Quantum process chromatography method based on neural network, control system, storage medium and electronic equipment

Abstract

The invention provides a quantum process chromatography method based on a neural network, a control system, a storage medium and electronic equipment. The method comprises the following steps: acquiring a measured data set; inputting the data set into a neural network model to obtain a prediction matrix; processing to obtain fidelity between the prediction matrix and a preset ideal matrix, and judging whether a preset first threshold value is met or not; if yes, representing the quantum process by using the output prediction matrix, and if not, updating parameters of the neural network model through a comprehensive loss function; inputting the data set to obtain an updated prediction matrix; by constructing the neural network model to process the input data set, the neural network model can efficiently learn the quantum process from the data set, so that the quantum process matrix is more efficiently recovered, dependence on a large amount of experimental data is reduced, calculation time and resource requirements are reduced, and calculation efficiency is improved. And performing parameter updating on the neural network model through the comprehensive loss function to ensure that the neural network model can accurately fit the data set.

Description

Technical Field

[0001] This disclosure relates to the field of quantum computing, and more particularly to a method for quantum process tomography based on neural networks, a control system, a storage medium, and an electronic device. 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 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 comprehensively revealing the properties of the quantum process.

[0003] Existing quantum process tomography methods for preparing and measuring large numbers of quantum states typically rely on extensive experimental data and complex mathematical calculations, which are not only time-consuming but also costly. When dealing with large-scale quantum systems, the demand for computational resources grows exponentially, severely limiting practical applications. Furthermore, due to the influence of noise and systematic errors, the estimation results are often unstable and it is difficult to guarantee high accuracy. Summary of the Invention

[0004] To address the shortcomings of existing quantum process tomography methods, this disclosure proposes a neural network-based quantum process tomography method, control system, storage medium, and electronic device. By constructing a neural network model, the quantum process can be recovered more efficiently, reducing reliance on large amounts of experimental data, reducing processing time and resource requirements, and ensuring consistency between the predicted matrix and the ideal matrix.

[0005] To achieve the above objectives, this disclosure provides a quantum process tomography method based on neural networks, comprising:

[0006] Step S1: Obtain the measurement dataset, wherein the dataset is the expected value obtained by processing the quantum state through the subprocess to be measured;

[0007] Step S2: The dataset is input into the neural network model to obtain the prediction matrix;

[0008] Step S3: Process the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset first threshold.

[0009] If so, the prediction matrix output by the neural network model is used to characterize the quantum process, and the process ends.

[0010] If not, the neural network model updates its parameters using a comprehensive loss function and proceeds to step S4;

[0011] Step S4: The dataset is input into the updated neural network model to obtain the updated prediction matrix and then the process returns to step S3.

[0012] Optionally, methods for obtaining the measurement dataset include:

[0013] The quantum state is used to obtain the output state through the subprocess to be measured;

[0014] The output state is measured multiple times according to a set of preset measurement operators to obtain the expected values ​​corresponding to different measurement operators as the dataset.

[0015] Optionally, the method for inputting the dataset into the neural network model to obtain the prediction matrix includes:

[0016] The neural network model is used to obtain the prediction operator corresponding to the dataset, and the prediction matrix is ​​obtained by processing the prediction operator.

[0017] Optionally, the method by which the neural network model updates its parameters through a comprehensive loss function includes:

[0018] The neural network model is initialized with parameters;

[0019] The input dataset is received to obtain the corresponding predicted value, and a comprehensive loss function is obtained by processing the predicted value and the dataset.

[0020] The gradient of the neural network model is obtained by processing the comprehensive loss function.

[0021] The parameters of the neural network model are updated based on the gradient.

[0022] Optionally, the comprehensive loss function includes a weighted sum of mean squared error loss, L1 regularization loss, and trace distance loss.

[0023] Optionally, the method for updating the parameters of the neural network model based on the gradient includes:

[0024] The first-order moment estimate and the second-order moment estimate of the gradient are obtained by processing, and the first-order moment estimate and the second-order moment estimate are corrected for deviation.

