Multi-dimensional quantum state accurate measurement and control method based on machine learning and adaptive feedback

Abstract

The invention discloses a multi-dimensional quantum state accurate measurement and control method based on machine learning and adaptive feedback, relates to the field of quantum state measurement and control, and remarkably improves the efficiency and precision of quantum state feature extraction, reduces the measurement times, reduces the noise influence and improves the accuracy of quantum state feature extraction through the combination of a quantum state chromatography technology and a machine learning model. And through the design of a self-adaptive feedback control algorithm, control parameters can be adjusted in real time, small changes of the quantum state can be quickly responded, and accurate control over the quantum state is achieved.

Description

Technical Field

[0001] The present invention relates to the field of quantum state measurement and control, and specifically to a multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback. Background Art

[0002] Precise measurement and control of quantum states is one of the core tasks of quantum information science and is of great significance for the realization of technologies such as quantum computing, quantum communication and quantum precision measurement. Existing technologies mainly rely on quantum state tomography (QST) to obtain the density matrix of a quantum system, which is complete information describing the quantum state. Quantum state tomography usually involves multiple measurements of a quantum system, each of which is performed on a different basis to collect comprehensive information about the quantum state. This information is then used to reconstruct the density matrix, providing a basis for further analysis and control of the quantum state.

[0003] In addition, quantum control theory provides mathematical tools and methods for the precise manipulation of quantum states, including the modeling of quantum systems, the selection of control parameters, and the design of feedback mechanisms. By precisely controlling the evolution of quantum states, the execution of quantum algorithms and the generation of quantum entanglement can be achieved. The application of machine learning techniques, especially in the classification and prediction of quantum states, provides new possibilities for the automatic identification and optimization of quantum states. These techniques combine the precision of quantum physics with the adaptability of machine learning, opening up new paths for the intelligent processing of quantum states.

[0004] Although existing technologies have made significant progress in quantum state measurement and control, there are still some key defects and challenges. First, the quantum state tomography process often requires a large number of measurements, which is not only time-consuming and labor-intensive in experiments, but also easily affected by measurement noise, resulting in insufficient accuracy of the reconstructed density matrix. Secondly, existing quantum control methods often face the difficulties of control parameter selection and optimization when dealing with high-dimensional quantum systems, making it difficult to achieve fast and accurate quantum state adjustment. In addition, although machine learning technology has shown potential in quantum state identification, existing methods generally lack an in-depth understanding of the physical properties of quantum states, limiting their application in complex quantum systems. Summary of the invention

[0005] In view of the defects of the prior art, the present invention proposes a multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback. Through the training of deep learning models, the understanding of the physical properties of quantum states is enhanced, and the accuracy of quantum state identification and prediction is improved.

[0006] Among them, the multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback includes the following steps:

[0007] S1. Using quantum state tomography, project the multidimensional quantum state by measuring the projection operator to obtain the probability distribution, and estimate the density matrix through the probability distribution;

[0008] S2. Extract features of quantum states based on density matrix;

[0009] S3. Construct and train a quantum state deep learning network model through the characteristic vector of the quantum state and the corresponding target quantum state;

[0010] S4. According to an adaptive feedback control algorithm based on quantum control theory, the distance between the quantum state and the target state is minimized, and the control parameters corresponding to the control target are output;

[0011] Wherein, the step S3 specifically includes the following sub-steps:

[0012] S301. Use the quantum state feature vector to construct a quantum state deep learning network model, wherein the quantum state deep learning network model includes a quantum convolution layer, a quantum pooling layer, and a fully connected layer, wherein the quantum convolution layer is used to capture the spatial characteristics of the quantum state, the quantum pooling layer is used to reduce the feature dimension, and the fully connected layer is used for result prediction;

[0013] S302. Measure the difference between the predicted density matrix and the target density matrix by the Frobenius norm;

[0014] S303. Minimize the loss function by gradient descent algorithm.

