Method and system for learning latent constraint structure based on quantum measurement data

Abstract

The application provides a potential constraint structure learning method and system based on quantum measurement data, which comprises the following steps: constructing a quantum measurement data set; training a preset Transformer structure encoder using the quantum measurement data set, and extracting an inter-variable dependency graph under a mask condition; extracting a support set for a target position according to the inter-variable dependency graph, and performing parity check verification and GF(2) Gaussian elimination processing on the support set of each target position; mapping a quantum bit linear constraint set to a verified Pauli generator; constructing a new Pauli measurement basis according to the commutation space of the verified stabilizer generator set; repeating the model learning stage and the statistical verification stage until a preset convergence condition is met, and determining the complete set of stabilizer generators. Through the application, efficient, interpretable and high-reliability quantum system structure discovery is realized, and the calculation and experimental overhead is reduced.

Description

Technical Field

[0001] This application relates to the field of quantum information science and technology, specifically to a method and system for learning potential constraint structures based on quantum measurement data. Background Technology

[0002] The complete state space of a quantum system grows exponentially with the number of qubits. While traditional quantum state tomography can theoretically recover the complete quantum state, it is generally not scalable in terms of experimental measurement complexity and post-processing complexity. Existing techniques fall into two categories: (1) Reconstruction methods: such as compressed sensing tomography, prior-based neural network tomography, matrix product state approximation, etc., the goal is still to reconstruct the complete quantum state or its approximate representation. For example, in the patent "CN202411134987.6, a compressed quantum state tomography method based on prior knowledge", it is based on compressed sensing quantum state tomography, adopts low-rank structure prior of quantum state and random Pauli measurement, realizes quantum state reconstruction by minimizing trace norm, and introduces ideal state prior to further reduce measurement resource consumption. This type of method is highly dependent on structure prior and still faces the problems of high complexity and insufficient interpretability in high-dimensional scenarios.

[0003] (2) Predictive methods: such as shadow tomography and Pauli observable estimation, focus on estimating given observations rather than discovering underlying structural rules that can explain the source of the measurement data. These methods are usually task-oriented and are difficult to produce reusable and interpretable representations of latent constraints.

[0004] Furthermore, existing stable substructure learning methods are mostly based on the premise that "the structure of the stable substructure is known" or "it can be recovered through a specific Clifford process". However, under real-world constrained measurement conditions, the topology, support set, and representation of the constraints are often uncertain and difficult to pre-determine directly.

[0005] In summary, existing technologies struggle to address three core challenges simultaneously: First, how to directly uncover hidden local, global, or hybrid constraints in quantum systems when only limited Pauli measurement data is available; second, how to perform physical consistency verification and independence screening on the uncovered candidate constraints to ensure their effectiveness and conciseness; and third, how to adaptively select subsequent measurement bases based on the discovered constraint structures to reduce the overall number of measurement setups and improve measurement and learning efficiency.

[0006] The aforementioned bottlenecks not only restrict the efficiency and accuracy of quantum device characterization, but also hinder the exploration of the underlying laws of complex quantum systems in the noisy quantum era. Therefore, developing innovative methods that can simultaneously solve the above problems is the key to promoting quantum information processing technology from theory to practical application, and is of great significance to the development of quantum computing, quantum simulation and other fields. Summary of the Invention

[0007] In view of the shortcomings of the prior art, the purpose of this application is to provide a latent constraint structure learning method and system based on quantum measurement data.

[0008] A first aspect of this application provides a latent constraint structure learning method based on quantum measurement data, comprising: Construct a Pauli measurement basis and a quantum measurement dataset, wherein the samples in the quantum measurement dataset are ±1 bit strings measured under the Pauli measurement basis; The pre-defined Transformer structure encoder is trained using the quantum measurement dataset. Single-bit mask prediction is performed for each target position, and the dependency graph between variables under the mask condition is extracted through structure mask attention. Based on the variable dependency graph, support sets are extracted for the target locations to determine the support set for each target location; Parity check and GF(2) Gaussian elimination are performed on the support set of each target location to determine the set of linear constraints for the qubit. Map the set of linear constraints of the qubits to verified Pauli generators to determine the set of verified stable subgenerators. Based on the commutation space of the verified stable sub-generator set, a new Pauli measurement basis is constructed. The model learning phase and statistical verification phase are repeated until the preset convergence condition is met, and the complete set of stable sub-generators is determined.

