Predictive error driven quantum measurement basis self-reconfiguration and povm compensation method and system

Abstract

The application belongs to the technical field of quantum measurement technology, and discloses a method and system for predicting error-driven quantum measurement basis self-reconfiguration and POVM compensation. The method learns the change rule of the measurement error matrix through historical measurement data, predicts the error drift trend at a future time, and actively adjusts the measurement basis according to the prediction result. Meanwhile, the measurement operator is compensated and corrected under the positive operator value measurement (POVM) physical constraint, thereby forming a closed-loop calibration process of measurement, learning, prediction, basis reconstruction, operator compensation and feedback update. Compared with the prior art, the application uses the prediction error matrix as the basis for measurement basis reconstruction and measurement operator compensation, and forms a unified closed-loop calibration mechanism combined with the POVM physical constraint. The application can learn the error evolution trend, predict the future drift risk, actively adjust the measurement basis, and compensate the measurement operator under the POVM constraint, so as to realize the long-term stable operation of the quantum measurement system.

Description

Technical Field

[0001] This invention relates to the field of quantum measurement technology and is applicable to systems requiring long-term stable quantum measurements, such as quantum key distribution, quantum computing readout, quantum state tomography, and quantum sensing. It is particularly suitable for application scenarios where there are measurement substrate drift, environmental disturbances, and dynamic changes in measurement errors. Specifically, it relates to a prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method and system. Background Technology

[0002] Quantum communication, quantum computing, quantum state tomography, and quantum sensing systems typically require quantum measurements to determine states and read information. For the quantum state to be measured, ρ, the ideal measurement probability can be expressed as P = Tr(Mρ), where M represents the ideal measurement operator. In practical systems, components such as polarization analyzers, phase decision units, interferometers, single-photon detectors, and readout circuits may be affected by temperature variations, mechanical vibrations, device aging, voltage drift, and optical path disturbances, causing the actual measurement operator to shift relative to the ideal measurement operator.

[0003] The actual measurement process can be approximated as M′=M+ΔM, where ΔM represents the measurement error. During continuous system operation, the measurement error may gradually accumulate, manifesting as measurement basis shift, measurement probability distribution deviation, and increased quantum state decision error. For quantum communication systems, this deviation may cause fluctuations in the quantum bit error rate; for quantum computing readout systems, it may increase readout error; and for quantum tomography and quantum sensing systems, it may affect reconstruction fidelity, measurement sensitivity, and long-term consistency.

[0004] Current quantum measurement calibration methods mostly employ manual periodic calibration, reference state calibration, or fixed error matrix compensation. These methods are applicable to certain conditions under relatively stable environments, but in long-term continuous operation or dynamic disturbance scenarios, fixed calibration periods are not easy to reflect the trend of error matrix changes over time, and fixed error matrix compensation is more inclined to deal with errors that have already occurred, making it difficult to make advance judgments on subsequent drift risks.

[0005] Some error mitigation methods primarily focus on numerical correction of measurement results, neglecting to consider whether the corrected measurement operators still satisfy the physical realizability conditions of quantum measurement. When ill-conditioned, amplified, or negative probability components exist in the compensation matrix inversion process, the corrected measurement operators may deviate from the POVM completeness or positive semidefiniteness requirements, affecting the reliability and engineering applicability of the compensation results. Therefore, it is necessary to propose a method that can learn error evolution trends using historical measurement data, predict future drift risks, proactively adjust the measurement basis, and perform measurement operator compensation under POVM constraints to support the long-term stable operation of quantum measurement systems. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, this invention proposes a prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method and system.