[0015] Furthermore, the step S4 specifically includes the following sub-steps:

[0016] S401. Define the quantum state fidelity performance index and construct an objective function that minimizes the difference with the target state;

[0017] S402. Calculate the gradient of the objective function relative to the control parameter according to the derivative of the differential quantum state relative to the control parameter;

[0018] S403. Update control parameters.

[0019] Furthermore, in step S401, the calculation process of the quantum state fidelity is:

[0020]

[0021] Wherein, ρ represents the quantum state density matrix, and ρ target represents the density matrix of the target quantum state, represents the conjugate transpose of the target quantum state density matrix, Tr represents the trace operation, which is used to calculate the trace of the density matrix, Represents the quantum state fidelity, which is used to measure the closeness between the quantum state density matrix and the target quantum state density matrix.

[0022] Furthermore, in step S402, the specific process of calculating the gradient of the objective function relative to the control parameter is as follows:

[0023]

[0024] Among them, the represents the gradient of the control parameter u, represents the objective function, represents the partial derivative, represents the partial derivative of the control parameter u, and ρ(u) represents the quantum state density matrix that depends on the control parameter u.

[0025] Furthermore, the step S403 specifically updates the control parameters by gradient descent, and the process is as follows:

[0026]

[0027] Among them, the u new represents the updated control parameter, the u represents the control parameter, the Represents the objective function The gradient of the control parameter u, η represents the learning rate.

[0028] Furthermore, the step S1 specifically includes the following sub-steps:

[0029] S101. Define a measurement operator and a corresponding projection operator for each measurement basis;

[0030] S102. Construct a measurement model, perform projection operator measurement on the quantum state, obtain a probability distribution, and associate the probability distribution with a density matrix;

[0031] S103. Define an error function according to the measurement result of the projection operator;

[0032] S104. Minimize the error function according to the least squares estimation method and estimate the density matrix.

[0033] Furthermore, in step S103, the probability distribution is specifically expressed as:

[0034]

[0035] Among them, the p j Indicates that in the measurement base M j The probability distribution of the measured j represents the projection operator, the <ψ| and |ψ> represent the left vector and right vector of the quantum state ρ respectively, the Denotes the measurement operator M j The conjugate transpose of M j Represents the measurement operator.

[0036] Furthermore, in step S104, the density matrix estimation process is expressed as:

[0037]

[0038] Wherein, ρ represents the quantum state density matrix, σ represents any possible density matrix candidate for minimizing the error function, r represents the number of measurement bases, and j represents the index of the measurement base.

[0039] Furthermore, in step S2, feature extraction is specifically to extract the quantum Fisher information matrix as a feature vector describing the quantum characteristics, and the quantum Fisher information matrix is ​​expressed as:

[0040] F jk =2Re(Tr(ρL j L k ))-Tr(ρL j )Tr(ρL k );

[0041] Among them, the F jk represents the element of the quantum Fisher information matrix, which is used to describe the accuracy of quantum state parameter estimation, the Re represents the real part, which is used to extract the real part of the complex number, the ρ represents the quantum state density matrix, and the L j represents the operator derivative related to the quantum state parameter j, the L k represents another operator derivative related to the quantum state parameter k.

[0042] Furthermore, in step S302, the Frobenius norm is expressed as:

[0043]

[0044] Among them, the represents the loss function, the ρ target，i represents the target density matrix, the ρ predicted represents the prediction density matrix, and F represents the Frobenius norm.

[0045] The beneficial effects of the invention are:

[0046] The present invention significantly improves the efficiency and accuracy of quantum state feature extraction, reduces the number of measurements, and reduces the impact of noise through the combination of quantum state tomography technology and machine learning models. Through the design of an adaptive feedback control algorithm, it can adjust control parameters in real time, quickly respond to small changes in the quantum state, and achieve precise manipulation of the quantum state. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A method flow chart of a method for precise measurement and control of multi-dimensional quantum states based on machine learning and adaptive feedback provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0049] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0050] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work are within the scope of protection of the present invention. It should be noted that relational terms such as the terms "first" and "second" are only used 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.