[0009] Optionally, the construction of the Pauli measurement basis and quantum measurement dataset includes: Determine the number of multiple qubits; The Pauli measurement basis is constructed based on the number of qubits. Based on a preset number of samplings and preset noise parameters, repeated sampling is performed under the Pauli measurement basis to determine multiple quantum observation samples and construct the quantum measurement dataset.

[0010] Optionally, the step of training a pre-defined Transformer structure encoder using the quantum measurement dataset, performing single-bit mask prediction for each target position, and extracting the inter-variable dependency graph under mask conditions through structure mask attention includes: The quantum measurement dataset is divided into a training set and a constraint set according to a preset ratio; The quantum observation samples in the training set are randomly masked to determine the quantum observation samples after random masking. The quantum observation sample with random masking is input into the preset Transformer structure encoder, and the predicted value of the target position of the random mask is output to train the preset Transformer structure encoder. Based on the predicted value of the target position of the random mask and the actual value of the target position of the random mask, the binary cross-entropy loss is determined using the binary cross-entropy loss function. The binary cross-entropy loss is used to optimize the preset Transformer structure encoder to determine the trained Transformer structure encoder. The quantum observation samples in the constraint set are randomly masked and then input into the trained Transformer structure encoder. The dependency graph between variables under the masked conditions is extracted in the last layer of self-attention of the trained Transformer structure encoder.

[0011] Optionally, the step of extracting support sets for target locations based on the inter-variable dependency graph, and determining the support set for each target location, includes: Based on the dependency graph between variables, determine the candidate position sequence for each target position, sorted in descending order of dependency. According to the candidate position sequence of each target position, a greedy variable addition strategy is sequentially applied to the candidate positions, and the trained Transformer structure encoder is input to determine the predicted value of the target position. The prediction accuracy of the target location is determined based on the predicted value and the actual value of the target location. Based on the candidate position sequence of each target position, the candidate position sequence before the candidate position whose prediction accuracy is not less than a preset accuracy threshold is determined as the support set of the target position, and the support set of each target position is determined.

[0012] Optionally, the parity check verification and GF(2) Gaussian elimination process performed on the support set for each target location to determine the set of linear constraints for the qubit includes: For each target location, parity check is performed on the support set. Candidate locations with a sample ratio of actual verification parity product result of 1 that is less than the weight-aware verification threshold are removed to determine the stable support set for each target location. Gaussian elimination is performed sequentially on the stable support set of each target location to determine the linear constraint set of the qubit.

[0013] Optionally, the step of constructing a new Pauli measurement basis based on the commutation quotient space of the verified stable sub-generator set, repeatedly executing the model learning phase and the statistical verification phase until a preset convergence condition is met, and determining the complete set of stable sub-generators, includes: During the model learning phase, based on the search pattern of the quotient space, a trained Transformer structure encoder is used to search for multiple potential constraints under the new Pauli measurement basis. The constraint structure learning is performed iteratively. The set of verified stable sub-generators determined in each iteration is subjected to physical consistency screening with the set of historical verified stable sub-generators to determine whether the set of verified stable sub-generators is a new constraint. The model parameters of the trained Transformer structure encoder in the previous round are reused as the initial model parameters of the Transformer structure encoder model in the next round. The constraint structure learning is performed iteratively until there are no new constraints for a consecutive preset number of rounds, and then the model is switched to the verification mode of the statistical verification phase. In the verification mode of the statistical verification stage, based on a preset number of measurement samples, a bitwise multiplication operation is performed on all measurement positions corresponding to the verified stable subgenerator set to determine the odd-even product result of each measurement sample. The percentage of measurement samples with a parity product result of 1 is statistically analyzed to determine the average parity product result. If the average parity product result is not less than the preset verification threshold, the set of verified stable sub-generators is included in the complete set of stable sub-generators; if the average parity product result is less than the preset verification threshold, the set of verified stable sub-generators is discarded, and the verification result is determined. Based on the verification results, the complete set of stable subgenerators is determined.