[0025] The parameters of the neural network model are updated based on the corrected first-order moment estimates and second-order moment estimates.

[0026] Optionally, the neural network model receives the dataset, maps the data of the dataset through at least one or more fully connected layers and activation functions, and obtains the operator tensor corresponding to the dataset.

[0027] This disclosure also includes a neural network-based quantum process tomography control system, comprising:

[0028] The data processing module acquires the measured dataset;

[0029] The neural network module constructs a neural network model, receives the dataset sent by the data processing module to train the neural network model, and obtains the corresponding prediction matrix based on the dataset.

[0030] The processing and evaluation module processes the fidelity between the predicted matrix and the preset ideal matrix, and determines whether it meets a preset first threshold. If yes, the predicted matrix output by the neural network model is used to characterize the quantum process; otherwise, the neural network model updates its parameters through a comprehensive loss function, inputs the dataset into the updated neural network model, and obtains an updated predicted matrix, until the fidelity between the obtained predicted matrix and the ideal matrix meets the preset first threshold.

[0031] This disclosure also includes a computer-readable storage medium storing a computer program for running a quantum process tomography method, wherein the computer program causes a computer to perform the quantum process tomography method as described in any of the above technical solutions.

[0032] This disclosure also includes an electronic device comprising:

[0033] One or more processors; memory; and

[0034] 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 quantum process tomography as described in any of the above technical solutions.

[0035] The above technical solution has the following beneficial effects:

[0036] 1. The quantum state is processed through the subprocess to be measured to obtain a dataset. The dataset is input into the neural network model to obtain a prediction matrix. The fidelity between the prediction matrix and the preset ideal matrix is ​​obtained. The parameters of the neural network model are updated to make the prediction matrix meet the first threshold, so that the neural network model can efficiently learn the quantum process from the dataset, thereby more efficiently recovering the quantum process matrix, reducing the dependence on a large amount of experimental data, and reducing the time and resource requirements for processing.

[0037] 2. The gradient of the neural network model is obtained by processing the comprehensive loss function. The parameters of the neural network model are updated by the gradient, so that the comprehensive loss function is reduced until the second threshold is met. After convergence, the training of the neural network model is completed, ensuring that the neural network model can accurately fit the dataset and recover the Choi matrix of the quantum process from the dataset more accurately, thereby improving the accuracy and robustness of the prediction matrix. Attached Figure Description

[0038] 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.

[0039] Figure 1 This is a flowchart of the quantum process tomography method proposed in this disclosure;

[0040] Figure 2 A flowchart illustrating the method for obtaining the measurement dataset in this disclosure;

[0041] Figure 3 This is a flowchart illustrating the method by which the neural network model updates parameters using a comprehensive loss function in this disclosure;

[0042] Figure 4 This is a flowchart of the method for updating the parameters of a neural network model based on gradients in this disclosure;

[0043] Figure 5 Here is a flowchart of the training method proposed in this disclosure;

[0044] Figure 6 This is a schematic diagram of the control system proposed in this disclosure;

[0045] Figure 7 This is a comparison chart of the fidelity between the predicted matrix and the ideal matrix in this disclosure;

[0046] Figure 8 This is a graph showing how the overall loss function changes with the number of training iterations in this disclosure.

[0047] Legend:

[0048] 1. Data processing module; 2. Neural network module; 3. Processing and evaluation module; 4. Optimization and training module. Detailed Implementation

[0049] 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.

[0050] Existing quantum process tomography methods for preparing and measuring large numbers of quantum states are not only time-consuming and costly, but the increasing demand for computing resources limits their practical applications and makes it difficult to guarantee high accuracy.