[0051] Moreover, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of more restrictions, an element defined by the phrase "comprises a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

[0052] The features and performance of the present invention are further described in detail below in conjunction with the embodiments.

[0053] Among them, Figure 1, a multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback, comprising the following steps: S1. using quantum state tomography technology, projecting the multi-dimensional quantum state by measuring the projection operator to obtain the probability distribution, and estimating the density matrix by the probability distribution;

[0054] S2. Extract features of quantum states based on density matrix;

[0055] S3. Construct and train a quantum state deep learning network model through the characteristic vector of the quantum state and the corresponding target quantum state;

[0056] S4. According to an adaptive feedback control algorithm based on quantum control theory, the distance between the quantum state and the target state is minimized, and the control parameters corresponding to the control target are output;

[0057] Wherein, the step S3 specifically includes the following sub-steps:

[0058] S301. Use the quantum state feature vector to construct a quantum state deep learning network model, wherein the quantum state deep learning network model includes a quantum convolution layer, a quantum pooling layer, and a fully connected layer, wherein the quantum convolution layer is used to capture the spatial characteristics of the quantum state, the quantum pooling layer is used to reduce the feature dimension, and the fully connected layer is used for result prediction;

[0059] S302. Measure the difference between the predicted density matrix and the target density matrix by the Frobenius norm;

[0060] S303. Minimize the loss function by gradient descent algorithm.

[0061] Furthermore, the step S4 specifically includes the following sub-steps:

[0062] S401. Define the quantum state fidelity performance index and construct an objective function that minimizes the difference with the target state;

[0063] S402. Calculate the gradient of the objective function relative to the control parameter according to the derivative of the differential quantum state relative to the control parameter;

[0064] S403. Update control parameters.

[0065] Furthermore, in step S401, the calculation process of the quantum state fidelity is:

[0066]

[0067] Wherein, ρ represents the quantum state density matrix, and ρ target represents the density matrix of the target quantum state, represents the conjugate transpose of the target quantum state density matrix, Tr represents the trace operation, which is used to calculate the trace of the density matrix, Represents the quantum state fidelity, which is used to measure the closeness between the quantum state density matrix and the target quantum state density matrix.

[0068] Furthermore, in step S402, the specific process of calculating the gradient of the objective function relative to the control parameter is as follows:

[0069]

[0070] Among them, the represents the gradient of the control parameter u, represents the objective function, represents the partial derivative, represents the partial derivative of the control parameter u, and ρ(u) represents the quantum state density matrix that depends on the control parameter u.

[0071] Furthermore, the step S403 specifically updates the control parameters by gradient descent, and the process is as follows:

[0072]

[0073] Among them, the u new represents the updated control parameter, the u represents the control parameter, the Represents the objective function The gradient of the control parameter u, η represents the learning rate.

[0074] Specifically, in the above embodiment, the quantum state fidelity is used as an indicator to measure the closeness between the current quantum state and the target quantum state. The calculation of the fidelity is based on the trace operation. The trace operation calculates the product of the two, and the obtained fidelity value is between 0 and 1. The larger the value, the closer the current quantum state is to the target quantum state. Further, the objective function is defined as the complement of the quantum state fidelity or its inverse, which is used to minimize the difference between the current quantum state and the target quantum state during the optimization process. The gradient reflects the sensitivity of the objective function to the change of the control parameter uu, and the calculated gradient is used to adjust the control parameter to optimize the quantum state.

[0075] Furthermore, the step S1 specifically includes the following sub-steps:

[0076] S101. Define a measurement operator and a corresponding projection operator for each measurement basis;

[0077] S102. Construct a measurement model, perform projection operator measurement on the quantum state, obtain a probability distribution, and associate the probability distribution with a density matrix;

[0078] S103. Define an error function according to the measurement result of the projection operator;

[0079] S104. Minimize the error function according to the least squares estimation method and estimate the density matrix.