[0014] Optionally, the step of performing a physical consistency screening process on the verified stable sub-generator set determined in each iteration and the historical verified stable sub-generator set to determine whether the verified stable sub-generator set is a new constraint includes: The verified Pauli generators in the set of verified stable sub-generators are normalized to determine the verified Pauli generators after normalization. In the historical generator dictionary composed of historical Pauli generator sets, the normalized verified Pauli generators are looked up. If the normalized verified stable sub-generator set already exists, it is discarded; otherwise, it is determined as the deduplicated verified stable sub-generator set. Based on the deduplicated verified stable generator set, the average parity expectation value of the deduplicated verified stable generator set on the corresponding quantum measurement dataset is calculated. If the average parity expectation value is less than a preset expectation threshold, it is discarded. If the average parity expectation value is not less than the preset expectation threshold, it is determined as a verified stable generator set that has been screened by physical characteristics. The verified stable sub-generator set filtered by physical features and the historical generator set are encoded as symplectic vectors over a two-source domain. Incremental Gaussian elimination is performed on the symplectic vectors in the two source domains. Verified Pauli generators whose rank changes are identified as new constraints, while verified Pauli generators whose rank remains unchanged are removed.

[0015] A second aspect of this application provides a latent constraint structure learning system based on quantum measurement data, comprising: The data acquisition module is used to construct the Pauli measurement base and the quantum measurement dataset, wherein the samples of the quantum measurement dataset are ±1 bit strings measured under the Pauli measurement base; The model training module uses the quantum measurement dataset to train a preset Transformer structure encoder, performs single-bit mask prediction for each target position, and extracts the inter-variable dependency graph under the mask condition through structure mask attention. The support set search module extracts the support set for the target location based on the dependency graph between variables, and determines the support set for each target location. Support set simplification module is used to perform parity check verification and GF(2) Gaussian elimination on the support set of each target location to determine the set of linear constraints of the qubit; A verified Pauli generator generation module is used to map the set of linear constraints of the qubits to verified Pauli generators and determine the set of verified stable subgenerators. The iterative optimization module is used to construct a new Pauli measurement basis based on the commutation space of the verified stable sub-generator set, repeatedly execute the model learning phase and the statistical verification phase until the preset convergence condition is met, and determine the complete set of stable sub-generators.

[0016] A third aspect of this application provides a non-transitory computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of any of the methods provided in the first aspect of this application.

[0017] A fourth aspect of this application provides an electronic device comprising: A memory on which computer programs are stored; A processor for executing the computer program in the memory to implement the steps of any of the methods provided in the first aspect of this application.

[0018] The latent constraint structure learning method based on quantum measurement data proposed in this application constructs a quantum measurement dataset and trains a Transformer encoder. It performs single-bit mask prediction for each target position and extracts the inter-variable dependency graph under the mask condition through structure mask attention. Combined with the support set search guided by the dependency graph, it can accurately identify the decisive condition dependency when only limited measurement results are available, effectively avoiding the exponential complexity brought about by the reconstruction of the complete quantum state. By performing parity check verification and GF(2) Gaussian elimination on the support set of each target position, a compact, interpretable and mutually independent set of latent linear constraints can be extracted from the high-dimensional quantum measurement bit string. The set of quantum bit linear constraints is mapped to verified Pauli generators. Finally, based on the set of verified stable generators, an adaptive iterative strategy combining the model learning stage and the statistical verification stage is used for incremental exploration. Invalid measurement configurations are reduced round by round, which greatly improves the data efficiency of constraint discovery and can efficiently and accurately determine the complete set of stable generators.

[0019] Other technical effects resulting from the additional features will be further illustrated in the corresponding embodiments. Attached Figure Description

[0020] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating a latent constraint structure learning method based on quantum measurement data according to an exemplary embodiment.

[0021] Figure 2 This is a schematic diagram illustrating a complete quantum state reconstruction turning to latent structure learning according to an exemplary embodiment.

[0022] Figure 3 This is a schematic diagram illustrating a closed-loop constraint structure learning process according to an exemplary embodiment.

[0023] Figure 4 This is a schematic diagram illustrating a dependency graph and support set search results under local, global, and mixed constraint scenarios according to an exemplary embodiment.