[0051] In some embodiments of this disclosure, reference is made to Figure 1 This disclosure provides a quantum process tomography method based on neural networks, comprising:

[0052] Step S1: Obtain the measurement dataset, wherein the dataset consists of the expected values ​​of the quantum state obtained by processing the quantum state through the subprocess to be measured;

[0053] Step S2: Input the dataset into the neural network model to obtain the prediction matrix;

[0054] Step S3: Process the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset first threshold.

[0055] If so, the prediction matrix output by the neural network model will be used to characterize the quantum process, and the process will end.

[0056] If not, the neural network model updates its parameters using the comprehensive loss function and proceeds to step S4;

[0057] Step S4: Input the dataset into the updated neural network model to obtain the updated prediction matrix and return to step S3.

[0058] Specifically, a quantum state is the state of a qubit, and the measured subprocess refers to a quantum operation or evolution process that is precisely described and understood. The quantum state is input into the measured subprocess for processing to obtain an expected value. This expected value is then used as a dataset and input into a neural network model for calculation and processing to obtain a prediction matrix. The prediction matrix is ​​compared with the ideal matrix for fidelity calculation, and the resulting fidelity is compared with a preset first threshold. The first threshold ranges from 0 to 1; the closer it is to 1, the closer the prediction matrix is ​​to the ideal matrix. The first threshold is set based on a quantum error correction threshold. For example, an error rate of 1% is equivalent to a fidelity of 99%. The system then checks whether the preset first threshold is met. If it is, the predicted matrix output by the neural network is very close to the ideal matrix. The output predicted matrix is ​​used to characterize the quantum process. The neural network model can learn the Kraus operator from the dataset to recover the Choi matrix of the quantum process and use the neural network model to describe the measured subprocess. If the preset first threshold is not met, the neural network model is considered to have a bias.

[0059] The ideal matrix is ​​constructed using the generated real Kraus operators as the standard for the ideal model. Kraus operators represent the basic units of quantum processes, satisfying certain conditions (such as orthogonality), and their number can be flexibly adjusted to adapt to different low-rank reconstructions to describe quantum processes. Kraus operators are initialized by dividing a random unitary matrix by the square root of the number of Kraus operators to ensure the complete positive (CP) condition during initialization. The ideal matrix is ​​then constructed using these Kraus operators.

[0060] The parameters of the neural network model are updated by using a comprehensive loss function, thereby improving the similarity between the predicted matrix and the ideal matrix. The dataset is input into the updated neural network model to obtain the updated predicted matrix, and then processed again to obtain the fidelity between the updated predicted matrix and the ideal matrix until the fidelity meets the preset first threshold, thus completing the parameter update of the neural network model.

[0061] Furthermore, refer to Figure 7 The predicted Choi matrix is ​​obtained by processing the predicted Kraus operator, and then the fidelity between the predicted matrix and the ideal matrix is ​​obtained. The fidelity represents the overlap between two quantum states, ranging from 0 to 1. A fidelity closer to 1 indicates greater similarity between the two matrices. For quantum states represented in density matrix form, the predicted matrix ρ... est With the ideal matrix ρ ideal The formula for the fidelity F between them is:

[0062]

[0063] Here, Tr is the mathematical symbol for finding the trace of a matrix. For example, if the first threshold is set to 0.98, and the fidelity is greater than 0.98, it is believed that the neural network model can recover the Choi matrix well and accurately reflect the quantum process.

[0064] Reference Figure 2 In some embodiments of this disclosure, the method for obtaining the measurement dataset includes:

[0065] S11: The quantum state obtains the output state through the subprocess to be measured;

[0066] S12: Perform multiple measurements on the output state according to multiple preset measurement operators to obtain the expected values ​​corresponding to different measurement operators as the dataset.

[0067] Specifically, the input quantum state is precisely prepared. When the input quantum state passes through the quantum process to be measured, the quantum state evolves according to specific physical laws. The measurement operator is used to measure the quantum process. Due to the randomness of quantum measurement, repeated measurements on the same quantum state can yield a reliable expected value. For each measurement operator, the average of the results of multiple measurements is the expected value corresponding to that operator. The expected values ​​corresponding to different measurement operators are used as a dataset.

