machine learning model to obtain an updated prediction matrix, and the fidelity is obtained again by processing it with the ideal matrix until the fidelity meets the preset threshold.

[0136] In some embodiments of this disclosure, an embodiment of a computer-readable storage medium is also included, which stores a computer program for running a training method, wherein the computer program causes a computer to perform the following steps:

[0137] S11. Obtain the dataset, input the dataset into the machine learning model to obtain the predicted value, wherein the dataset is the measurement value obtained by measuring the quantum state through the subprocess to be measured;

[0138] S12. Input the measured and predicted values ​​into the preset loss function. The gradient of the parameters of the machine learning model is obtained by processing the loss function. The gradient is updated on the manifold curve through gradient constraint processing, thereby reducing the loss function.

[0139] S13. Obtain the change value of the loss function and determine whether the change value meets the preset convergence requirement. If so, end the training and use the machine learning model for the tomography of the subprocess to be measured.

[0140] If not, return to step S11 and retrieve the dataset again.

[0141] The computer-readable storage medium can be a computer storage medium or a communication medium. A communication medium includes any medium that facilitates the transfer of a computer program from one location to another. A computer storage medium can be any available medium accessible to a general-purpose or special-purpose computer. For example, a computer-readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the computer-readable storage medium. Of course, the computer-readable storage medium can also be a component of the processor. The processor and the computer-readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the ASIC can reside in a user equipment. Of course, the processor and the computer-readable storage medium can also exist as discrete components in a communication device.

[0142] Specifically, the computer-readable storage medium can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as Static Random-Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium accessible to general-purpose or special-purpose computers.

[0143] In some embodiments of this disclosure, an electronic device is also included, comprising:

[0144] One or more processors; memory; and

[0145] One or more programs, wherein the programs are stored in memory and configured to be executed by one or more processors, the programs including steps for performing the following:

[0146] S11. Obtain the dataset, input the dataset into the machine learning model to obtain the predicted value, wherein the dataset is the measurement value obtained by measuring the quantum state through the subprocess to be measured;

[0147] S12. Input the measured and predicted values ​​into the preset loss function. The gradient of the parameters of the machine learning model is obtained by processing the loss function. The gradient is updated on the manifold curve through gradient constraint processing, thereby reducing the loss function.

[0148] S13. Obtain the change value of the loss function and determine whether the change value meets the preset convergence requirement. If so, end the training and use the machine learning model for the tomography of the subprocess to be measured.

[0149] If not, return to step S11 and retrieve the dataset again.

[0150] A memory is used to store computer programs. This memory may include high-speed random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0151] A processor is used to execute computer programs stored in memory. The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0152] Optionally, the memory can be either standalone or integrated with the processor.

[0153] When memory is a device independent of the processor, electronic devices may also include a bus. This bus is used to connect the memory and the processor. This bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc.

[0154] It should be noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of software products. These computer software products can be stored in computer-readable storage media, such as ROM / RAM, magnetic disks, optical disks, etc., and include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or certain portions of the embodiments. In this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further restrictions, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0155] Finally, it should be noted that the above description is only a preferred embodiment of this disclosure and is not intended to limit this disclosure. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the protection scope of this disclosure.

Claims

1. A training method based on a machine learning model, characterized in that, include: S11. Obtain a dataset, which is input into a machine learning model to obtain predicted values, wherein the dataset is the measurement value obtained by measuring the quantum state through the subprocess to be measured; S12. The measured value and the predicted value are input into a preset loss function. The gradient of the parameters of the machine learning model is obtained by processing according to the loss function. The gradient is updated on the manifold curve through gradient constraint processing, thereby reducing the loss function. S13. Obtain the change value of the loss function, determine whether the change value meets the preset convergence requirement, if so, end the training, and use the machine learning model for the tomography of the subprocess to be measured. If not, return to step S11 and retrieve the dataset again.

2. The training method according to claim 1, characterized in that, The loss function consists of least squares error loss and L1 regularization loss.

3. The training method according to claim 1, characterized in that, The step of updating the gradient on the manifold curve through gradient constraint processing includes: Initialize the operator matrix; In the tangent space of the manifold, a descent direction is determined, and the gradient is projected onto the tangent space to obtain a tangent vector, thereby updating the gradient. When determining the gradient update, it is determined whether the operator matrix satisfies the descent direction of the manifold constraint. If not, the gradient is shrunk; if so, the update is completed.

4. The training method according to claim 3, characterized in that, The gradient shrinking process includes: The stacking matrix is ​​obtained by processing the update amount of the tangent space and the operator matrix. The stacked matrix is ​​processed according to a preset learning rate, so that the gradient is updated along the descent direction that satisfies the manifold constraint.

5. The training method according to claim 1, characterized in that, The convergence requirements include: If the change value meets a preset first standard value within a consecutive number of training iterations, it indicates convergence, or If the number of training iterations is within a preset second standard value, and the change value does not meet the first standard value, then training ends, and the current minimum loss function is obtained.

6. A quantum process tomography method based on a machine learning model, characterized in that, include: S21. Obtain the measurement dataset, wherein the dataset consists of measurement values ​​obtained by processing the quantum state through the subprocess to be measured; S22. The dataset is input into a machine learning model for processing to obtain a prediction matrix; S23. Process the results to obtain the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset threshold. If so, the prediction matrix is ​​used to represent the subprocess to be measured, and the process ends; If not, the gradient of the machine learning model parameters is updated using the loss function to obtain the updated machine learning model; S24. The dataset is input into the updated machine learning model to obtain the updated prediction matrix and return to step S23.

7. The quantum process tomography method according to claim 6, characterized in that, The dataset is input into the machine learning model to obtain a prediction matrix, including: The machine learning model obtains the corresponding operators based on the dataset, and the operators are linearly combined and input into the matrix definition to obtain the prediction matrix.

8. A training system for a machine learning model, characterized in that, include: The first data processing module acquires a dataset, which is a quantum state processed by a subprocess to be measured to obtain measurement values, and the dataset is input into a machine learning model to obtain prediction values. The first model processing module establishes a machine learning model, receives the dataset and the predicted value sent by the first data processing module, and inputs the dataset and the predicted value into a preset loss function. The training update module obtains the gradient of the parameters of the machine learning model based on the loss function, updates the gradient on the manifold curve through gradient constraint processing, reduces the loss function, obtains the change value of the loss function, and determines whether the change value meets the preset convergence requirement. If yes, the training ends and the machine learning model is used for the tomography of the subprocess to be measured. If not, the dataset is re-acquired.

9. A control system for quantum process tomography, characterized in that, include: The second data processing module acquires the measured dataset; The second model processing module receives the dataset sent by the second data processing module and inputs it into the machine learning model to obtain a prediction matrix; The evaluation module processes the prediction matrix to obtain the fidelity between the prediction matrix and the preset ideal matrix, and determines whether it meets the preset threshold. If yes, the prediction matrix is ​​used to represent the sub-process to be measured, and the process ends. If no, the gradient of the machine learning model parameters is updated through the loss function to obtain an updated machine learning model. The dataset is input into the updated machine learning model to obtain an updated prediction matrix, until the fidelity meets the preset threshold.

10. A computer-readable storage medium, characterized in that, It stores a computer program for running a training method, wherein the computer program causes a computer to perform the training method as described in any one of claims 1-5.

11. An electronic device, characterized in that, include: One or more processors; Memory; as well as One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including methods for performing the training method as described in any one of claims 1-5.

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