[0024] Figure 5 This is a schematic diagram illustrating the training loss and prediction accuracy of a pre-defined Transformer structure encoder under different constraint types, system sizes, and noise levels, according to an exemplary embodiment.

[0025] Figure 6This is a schematic diagram illustrating a comparison of the robustness of different models under varying noise and qubit size according to an exemplary embodiment.

[0026] Figure 7 This is a schematic diagram of the dynamic curve of adaptive constraint structure learning on GHZ, Ring Graph, and Star Graph structures according to an exemplary embodiment.

[0027] Figure 8 This is a schematic diagram of a potential constraint structure learning system based on quantum measurement data, according to an exemplary embodiment. Detailed Implementation

[0028] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application. These all fall within the protection scope of the present application.

[0029] The terms "comprising" and "having," and any variations thereof, in the embodiments of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such processes, methods, products, or devices.

[0030] In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0031] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature.

[0032] Existing methods for analyzing and reconstructing the state and physical laws of quantum systems from quantum measurement data include three categories: quantum state reconstruction, observation prediction, and stabilizer learning. Quantum state reconstruction methods suffer from high complexity and insufficient interpretability in high dimensions; observation prediction methods struggle to obtain reusable and interpretable latent constraints; and stabilizer learning cannot adapt to scenarios where constraints are unknown under real-world constrained measurements. Furthermore, none of these methods simultaneously fulfill the three core requirements of directly mining constraints under constrained Pauli measurements, screening candidate constraints for physical consistency and independence, and adaptively planning subsequent measurements based on existing constraints. To address these issues, this application provides a latent constraint structure learning method based on quantum measurement data to resolve the aforementioned problems.

[0033] Figure 1 This is a flowchart illustrating a latent constraint structure learning method based on quantum measurement data according to an exemplary embodiment. Figure 2 This is a schematic diagram illustrating a complete quantum state reconstruction turning to latent structure learning according to an exemplary embodiment. Figure 3 This is a schematic diagram illustrating a closed-loop constraint structure learning process according to an exemplary embodiment.

[0034] Reference Figures 1 to 3 As shown in one embodiment of this application, a latent constraint structure learning method based on quantum measurement data is provided, including S11 to S16.

[0035] S11, construct the Pauli measurement basis and quantum measurement dataset.

[0036] Specifically, the quantum measurement dataset consists of ±1 bit strings measured under the Pauli measurement basis.

[0037] S12 uses a quantum measurement dataset to train a pre-defined Transformer structure encoder, performs single-bit mask prediction for each target position, and extracts the inter-variable dependency graph under the mask condition through structure mask attention.

[0038] S13. Based on the dependency graph between variables, the support set of the target location is extracted to determine the support set of each target location.

[0039] S14, perform parity check verification and GF(2) Gaussian elimination on the support set of each target location to determine the set of linear constraints for the qubit.

[0040] S15, map the set of linear constraints of qubits to verified Pauli generators, and determine the set of verified stable generators.

[0041] S16. Construct a new Pauli measurement basis based on the commutation space of the verified stable sub-generator set, and repeat the model learning phase and statistical verification phase until the preset convergence condition is met, and determine the complete set of stable sub-generators.

[0042] In the embodiments described above, by constructing a quantum measurement dataset and training a Transformer encoder, single-bit mask prediction is performed for each target position. The dependency graph between variables under the mask condition is extracted through structural mask attention. Combined with the support set search guided by the dependency graph, the decisive condition dependency can be accurately identified when only limited measurement results are available, effectively avoiding the exponential complexity brought about by the reconstruction of the complete quantum state. By performing parity check verification and GF(2) Gaussian elimination on the support set of each target position, a compact, interpretable and mutually independent set of potential linear constraints can be extracted from the high-dimensional quantum measurement bit string. The set of linear constraints of the quantum bits is mapped to verified Pauli generators. Finally, based on the set of verified stable generators, an adaptive iterative strategy combining the model learning stage and the statistical verification stage is used for incremental exploration. Invalid measurement configurations are reduced round by round, which greatly improves the data efficiency of constraint discovery and can efficiently and accurately determine the complete set of stable generators.