[0068] First, prepare a series of known probe (input) quantum states ρ i These states are then passed through the measurand subprocess P to produce the corresponding output state ρ. j =P(ρ i Subsequently, for each output state ρ j Using a set of predefined measurement operators M j Perform multiple measurements, average the results of each measurement, and obtain the expected values ​​of the output state with respect to different measurement operators. Use these expected values ​​as the dataset input to the neural network model.

[0069] Furthermore, the dataset can be divided into a training set and a validation set, which are used for training the neural network model and calculating and validating the fidelity of the prediction matrix, respectively. The training set and validation set are randomly divided to ensure the similarity of the data distribution and improve the generalization ability of the neural network model. The training set accounts for a larger proportion, generally 70%-90%, while the validation set accounts for 10%-30%.

[0070] In some embodiments of this disclosure, the method of inputting a dataset into a neural network model to obtain a prediction matrix includes:

[0071] The prediction operators corresponding to the dataset are obtained through a neural network model, and the prediction matrix is ​​obtained by processing the prediction operators.

[0072] Specifically, the neural network model receives a dataset, extracts data features through multi-layer nonlinear transformations (such as the ReLU activation function), obtains the parameters of the Kraus operator, constructs a quantum process description based on the parameters of the Kraus operator, and uses the Choi matrix to map the quantum process into a matrix to obtain the prediction matrix.

[0073] Reference Figure 3 In some embodiments of this disclosure, the method for updating parameters of a neural network model through a comprehensive loss function includes:

[0074] S31: Initialize the parameters of the neural network model;

[0075] S32: Receive the input dataset to obtain the corresponding predicted value, and process the predicted value and dataset to obtain the comprehensive loss function;

[0076] S33: Obtain the gradient of the neural network model based on the comprehensive loss function;

[0077] S34: Update the parameters of the neural network model based on the gradient.

[0078] Specifically, the neural network model uses a random number generator to initialize its parameters, ensuring random initialization. After parameter initialization, the model receives the dataset, performs forward propagation on the input data, processes it to obtain the model's predictions, and then processes the data based on the predictions to obtain a comprehensive loss function. Based on the loss value, it performs backpropagation, uses automatic differentiation to obtain the gradient of the loss function with respect to the parameters, and sets the learning rate to 1e based on this gradient. -3 Updating the parameters of a neural network using optimization algorithms can effectively improve the convergence speed and stability of the model.

[0079] Furthermore, the gradient of the comprehensive loss function with respect to the parameters is obtained through automatic differentiation. Taking the weight matrix W and bias vector b of the fully connected layer in the neural network model as an example, during backpropagation, starting from the comprehensive loss function L, the gradient of the comprehensive loss function L with respect to each weight matrix W is obtained according to the chain rule. ij and bias vector b i The partial derivatives are used to obtain the gradient matrix. and gradient vector For example, in processing the mean squared error loss with respect to a certain weight W ij When calculating the gradient, the error between the predicted value and the dataset is first processed, and then the weight is differentiated based on the error. The gradient of the neural network parameters is obtained by backpropagation step by step.

[0080] In some embodiments of this disclosure, the overall loss function includes a weighted sum of mean squared error loss, L1 regularization loss of the operator, and trace distance loss;

[0081] Mean squared error loss (L2 loss) is the sum of the squared differences between the predicted value and the dataset;

[0082] L1 regularization loss is the norm of the operator;

[0083] The trace distance loss is the norm between the product of the conjugate transpose of the operator set and itself and the identity matrix.