[0080] Furthermore, in step S103, the probability distribution is specifically expressed as:

[0081]

[0082] Among them, the p j Indicates that in the measurement base M j The probability distribution of the measured j represents the projection operator, the <ψ| and |ψ> represent the left vector and right vector of the quantum state ρ respectively, the Denotes the measurement operator M j The conjugate transpose of M j Represents the measurement operator.

[0083] Specifically, in quantum state tomography, the goal is to estimate or reconstruct the density matrix of an unknown quantum state through a series of measurements. In this embodiment, a set of measurement operators M is selected. j , corresponding to different measurement bases, each measurement operator M j are all associated with a specific measurement result, the formula p j Calculated by trace operation, is a projection operator that projects the quantum state onto the j For a pure state |ψ>, the density matrix ρ can be expressed as ρ = |ψ><ψ|. Therefore, p j The calculation can be further expanded as:

[0084]

[0085] here It is M j Acting on the quantum state |ψ>, then Then, we apply it to the result and finally calculate the inner product with |ψ>. In physics, this expression is used to measure the quantum state |ψ> under the measurement operator M. j The size of the projection into the subspace.

[0086] Further, for the above embodiment is the square of the modulus, which is used to emphasize the probability p j With M j The square of the amplitude of the projection of |ψ> is proportional to |ψ>, that is, when the quantum state |ψ> is parallel to the measurement operator M j When the overlap of the subspaces is large, then p j will be very high, indicating a high probability of being observed under this measurement basis.

[0087] Furthermore, in step S104, the density matrix estimation process is expressed as:

[0088]

[0089] Wherein, ρ represents the quantum state density matrix, σ represents any possible density matrix candidate for minimizing the error function, r represents the number of measurement bases, and j represents the index of the measurement base.

[0090] Furthermore, in step S2, feature extraction is specifically to extract the quantum Fisher information matrix as a feature vector describing the quantum characteristics, and the quantum Fisher information matrix is ​​expressed as:

[0091] F jk =2Re(Tr(ρL j L k ))-Tr(ρL j )Tr(ρL k );

[0092] Among them, the F jk represents the element of the quantum Fisher information matrix, which is used to describe the accuracy of quantum state parameter estimation, the Re represents the real part, which is used to extract the real part of the complex number, the ρ represents the quantum state density matrix, and the L j represents the operator derivative related to the quantum state parameter j, the L k represents another operator derivative related to the quantum state parameter k.

[0093] Specifically, the quantum Fisher information matrix is ​​used to evaluate the accuracy and uncertainty of quantum parameter estimation. The elements of the matrix F jk By L j and L k The expected value of the trace is calculated to improve the relevance and accuracy of parameter estimation; for the L j and L k , respectively represent the operator derivatives related to two different parameters of the quantum state. The above parameters can be any adjustable or observable properties in the quantum system. It should be noted that the parameters of the quantum state are not diagonalized in some cases, or are non-orthogonal in the representation of the quantum state. This embodiment uses L j and L k It allows to consider non-diagonalization or non-orthogonality, thus more accurately describing the response of quantum states to different parameters; while for L j and L k The influence parameters represented are, for example, L j represents the derivative of the operator related to the polarization angle of the quantum bit. When the quantum state depends on the polarization angle, then L jThe sensitivity of the quantum state to changes in polarization angle will be quantified. In addition, L k represents the phase of the quantum bit. When the quantum state depends on the phase, L k will quantify the sensitivity of the quantum state to phase changes, while the above formula only shows the L j and L k , and when the quantum state depends on multiple parameters, multiple operators can be chosen, each corresponding to a specific parameter or degree of freedom in the system.

[0094] Furthermore, in step S302, the Frobenius norm is expressed as:

[0095]

[0096] Among them, the represents the loss function, the ρ target，i represents the target density matrix, the ρ predicted represents the prediction density matrix, and F represents the Frobenius norm.