[0007] The technical solution of this invention is implemented as follows: A prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method includes the following steps: S1: Collect the actual measurement probability Pobs, detector count, measurement substrate state, detector state and environmental state information during the operation of the quantum measurement system, construct the measurement state vector X(t), and store the measurement state vector X(t) in the measurement memory bank. The measurement memory bank also stores at least the following historical measurement data: historical error matrix, risk score and quality index, to provide a data foundation for subsequent error learning and drift prediction. S2: During the online learning phase of the error matrix, an error propagation model is established based on the relationship between the ideal measurement probability (Pideal) and the actual measurement probability (Pobs), and the real-time error matrix is ​​estimated online based on the historical measurement data in the measurement memory. The real-time error matrix here One of the subsequent historical error matrices is the error matrix obtained after measurement and estimation at the current moment. Its difference from the "previous moment's real-time error matrix" lies in its real-time nature. However, at the next moment, the real-time nature of the "current moment's real-time error matrix" will be lost, while the "next moment's real-time error matrix" will possess real-time characteristics. Ultimately, all these matrices, which at a certain moment are respectively called the real-time matrix of that moment, will all enter the set of historical error matrices, forming a historical error matrix sequence. S3: Construct the error state vector S(t) based on the historical error matrix sequence, and predict the prediction error matrix for future times. The system can utilize the LSTM network to learn the time-varying pattern of the error matrix and combine it with a Kalman filter to perform state correction on the prediction results, thereby reducing the impact of random noise on the prediction results. Based on the prediction error matrix The system constructs drift risk indicators. : ; in, express Norm. Comprehensive risk score. Drift risk indicators Error variance Error drift rate and error residual Weighted composition: ; in, to This refers to the risk weighting coefficient. S4: When the comprehensive risk score G reaches the preset risk threshold At this time, the system initiates the active calibration process. During the measurement substrate self-reconstruction phase, the system calculates the calibration based on the prediction error matrix. Calculate the base compensation amount The measurement substrate compensation amount can be expressed as: ; in, Indicates the amount of angle compensation measured. The phase compensation amount is expressed by the system updating the measurement substrate according to the following formula: ; in, Indicates the measurement basis before reconstruction. This represents the reconstructed measurement basis; S5: Based on the prediction error matrix Construct a compensation matrix C, and use the compensation matrix C to compensate and correct the actual measurement probability Pobs and the measurement operator to obtain the initial corrected measurement result and the initial corrected measurement operator; S6: Apply POVM constraint processing to the initial modified measurement operators to ensure that the modified set of measurement operators satisfies the completeness constraint. and positive semidefinite constraints Let I be the identity matrix, and then the corrected measurement operator is obtained. and corrected measurement results ; S7: Based on the corrected measurement results The measurement fidelity F, quantum bit error rate (QBER), error residual Re, and comprehensive quality index Q are calculated. Based on the comprehensive quality index Q, the error learning parameters, drift prediction parameters, measurement basis reconstruction parameters, and compensation parameters are updated, forming a closed-loop calibration process of measurement, learning, prediction, reconstruction, compensation, and feedback update.

[0008] Preferably, in step S2, the real-time error matrix is ​​estimated online. The process is implemented jointly using a recursive least squares algorithm and a Bayesian online learning algorithm, where the real-time error matrix... The update process satisfies: , where k and t represent the iteration step and the physical measurement time point, respectively, K(k) is the update gain matrix, and e(k) is the measurement residual.

[0009] Preferably, in step S3, by constructing an error state vector S(t)=[e11,e12,e21,e22], using an LSTM network to learn the long-term evolution law of the error matrix, and employing a Kalman filter to correct the prediction results, the prediction error matrix is ​​obtained. .

[0010] Preferably, the comprehensive risk score G is constructed by the drift risk index R, error variance σE², error drift rate vE, and error residual Re, and is used to assess the future measurement drift risk and trigger the active calibration process.

[0011] Preferably, the measurement substrate self-reconstruction process includes reconstructing the measurement substrate based on the prediction error matrix. The corresponding predicted measurement probability deviation is used to construct the measurement basis perturbation Jacobian matrix, and the measurement angle compensation amount Δθ and phase compensation amount Δφ are solved by the regularized least squares method to generate the measurement basis compensation vector ΔB, thereby updating the measurement basis. Through this process, the prediction error matrix is ​​not only used for measurement result compensation, but also participates in measurement direction adjustment, enabling the system to actively correct the measurement basis before the error further expands.

[0012] Preferably, the compensation matrix C is constructed using a regularized inverse matrix and modified to adjust for the actual measurement probability or measurement operator. The regularized compensation matrix can be expressed as: ,in, This represents the transpose of the prediction error matrix. Represents the regularization coefficient. Represents the identity matrix. The condition number of the prediction error matrix can be used as a basis. Adaptive settings are used to strike a balance between compensation accuracy and noise suppression.