[0084] Specifically, the neural network model updates its parameters using a comprehensive loss function L. This comprehensive loss function includes mean squared error loss (L2 loss), L1 regularization loss of the operator, and trace distance loss. The mean squared error loss is used to process the sum of the squared differences between the predicted value data-pred and the expected value data of the dataset. This sum is used to measure the difference between the predicted result and the actual data in the neural network model, ensuring that the neural network model can accurately fit the data. The algorithm formula is as follows:

[0085] L2 = Σ((data-data-pred) 2 );

[0086] The L1 regularization loss is used to obtain the L1 norm of the kraus-block operator, which is then multiplied by a weight coefficient. The operator block is the channel through which the operator interacts with the environment and the system. In this embodiment, the weight coefficient is set relatively small, at 0.001, to prevent overfitting of the neural network model and improve its generalization ability. By penalizing larger weight values, the sparsity of the neural network model is promoted. The algorithm formula is as follows:

[0087] L1=0.001·||kraus-block||1;

[0088] The trace distance loss (trance_cost) process yields the complete positive definiteness and normalization properties of the operator set. The operator set represents a quantum process by stacking multiple Kraus operators. These are treated as a whole during the loss function construction, first obtaining the conjugate transpose of the Kraus operators. With itself (kraus_op) m The result of multiplication, opsum, is then processed to obtain the L1 norm between opsum and the identity matrix I. This norm ensures that the Kraus operator satisfies the physical constraints of the quantum process, namely, complete positive definiteness and normalization conditions, guaranteeing that the reconstructed prediction matrix conforms to quantum physical laws. The algorithm formula is as follows:

[0089]

[0090] trace_cost = |lopsum - I||1;

[0091] The comprehensive loss function L is a weighted sum of the mean squared error loss, L1 regularization loss, and trace distance loss. The algorithm formula is as follows:

[0092] L=L2+0.001·L1+0.001·trace_cost;

[0093] By minimizing the comprehensive loss function, the neural network model can accurately fit the data and meet the physical consistency requirements, accurately recovering the Choi matrix of the quantum process from the input measurement data, thereby improving the performance of the neural network model and the accuracy of matrix reconstruction.

[0094] Reference Figure 4 In some embodiments of this disclosure, the method for updating the parameters of a neural network model based on gradients includes:

[0095] S341: Process the obtained first-order moment estimate and second-order moment estimate of the gradient, and correct the deviation of the first-order moment estimate and second-order moment estimate;

[0096] S342: Update the parameters of the neural network model based on the corrected first-order moment estimates and second-order moment estimates.

[0097] Specifically, the Adam optimizer updates the parameters based on the processed gradients. The Adam optimizer obtains the first moment estimate (mean) and second moment estimate (uncentered variance) of the gradient. For the gradient matrix... and gradient vector At each update step t, the first moment estimate m t The formula for calculating using the exponentially weighted moving average is:

[0098]

[0099] Where β1 is the decay rate of the first-order moment estimate, set to 0.9. This represents the gradient of the current step;

[0100] Second moment estimate V t The formula is:

[0101]

[0102] Here, β2 is the decay rate of the second-order moment estimate, set to 0.999. The estimates β1 and β2 are continuously updated with each update step to more accurately adjust the parameters.

[0103] Since the initial estimates of the first and second moments are both 0, there will be a bias. Therefore, it is necessary to correct the bias of the first and second moment estimates.

[0104] The corrected first-order moment estimate is:

[0105]

[0106] The corrected second-order moment estimate is:

[0107]

[0108] Where t is the current update step number. Bias correction helps the neural network model learn more stably in the early stages of training.

[0109] The parameters are updated using the corrected first-order moment estimates and second-order moment estimates. In this embodiment, the learning rate is set to α = 1e -3 The update formula for parameters θ (such as weight W and bias b) is:

[0110]

[0111] Where ∈ is a very small constant (usually taken as 1e). -8 This is used to prevent the denominator from being zero. For example, for the weight matrix W, each element W is updated according to the above formula. ij The bias vector b is also updated accordingly, and the parameters are continuously adjusted to gradually reduce the comprehensive loss function, so that the neural network model can better fit the data of quantum process tomography and improve the estimation accuracy of the neural network model for quantum processes.