[0097] Specifically, the above embodiment evaluates and optimizes the prediction accuracy of the model by quantifying the difference between the prediction density matrix and the target density matrix. The Frobenius norm is selected as the core component of the loss function because of its directness and effectiveness in measuring the difference between the two matrices. The Frobenius norm provides a method with high computational efficiency and easy gradient calculation by summing the squares of the matrix element differences and then taking the square root; the quantum state density matrix is ​​the quantum state prediction made by the model based on the input feature vector, and the target density matrix represents the actual observed or theoretically expected quantum state. The difference between the two is quantified by the Frobenius norm. The obtained loss function reflects the accuracy of the model prediction in the entire parameter space. The calculation result of the loss function is used to guide the parameter update during the model training process. By minimizing the loss function, the model learns how to adjust its parameters to reduce the prediction error, thereby improving the accuracy of the quantum state prediction.

[0098] Further, as a preferred implementation of the above embodiment, a multi-dimensional quantum state precise measurement and control system based on machine learning and adaptive feedback is proposed. The system is implemented based on the multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback described in any of the above items, and specifically includes:

[0099] A density matrix estimation module is used to use quantum state tomography technology to project multidimensional quantum states by measuring projection operators to obtain probability distributions, and estimate density matrices through probability distributions;

[0100] A feature extraction module, used to extract features of quantum states according to a density matrix;

[0101] A deep learning module is used to construct and train a quantum state deep learning network model through the characteristic vector of the quantum state and the corresponding target quantum state;

[0102] A feedback control module is used to control the distance between the minimized quantum state and the target state according to an adaptive feedback control algorithm based on quantum control theory, and output a control parameter corresponding to the control target;

[0103] The deep learning module specifically includes:

[0104] A model building training unit, used to build a quantum state deep learning network model using a quantum state feature vector, wherein the quantum state deep learning network model includes a quantum convolution layer, a quantum pooling layer, and a fully connected layer, wherein the quantum convolution layer is used to capture the spatial characteristics of the quantum state, the quantum pooling layer is used to reduce the feature dimension, and the fully connected layer is used for result prediction;

[0105] The loss function definition unit is used to measure the difference between the predicted density matrix and the target density matrix through the Frobenius norm; the gradient optimization unit is used to minimize the loss function through the gradient descent algorithm.

[0106] Furthermore, the feedback control module specifically includes:

[0107] An objective function construction unit, used to define a quantum state fidelity performance index and construct an objective function that minimizes the difference from the target state;

[0108] A gradient calculation unit, used for calculating the gradient of the objective function relative to the control parameter according to the derivative of the differential quantum state relative to the control parameter;

[0109] The parameter updating unit is used to update the control parameters.

[0110] Furthermore, the density matrix estimation module specifically includes:

[0111] A projection unit, used to define a measurement operator and a corresponding projection operator for each measurement basis;

[0112] A probability calculation unit is used to construct a measurement model, perform projection operator measurement on the quantum state, obtain the probability distribution, and associate the probability distribution with the density matrix;

[0113] An error function definition unit, used for defining an error function according to a measurement result of a projection operator;

[0114] The density matrix estimation unit is used to estimate the density matrix by minimizing the error function according to the least squares estimation method.

[0115] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art do not deviate from the spirit and scope of the present invention, and should be within the scope of protection of the claims attached to the present invention.