[0013] Preferably, the corrected measurement probability can be expressed as: ; when When negative probability components or normalization biases appear in the system, the system can project them onto the probability simplex space to satisfy the following conditions: and During the POVM constraint compensation phase, the system applies completeness and positive semidefinite constraints to the corrected measurement operators, ensuring that the set of corrected measurement operators satisfies: , , in, Let represent the i-th correction measurement operator. For the initial correction measurement operator... The system can first perform a semi-definite projection to obtain... , then calculate And through normalization correction, a corrected measurement operator satisfying the POVM constraint is obtained: ; in, For the i-th POVM measurement operator, Let i be the measurement operator after positive semidefinite projection. The normalized matrix is ​​obtained by summing all positive semidefinite measurement operators.

[0014] Through the above processing, the system constrains the physical realizability of the measurement operator while performing numerical compensation, thereby reducing the possibility of non-physical results such as negative probability, operator incompleteness, or matrix inversion divergence.

[0015] Preferably, the measurement fidelity F, quantum error rate (QBER), error residual Re, and comprehensive quality index Q are calculated based on the corrected measurement results. The comprehensive quality index Q can be weighted by the measurement fidelity, quantum error rate, error residual, and error fluctuation variance. ; Among them, β1 to β4 are the quality evaluation weight coefficients, Ve represents the error fluctuation variance, and the higher the comprehensive quality index Q, the better the overall performance of the corrected measurement results in terms of fidelity, bit error rate and residual control. The decision to start the deep reconstruction and parameter update process is based on the relationship between Q and the preset quality threshold Qth.

[0016] This invention also provides a prediction error-driven quantum measurement basis self-reconfiguration and POVM compensation system, comprising: The quantum measurement module performs polarization, phase, or readout measurements after the quantized substate ρ enters the module. The measurement data acquisition module is used to acquire data on actual measurement probability Pobs, detector count, measurement substrate status, detector status, and environmental status. The measurement memory module includes a measurement memory, into which the above data is sent to save the measurement state vector X(t), historical error matrix, risk score and comprehensive quality index Q. The online error matrix learning module estimates the real-time error matrix based on historical measurement data. , The error drift prediction module further predicts the future prediction error matrix based on the historical error matrix sequence. It outputs the drift risk index R and the comprehensive risk score G; The measurement-based self-reconstruction module, when the comprehensive risk score G reaches a preset threshold, uses the prediction error matrix to... Calculate the measurement base compensation amount ΔB, and generate a new measurement base B. new ; The measurement operator compensation module, based on the prediction error matrix... Construct the compensation matrix C and output the corrected measurement results under POVM constraints. and correction measurement operator ; The quality assessment module evaluates the correction effect based on measurement fidelity F, quantum bit error rate QBER, error residual Re, and comprehensive quality index Q. The feedback update module feeds back the evaluation and correction results to the measurement memory, error learning, drift prediction and basis reconstruction stages, forming a prediction-driven closed-loop calibration process.

[0017] Preferably, the quantum measurement module includes a polarization analyzer, a polarization beam splitter, and a single-photon detector. The sampling period of the measurement data acquisition module is set to Δt=10ms, and the measurement memory module stores the measurement state data within the most recent N=1000 time windows.

[0018] Preferably, the online learning module for the error matrix establishes an error propagation model based on the ideal measurement probability (Pideal) and the actual measurement probability (Pobs): , Where E represents the measurement error matrix, and the system obtains the ideal measurement probability Pideal through periodically or sparsely inserted reference quantum states.