[0112] In some embodiments of this disclosure, the neural network model receives a dataset, maps the data of the dataset through at least one or more fully connected layers and activation functions, and obtains the operator tensor corresponding to the dataset.

[0113] Specifically, a Haiku-based neural network model is constructed to learn Kraus operators from the input dataset and thus recover the Choi matrix of the quantum process. This neural network model consists of at least one or more fully connected layers, with the following structure: Input data first passes through a 128-dimensional fully connected layer and is activated by a ReLU function to introduce nonlinearity; then, the data passes through another 128-dimensional fully connected layer and another ReLU activation function; finally, the data passes through an output layer, which maps the features to a num_kraus×N×N dimensional space, where N is the dimension of the Hilbert space, and num_kraus is the number of Kraus operators. The number of operators is used to adjust the size of the quantum process representation, determining the rank of the quantum process and thus affecting the low-rank approximation effect. The output layer outputs tensors of shape (batch_size, num_kraus, N, N), where batch_size is the batch size, a parameter in neural network training that affects the amount of data involved in each computation during training; it is set to 32, and each tensor represents a Kraus operator. With this structure, neural network models can effectively learn the characteristics of quantum processes from limited data, providing support for subsequent quantum process tomography.

[0114] Reference Figure 5 In some embodiments of this disclosure, the disclosure also includes a method for training a neural network model, comprising:

[0115] S21: Receive the input dataset to obtain the corresponding predicted value, and process the predicted value and dataset to obtain the comprehensive loss function;

[0116] S22: Obtain the gradient of the neural network model by processing the comprehensive loss function;

[0117] S23: Update the parameters of the neural network model according to the gradient to gradually reduce the overall loss function;

[0118] S24: Monitor the change value of the comprehensive loss function. When the change value meets the preset second threshold, the comprehensive loss function converges, and the training of the neural network model is completed.

[0119] Specifically, the input dataset is fed into the neural network model. The data is processed according to the current parameters to generate corresponding predicted values, which are then used to obtain a comprehensive loss function. Based on this comprehensive loss function, the backpropagation algorithm is used to obtain the gradient of the neural network model. The gradient determines how changes in each parameter affect the value of the comprehensive loss function. The parameters of the neural network model are updated based on the gradient, and the parameters are adjusted accordingly to gradually decrease the value of the comprehensive loss function. The change in the comprehensive loss function is monitored to determine if the neural network model has converged. When the change in the comprehensive loss function meets a preset second threshold, the comprehensive loss function converges. The change value is the difference in the loss values. Optionally, the second threshold is set to 10. -3 The preset second threshold is set according to the specific problem and needs. If the second threshold is set too high, the neural network model may be considered to have completed training before it has converged, resulting in poor performance of the neural network model. If the second threshold is set too low, the training time may be prolonged.

[0120] The data used for training the neural network model in this embodiment are shown in Table 1 below:

[0121]

[0122]

[0123] Table 1

[0124] The neural network model was validated using a validation set. The results showed that the fidelity between the predicted matrix and the ideal matrix was greater than the first threshold (above 0.98), and the change in the loss value was less than the second threshold (less than 10). -3 .

[0125] Furthermore, refer to Figure 8 The trend of the overall loss function L during training with the number of training iterations. If the change in the overall loss function is less than 10 per 100 iterations at a certain stage... -3 When the neural network model has stabilized in terms of its ability to fit data and meet physical constraints, and is no longer affected by error data that could cause it to fail to converge fully, the training is considered complete.

[0126] Reference Figure 6 In some embodiments of this disclosure, the disclosure also includes a neural network-based quantum process tomography control system, comprising:

[0127] Data processing module 1 acquires the measured dataset;

[0128] Neural network module 2 is responsible for building a neural network model, receiving the dataset sent by data processing module 1 to train the neural network model, and obtaining the corresponding prediction matrix based on the dataset.