Claims

1. A multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback, characterized in that: The following steps are involved: S1. Using quantum state tomography, project the multidimensional quantum state by measuring the projection operator to obtain the probability distribution, and estimate the density matrix through the probability distribution; S2. Extract features of quantum states based on density matrix; S3. Construct and train a quantum state deep learning network model through the characteristic vector of the quantum state and the corresponding target quantum state; S4. According to an adaptive feedback control algorithm based on quantum control theory, the distance between the quantum state and the target state is minimized, and the control parameters corresponding to the control target are output; Wherein, the step S3 specifically includes the following sub-steps: S301. Use the quantum state feature vector to construct a quantum state deep learning network model, wherein the quantum state deep learning network model includes a quantum convolution layer, a quantum pooling layer, and a fully connected layer, wherein the quantum convolution layer is used to capture the spatial characteristics of the quantum state, the quantum pooling layer is used to reduce the feature dimension, and the fully connected layer is used for result prediction; S302. Measure the difference between the predicted density matrix and the target density matrix by the Frobenius norm; S303. Minimize the loss function by gradient descent algorithm.

2. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 1, characterized in that: The step S4 specifically includes the following sub-steps: S401. Define the quantum state fidelity performance index and construct an objective function that minimizes the difference with the target state; S402. Calculate the gradient of the objective function relative to the control parameter according to the derivative of the differential quantum state relative to the control parameter; S403. Update control parameters.

3. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 2, characterized in that: In step S401, the calculation process of the quantum state fidelity is: Wherein, ρ represents the quantum state density matrix, and ρ target represents the density matrix of the target quantum state, represents the conjugate transpose of the target quantum state density matrix, Tr represents the trace operation, which is used to calculate the trace of the density matrix, Represents the quantum state fidelity, which is used to measure the closeness between the quantum state density matrix and the target quantum state density matrix.

4. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 2, characterized in that: In step S402, the specific process of calculating the gradient of the objective function relative to the control parameter is as follows: Among them, the represents the gradient of the control parameter u, represents the objective function, represents the partial derivative, represents the partial derivative of the control parameter u, and ρ(u) represents the quantum state density matrix that depends on the control parameter u.

5. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 2, characterized in that: The step S403 specifically updates the control parameters by gradient descent, and the process is as follows: Among them, the u new represents the updated control parameter, the u represents the control parameter, the Represents the objective function The gradient of the control parameter u, η represents the learning rate.

6. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 1, characterized in that: The step S1 specifically includes the following sub-steps: S101. Define a measurement operator and a corresponding projection operator for each measurement basis; S102. Construct a measurement model, perform projection operator measurement on the quantum state, obtain a probability distribution, and associate the probability distribution with a density matrix; S103. Define an error function according to the measurement result of the projection operator; S104. Minimize the error function according to the least squares estimation method and estimate the density matrix.

7. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 6, characterized in that: In step S103, the probability distribution is specifically expressed as: Among them, the p j Indicates that in the measurement base M j The probability distribution of the measured j represents the projection operator, the <ψ| and |ψ> represent the left vector and right vector of the quantum state ρ respectively, the Denotes the measurement operator M j The conjugate transpose of M j Represents the measurement operator.

8. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 6, characterized in that: In step S104, the density matrix estimation process is expressed as: Wherein, ρ represents the quantum state density matrix, σ represents any possible density matrix candidate for minimizing the error function, r represents the number of measurement bases, and j represents the index of the measurement base.

9. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 1, characterized in that: In step S2, feature extraction is specifically to extract the quantum Fisher information matrix as a feature vector describing quantum characteristics, and the quantum Fisher information matrix is ​​expressed as: F jk =2Re(Tr(ρL j L k ))-Tr(ρL j )Tr(ρL k ); Among them, the F jk represents the element of the quantum Fisher information matrix, which is used to describe the accuracy of quantum state parameter estimation, the Re represents the real part, which is used to extract the real part of the complex number, the ρ represents the quantum state density matrix, and the L j represents the operator derivative related to the quantum state parameter j, the L k represents another operator derivative related to the quantum state parameter k.

10. The multi-dimensional quantum state precise measurement and control method based on machine learning and adaptive feedback as claimed in claim 1, characterized in that: In step S302, the Frobenius norm is expressed as: Among them, the represents the loss function, the ρ target,i represents the target density matrix, the ρ predicted represents the prediction density matrix, and F represents the Frobenius norm.

Images