[0019] Compared with the prior art, the present invention has the following beneficial effects: This invention proposes a prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method. Through an online error matrix learning mechanism, this invention continuously tracks measurement deviations during the operation of the quantum measurement system, freeing error description from complete reliance on manual periodic calibration or fixed error models. As measurement data accumulates, the real-time error matrix reflects changes caused by equipment status, environmental disturbances, and detector drift, providing a data foundation for subsequent error prediction, measurement substrate reconstruction, and measurement operator compensation. This invention identifies potential drift risks before measurement errors further amplify through an error drift prediction mechanism and supports system calibration during the risk formation phase. Compared to ex-post compensation methods, this mechanism helps reduce the impact of error peaks on measurement results and improves the stability of the quantum measurement system under continuous operating conditions. This invention employs a measurement substrate self-reconstruction mechanism to calculate the measurement substrate compensation amount based on the prediction error matrix and dynamically adjust the original measurement substrate. This mechanism not only numerically corrects the measurement results but also reduces the system deviation caused by substrate drift from the measurement direction itself, providing a more stable measurement response for polarization state measurements, quantum state tomography, and quantum communication receiver measurements. This invention introduces physical constraints of quantum measurement into the numerical compensation process through the POVM constraint compensation mechanism, ensuring that the corrected set of measurement operators satisfies completeness and positive semidefinite constraints. This mechanism helps reduce the likelihood of non-physical results such as negative probability, operator incompleteness, and matrix inversion divergence, thereby improving the reliability and engineering applicability of the compensation results. Attached Figure Description

[0020] Figure 1 This is a diagram illustrating the overall structure of the quantum measurement error self-learning calibration system based on historical measurement memory and prediction compensation according to the present invention. Figure 2 This is a schematic diagram of the online learning convergence process of the real-time error matrix in this invention; Figure 3 This is a comparison diagram of the effects before and after the measurement substrate self-reconstruction process driven by the prediction error matrix of this invention; Figure 4 This is a schematic diagram comparing the predictive-driven active calibration of the present invention with traditional ex-post calibration. Detailed Implementation

[0021] The present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0022] like Figure 1 As shown, the system of the present invention includes a quantum measurement module 100, a measurement data acquisition module 200, a measurement memory module 300, an error matrix online learning module 400, an error drift prediction module 500, a measurement basis self-reconstruction module 600, a measurement operator compensation module 700, a quality assessment module 800, and a feedback update module 900. The measurand state is... Upon entering the quantum measurement module 100, the raw measurement results are obtained. The measurement data acquisition module 200 collects measurement probability, detector count, measurement substrate state, detector state, and environmental state information, and forms a measurement state vector X(t). The measurement memory module 300 stores X(t), historical error matrix, risk score, and quality index, providing a data source for error learning and drift prediction.

[0023] The overall process of this invention is as follows: the substate to be measured After entering the quantum measurement module 100, polarization, phase, or readout measurements are completed, and the measurement data acquisition module 200 acquires the actual measurement probability Pobs, detector count, measurement substrate state, detector state, and environmental state. This data is then sent to the measurement memory module 300 to store the measurement state vector. The system first obtains historical error matrices, risk scores, and quality indicators. Then, the online error matrix learning module 400 estimates the real-time error matrix based on historical measurement data using the Recursive Least Squares (RLS) algorithm and a Bayesian online learning algorithm. The error drift prediction module 500 further learns the long-term evolution law of the error matrix using an LSTM network based on the historical error matrix sequence, and uses a Kalman filter to correct the prediction results, predicting the error matrix. It outputs the drift risk index R and the comprehensive risk score G. When the comprehensive risk score reaches a preset threshold, the measurement substrate self-reconstruction module 600 calculates the measurement substrate compensation amount based on the prediction error matrix. And generate a new measurement substrate B new The measurement operator compensation module 700 constructs a compensation matrix C based on the prediction error matrix and outputs the corrected measurement results under POVM constraints. and correction measurement operator The quality assessment module 800 evaluates the correction effect based on F, QBER, Re, and Q, and outputs the results. , The feedback update module 900 then feeds back the evaluation results to the measurement memory, updates the learning, prediction and compensation parameters, and feeds them back to the measurement memory module 300, the error matrix online learning module 400, and the error drift prediction module 500, thus forming a prediction-driven closed-loop calibration process.

[0024] The online learning module 400 for the error matrix establishes an error propagation model based on the ideal measurement probability (Pideal) and the actual measurement probability (Pobs). , Where E represents the measurement error matrix. The system can continuously estimate the error matrix using a recursive least squares algorithm and a Bayesian online update algorithm to obtain the real-time error matrix. .

[0025] like Figure 2 As shown, with the increase of learning rounds, the error residual Re=||e(k)||2 gradually decreases and tends to stabilize. After the rapid descent stage (initial learning), the stable convergence stage (model approximation) and the fine convergence stage (low residual optimization), this change indicates that the real-time error matrix has improved its approximation of the actual error matrix.