[0129] The evaluation module 3 processes the fidelity between the obtained prediction matrix and the preset ideal matrix, and determines whether it meets the preset first threshold. If it does, the prediction matrix output by the neural network model is used to characterize the quantum process; otherwise, the neural network model updates its parameters through a comprehensive loss function, inputs the dataset into the updated neural network model, and obtains an updated prediction matrix, until the fidelity between the obtained prediction matrix and the ideal matrix meets the preset first threshold.

[0130] Specifically, data processing module 1 acquires the input quantum state and passes it through the subprocess to be measured to generate the output state. The output state is then subjected to multiple measurements by a measurement operator, and the average is calculated to obtain the expected value estimate of the output state with respect to different measurement operators, which is used as the input dataset.

[0131] Neural network module 2 constructs a Haiku-based neural network model, receives the dataset sent by data processing module 1, and outputs the corresponding prediction matrix.

[0132] The evaluation module 3 compares the prediction matrix generated by the neural network module 2 with the ideal matrix to obtain the fidelity. The closer the fidelity is to 1, the more similar the prediction matrix is ​​to the ideal matrix. When the fidelity meets the preset first threshold, the neural network model is used as the corresponding measurement subprocess. If it does not meet the threshold, the neural network model updates its parameters through a comprehensive loss function. By minimizing the comprehensive loss function, the parameters of the neural network model are adjusted to make the prediction matrix of the neural network model more consistent with the actual situation and physical laws.

[0133] The quantum process tomography control system also includes an optimization training module 4, which updates and trains the parameters of the neural network model. The gradient obtained by the Adam optimizer is used to update the parameters of the neural network model, so that the value of the comprehensive loss function gradually decreases until it is less than the preset second threshold. When the comprehensive loss function is considered to have converged, the training process ends.

[0134] Furthermore, the training process in this embodiment involves a large number of matrix operations, which places high demands on the processor's computing power. To improve training speed, the parallel computing capabilities of the graphics processing unit (GPU) can be utilized. During neural network model training, data is distributed in parallel across multiple computing cores of the GPU, accelerating forward and backward propagation calculations. For example, when updating parameters using the Adam optimizer, gradients are obtained through parallel computing on the GPU, which can significantly shorten training time compared to using only the central processing unit (CPU).

[0135] The computing system's memory is used to store data and parameters. Due to the large volume of quantum tomography data, the data storage structure needs to be optimized. Training data is stored in blocks according to dimensions such as quantum state type and measurement time to improve data retrieval efficiency. Simultaneously, compression algorithms are used to store the parameters of the neural network model, such as Huffman coding to compress Kraus operator parameters, reducing storage space and improving overall system performance.

[0136] In some embodiments of this disclosure, the disclosure also includes a computer-readable storage medium storing a computer program for running a quantum process tomography method, wherein the computer program causes a computer to perform the following steps:

[0137] Step S1: Obtain the measurement dataset, wherein the dataset consists of the expected values ​​of the quantum state obtained by processing the quantum state through the subprocess to be measured;

[0138] Step S2: Input the dataset into the neural network model to obtain the prediction matrix;

[0139] Step S3: Process the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset first threshold.

[0140] If so, the prediction matrix output by the neural network model will be used to characterize the quantum process, and the process will end.

[0141] If not, the neural network model updates its parameters using the comprehensive loss function and proceeds to step S4;

[0142] Step S4: Input the dataset into the updated neural network model to obtain the updated prediction matrix and return to step S3.

[0143] 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.

[0144] 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.

[0145] In some embodiments of this disclosure, the disclosure also includes an electronic device comprising:

[0146] One or more processors; memory; and

[0147] 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:

[0148] Step S1: Obtain the measurement dataset, wherein the dataset consists of the expected values ​​of the quantum state obtained by processing the quantum state through the subprocess to be measured;

[0149] Step S2: Input the dataset into the neural network model to obtain the prediction matrix;

[0150] Step S3: Process the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset first threshold.