[0026] The error drift prediction module 500 reads the historical error matrix sequence, constructs the error state vector S(t), and uses an LSTM network to learn the law of error change over time. A Kalman filter is used to correct the state of the prediction result to reduce the influence of random noise on the prediction error matrix, resulting in... In one implementation, the drift risk index R can be expressed as:

[0027] The comprehensive risk score G can be derived from R and the error variance. The error drift rate vE and the error residual Re are weighted together to form: , Here, α1 to α4 are risk weight coefficients. When G reaches the preset risk threshold Gth, the system initiates the active calibration process.

[0028] like Figure 3 The figure shows a comparison of the effects before and after the measurement base self-reconstruction process driven by the prediction error matrix. The measurement base self-reconstruction module 600 calculates the measurement base compensation amount ΔB based on the prediction error matrix. ΔB can be expressed as ΔB=[Δθ,Δφ], where Δθ represents the measurement angle compensation amount and Δφ represents the phase compensation amount. The system follows B... new =B old +ΔB updates the measurement basis, causing the reconstructed measurement response curve to move closer to the target measurement direction. In the specific solution process, the prediction error matrix can be... The resulting prediction measurement probability bias is denoted as The measurement basis perturbation Jacobian matrix JB is constructed, and the measurement basis compensation amount ΔB can be obtained through regularized least squares. ; Here, JB represents the Jacobian matrix corresponding to the measurement basis perturbation, and μ represents the regularization coefficient. In this way, the probability deviation corresponding to the prediction error matrix can be converted into measurement angle compensation Δθ and phase compensation Δφ. This process shows that the prediction error matrix is ​​not only used for result compensation but also participates in measurement direction adjustment.

[0029] like Figure 4 The diagram illustrates a comparison between prediction-driven active calibration and traditional ex-post calibration. Traditional ex-post calibration typically adjusts the system after the error or risk indicators have reached a high level. This invention employs a prediction-driven calibration method, triggering basis reconstruction and operator compensation in advance when the comprehensive risk score approaches a threshold. This approach helps reduce error peaks and decrease fluctuations in quantum bit error rate or readout error.

[0030] The quality assessment module 800 can construct a comprehensive quality index Q based on measurement fidelity F, quantum bit error rate (QBER), error residual (Re), and error fluctuation variance (Ve). ; Wherein, β1 to β4 are the quality evaluation weight coefficients. The system can determine whether the current compensation result meets the requirements based on the comparison result between Q and the preset quality threshold Qth. When Q is higher than or equal to Qth, the system outputs the corrected measurement result; when Q is lower than Qth, the system can continue to adjust the measurement basis compensation amount, regularization coefficient, or prediction parameters.

[0031] In one specific embodiment, the system employs a single-qubit polarization state measurement platform, and the measurement objects include horizontal polarization states, vertical polarization states, positive 45° polarization states, and negative 45° polarization states. The measurement module 100 includes a polarization analyzer, a polarization beam splitter, and a single-photon detector. The system sampling period is set to Δt = 10 ms, and the measurement memory module 300 stores measurement state data within the most recent N = 1000 time windows. The drift risk threshold can be set to Gth = 0.08, the corrected fidelity threshold can be set to Fth = 0.98, the overall quality threshold can be set to Qth = 0.95, and the maximum depth reconstruction iteration count can be set to Lmax = 5. The above values ​​are used to illustrate an optional implementation and do not limit the scope of protection of this invention.

[0032] The system can obtain the ideal measurement probability Pideal through periodic or sparse insertion of reference quantum states. To reduce the impact of the calibration process on normal operational measurements, reference quantum states can be inserted according to a preset ratio, or temporarily inserted when the drift risk increases. The reference state measurement results and the actual observation results are jointly input into the online learning module 400 for error matrix estimation. and .

[0033] Considering the prediction error matrix There may be ill-conditioned, irreversible, or noise amplification issues. The measurement operator compensation module 700 introduces a regularization compensation mechanism. The regularization compensation matrix C can be expressed as: , Where λ represents the regularization coefficient, and I represents the identity matrix. λ can be determined based on the condition number of the error matrix. Adaptive settings. When When the value is small, λ can be a smaller value to maintain compensation accuracy; when When the value is large, λ can be appropriately increased to suppress noise amplification during the error inversion process. The corrected measurement probability can be expressed as: , when When negative probability components or normalization biases appear in the system, the system can project them onto the probability simplex space to satisfy the following conditions: and For the POVM measurement operator set, the system constructs the initial correction measurement operator based on the compensation matrix C. and to Perform a semi-definite projection to obtain Then calculate And normalization correction is applied: , in, For the i-th POVM measurement operator, Let i be the measurement operator after positive semidefinite projection. The normalized matrix is ​​obtained by summing all positive semidefinite measurement operators.

[0034] After the above processing, the set of measurement operators is corrected. satisfy and This process demonstrates that the system, while performing numerical compensation, also constrains the physical realizability of the measurement operator.

[0035] During a single operation, if the system detects that the comprehensive risk score G=0.11 corresponding to the prediction error matrix is ​​higher than the preset threshold Gth=0.08, the error drift prediction module 500 sends an active calibration trigger signal to the measurement base self-reconstruction module 600. The measurement base self-reconstruction module 600 calculates Δθ=0.35° and Δφ=0.02rad based on the prediction error matrix and generates a new measurement base Bnew. The measurement operator compensation module 700 corrects the measurement operator using a regularization compensation matrix C and performs positive semi-definite projection and completeness normalization on the corrected POVM operator. If the corrected fidelity Fcorr increases from 0.962 to 0.985 and the comprehensive quality index Q is higher than Qth, the system outputs the corrected measurement result Pcorr; if Fcorr is still lower than Fth, the system continues to adjust Δθ, Δφ, and λ within the maximum number of iterations Lmax, or triggers a manual calibration alarm. The above operational results show that this method can support early base reconstruction and operator compensation after predicting drift risk.

Claims

1. A prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method, characterized in that, Includes the following steps: S1: Collect the actual measurement probability Pobs, detector count, measurement substrate state, detector state, and environmental state information during the operation of the quantum measurement system, construct the measurement state vector X(t), and store X(t) as historical measurement data in the measurement memory bank. The measurement memory bank also stores at least the following historical measurement data: historical error matrix, risk score, and quality index. The system adopts a single-qubit polarization state measurement platform, and the measurement objects include horizontal polarization state, vertical polarization state, positive 45° polarization state, and negative 45° polarization state. The system includes a polarization analyzer, a polarization beam splitter, and a single-photon detector. S2: Establish an error propagation model based on the relationship between the ideal measurement probability (Pideal) and the actual measurement probability (Pobs), and estimate the real-time error matrix online based on historical measurement data. ; S3: Construct the error state vector S(t) based on the sequence of historical error matrices formed by all historical error matrices, and predict the prediction error matrix for future times. and according to Generate drift risk index R and comprehensive risk score G to construct drift risk index : , in, express Norm, comprehensive risk score Drift risk indicators Error variance Error drift rate and error residual Weighted composition; S4: When G reaches the preset risk threshold, according to Calculate the measurement base compensation amount ΔB, and according to B new =B old +ΔB updates the measurement basis, enabling self-reconstruction of the measurement basis, B old B represents the measurement basis before reconstruction. new This represents the reconstructed measurement basis; S5: According to Construct a compensation matrix C, and use C to compensate and correct the actual measurement probabilities Pobs and the measurement operator to obtain the initial corrected measurement results and the initial corrected measurement operator; S6: Apply POVM constraints to the initial modified measurement operators to ensure that the modified set of measurement operators satisfies the completeness constraints. and positive semidefinite constraints Let I be the identity matrix, and then we obtain the corrected measurement operator M. corr and corrected measurement results P corr ; S7: According to P corr Calculate the measurement fidelity F, quantum bit error rate (QBER), error residual (Re), and overall quality index (Q), and update the error learning parameters, drift prediction parameters, measurement basis reconstruction parameters, and compensation parameters based on Q.

2. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 1, characterized in that, In step S2, online estimation The process is implemented jointly using the Recursive Least Squares (RLS) algorithm and the Bayesian online learning algorithm. The update process satisfies: , where k and t represent the iteration step and the physical measurement time point, respectively, K(k) is the update gain matrix, and e(k) is the measurement residual.

3. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 1, characterized in that, In step S3, by constructing the error state vector S(t)=[e11,e12,e21,e22], the LSTM network is used to learn the long-term evolution law of the error matrix, and a Kalman filter is used to correct the prediction result to obtain... .

4. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 3, characterized in that, The comprehensive risk score G is constructed from the drift risk index R, error variance σE², error drift rate vE, and error residual Re, and is used to assess the future measurement drift risk and trigger the active calibration process.

5. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 4, characterized in that, The measurement substrate self-reconstruction process includes, according to The corresponding predicted measurement probability deviation is used to construct the measurement basis perturbation Jacobian matrix, and the measurement angle compensation amount Δθ and phase compensation amount Δφ are solved by the regularized least squares method to generate the measurement basis compensation vector ΔB, thereby updating the measurement basis.

6. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 5, characterized in that, The compensation matrix C is constructed using a regularized inverse matrix, and its expression is as follows: Where λ is the regularization coefficient and I is the identity matrix. Represents the prediction error matrix The transpose of .

7. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 3, characterized in that, The POVM constraint processing procedure includes performing semi-positive definite projection processing on the initial modified measurement operator and obtaining a set of modified measurement operators that satisfy the POVM completeness constraint through normalization correction.

8. The prediction error-driven quantum measurement substrate self-reconstruction and POVM compensation method as described in claim 3, characterized in that, The quality assessment process of the comprehensive quality index Q is as follows: the comprehensive quality index Q is constructed based on the measurement fidelity F, quantum bit error rate QBER, error residual Re and error fluctuation variance Ve, and the deep reconstruction and parameter update process is initiated based on the relationship between Q and the preset quality threshold Qth.

9. A prediction error-driven quantum measurement substrate self-reconfiguration and POVM compensation system, characterized in that, include: quantum The measurement module performs polarization, phase, or readout measurements after the quantum state ρ enters the quantum measurement module. The quantum measurement module adopts a single-qubit polarization state measurement platform. The measurement objects include horizontal polarization states, vertical polarization states, positive 45° polarization states, and negative 45° polarization states. The quantum measurement module includes a polarization analyzer, a polarization beam splitter, and a single-photon detector. The measurement data acquisition module is used to acquire data on actual measurement probability Pobs, detector count, measurement substrate status, detector status, and environmental status. The measurement memory module includes a measurement memory library. Data is sent to the measurement memory module to store the measurement state vector. Historical error matrix, risk score and comprehensive quality index; The online error matrix learning module estimates the real-time error matrix based on historical measurement data. , The error drift prediction module further predicts the future prediction error matrix based on the historical error matrix sequence. It outputs the drift risk index R and the comprehensive risk score G, and constructs the drift risk index. : , in, express Norm, comprehensive risk score Drift risk indicators Error variance Error drift rate and error residual Weighted composition; The measurement-based self-reconstruction module, when the comprehensive risk score G reaches a preset threshold, uses the prediction error matrix to... Calculate the measurement base compensation amount ΔB, and generate a new measurement base B. new ; The measurement operator compensation module, based on the prediction error matrix... Construct the compensation matrix C, and output the corrected measurement result P under POVM constraints. corr and correction measurement operator ; The quality assessment module evaluates the correction effect based on measurement fidelity F, quantum bit error rate QBER, error residual Re, and comprehensive quality index Q. The feedback update module feeds back the evaluation and correction results to the measurement memory, error learning, drift prediction and basis reconstruction stages, forming a prediction-driven closed-loop calibration process.

10. The prediction error-driven quantum measurement substrate self-reconfiguration and POVM compensation system as described in claim 9, characterized in that, The sampling period of the measurement data acquisition module is set to Δt=10ms, and the measurement memory module stores the measurement status data within the most recent N=1000 time windows.

11. The prediction error-driven quantum measurement substrate self-reconfiguration and POVM compensation system as described in claim 9, characterized in that, The online learning module for the error matrix establishes an error propagation model based on the ideal measurement probability (Pideal) and the actual measurement probability (Pobs): ， Where E represents the measurement error matrix, and the system obtains the ideal measurement probability Pideal through periodically or sparsely inserted reference quantum states.

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