[0151] If so, the prediction matrix output by the neural network model will be used to characterize the quantum process, and the process will end.

[0152] If not, the neural network model updates its parameters using the comprehensive loss function and proceeds to step S4;

[0153] Step S4: Input the dataset into the updated neural network model to obtain the updated prediction matrix and return to step S3.

[0154] 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.

[0155] 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.

[0156] Optionally, the memory can be either standalone or integrated with the processor.

[0157] 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.

[0158] 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.

[0159] 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 quantum process tomography method based on neural networks, characterized in that, include: Step S1: Obtain the measurement dataset, wherein the dataset is the expected value obtained by processing the quantum state through the subprocess to be measured; Step S2: The dataset is input into the neural network model to obtain the prediction matrix; Step S3: Process the fidelity between the predicted matrix and the preset ideal matrix, and determine whether it meets the preset first threshold. If so, the prediction matrix output by the neural network model is used to characterize the quantum process, and the process ends. If not, the neural network model updates its parameters using a comprehensive loss function and proceeds to step S4; Step S4: The dataset is input into the updated neural network model to obtain the updated prediction matrix and then the process returns to step S3.

2. The quantum process tomography method according to claim 1, characterized in that: The dataset for obtaining measurements includes: The quantum state is used to obtain the output state through the subprocess to be measured; The output state is measured multiple times according to a set of preset measurement operators to obtain the expected values ​​corresponding to different measurement operators as the dataset.

3. The quantum process tomography method according to claim 1, characterized in that: The dataset is input into the neural network model to obtain the prediction matrix, which includes: The neural network model is used to obtain the prediction operator corresponding to the dataset, and the prediction matrix is ​​obtained by processing the prediction operator.

4. The quantum process tomography method according to claim 1, characterized in that: The neural network model updates its parameters through a comprehensive loss function, including: The neural network model is initialized with parameters; The input dataset is received to obtain the corresponding predicted value, and a comprehensive loss function is obtained by processing the predicted value and the dataset. The gradient of the neural network model is obtained by processing the comprehensive loss function. The parameters of the neural network model are updated based on the gradient.

5. The quantum process tomography method according to claim 4, characterized in that: The comprehensive loss function includes the weighted sum of mean squared error loss, L1 regularization loss, and trace distance loss.

6. The quantum process tomography method according to claim 4, characterized in that: The step of updating the parameters of the neural network model according to the gradient includes: The first-order moment estimate and the second-order moment estimate of the gradient are obtained by processing, and the first-order moment estimate and the second-order moment estimate are corrected for deviation. The parameters of the neural network model are updated based on the corrected first-order moment estimates and second-order moment estimates.

7. The quantum process tomography method according to claim 1, characterized in that: The neural network model receives the dataset, maps the data of the dataset through at least one or more fully connected layers and activation functions, and obtains the operator tensor corresponding to the dataset.

8. A quantum process tomography control system based on a neural network, characterized in that, include: The data processing module acquires the measured dataset; The neural network module constructs a neural network model, receives the dataset sent by the data processing module to train the neural network model, and obtains the corresponding prediction matrix based on the dataset. The processing and evaluation module processes the fidelity between the predicted matrix and the preset ideal matrix, and determines whether it meets a preset first threshold. If yes, the predicted matrix output by the neural network model is used to characterize the quantum process; otherwise, the neural network model updates its parameters through a comprehensive loss function, inputs the dataset into the updated neural network model, and obtains an updated predicted matrix, until the fidelity between the obtained predicted matrix and the ideal matrix meets the preset first threshold.

9. A computer-readable storage medium, characterized in that, It stores a computer program for running a quantum process tomography method, wherein the computer program causes a computer to perform the quantum process tomography method as described in any one of claims 1-7.

10. 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 quantum process tomography as described in any one of claims 1-7.

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