[0043] In some specific embodiments of this application, for S11, constructing the Pauli measurement basis and quantum measurement dataset can be carried out using S111 to S113.

[0044] S111 determines the number of multiple qubits.

[0045] S112, construct the Pauli measurement basis based on the number of multiple qubits.

[0046] S113. Based on the preset number of samplings and preset noise parameters, repeatedly sample under the Pauli measurement basis to determine multiple quantum observation samples and construct a quantum measurement dataset.

[0047] Based on the above steps S111 to S113, for example, a Pauli measurement basis s∈{X,Y,Z}^n is set for n qubits, and N observation results are obtained by repeatedly sampling under the Pauli measurement basis. Each observation result is a binary / symbol sequence of length n.

[0048] Specifically, the code for the quantum measurement dataset supports both stable subdata generated by the stable subdata sampling module (sample_stabilizer_data) and controllable constraint data such as the controllable constraint sample generation module (sample_6bit_constraint). Bit flip noise can be injected through the bit flip noise injection module (add_bitflip_noise) to simulate a noisy quantum experimental environment.

[0049] The embodiments described above in this application, by determining multiple qubits and constructing a Pauli measurement basis, and generating quantum observation sequences through repeated sampling based on preset sampling times and noise parameters, achieve standardization of measurement configuration and efficient automation of data acquisition. Simultaneously, relying on a data generation mechanism that supports stable subdata generation, controllable constraint construction, and qubit-flipping noise injection, it can flexibly simulate real noisy quantum experimental environments, effectively improving the diversity, controllability, and noise robustness of the dataset. This provides high-quality, realistic training data support for subsequent dependency graph modeling and quantum constraint discovery algorithms, significantly enhancing the model's generalization ability and engineering practicality under complex noise conditions.

[0050] In some specific embodiments of this application, for S12, a preset Transformer structure encoder is trained using a quantum measurement dataset, and a single-bit mask prediction is performed for each target position. The dependency graph between variables under the mask condition is extracted through structure mask attention. This can be implemented as S121 to S126.

[0051] S121, the quantum measurement dataset is divided into a training set and a constraint set according to a preset ratio.

[0052] Specifically, the preset ratio can be, but is not limited to, 4:1, where 80% of the quantum test dataset is used as the training set and 20% of the quantum test dataset is used as the constraint set.

[0053] The preset ratio can be adjusted adaptively according to experimental needs and is not limited to this ratio.

[0054] The training set is used to train the pre-defined Transformer structure encoder, and the constraint set is used for constraint exploration.

[0055] S122, Randomly mask the quantum observation samples in the training set to determine the quantum observation samples after random masking.

[0056] Specifically, [mask] markers are introduced at random positions of quantum observation samples in the quantum measurement dataset to achieve random masking.

[0057] S123: Input the quantum observation sample with random masking into the preset Transformer structure encoder, output the predicted value of the target position of the random mask, and train the preset Transformer structure encoder.

[0058] Specifically, the pre-defined Transformer structure encoder encodes the quantum observation samples with introduced [mask] tags into a token sequence and predicts the qubit value of the target position with introduced [mask] tags.

[0059] The pre-defined Transformer structure encoder learns the conditional dependency of the objective "whether the masked variable can be determined when some variables are known" through joint single-bit prediction.

[0060] During training, mechanisms such as learning rate warmup, cosine decay, and gradient pruning can be used to improve stability.

[0061] S124. Based on the predicted value of the target position of the random mask and the actual value of the target position of the random mask, the binary cross-entropy loss function is used to determine the binary cross-entropy loss.

[0062] S125 uses binary cross-entropy loss to optimize the preset Transformer structure encoder and determines the trained Transformer structure encoder.

[0063] Specifically, the prediction accuracy of the target location is determined based on the binary cross-entropy loss function, and this accuracy is used as the basis for backpropagation.

[0064] S126: After randomly masking the quantum observation samples in the constraint set, input them into the trained Transformer structure encoder. Extract the inter-variable dependency graph under the mask condition in the last layer of self-attention of the trained Transformer structure encoder.

[0065] Specifically, the quantum observation samples in the constraint set are randomly masked, as detailed in step S122 above, which will not be repeated here. The randomly masked quantum observation samples in the constraint set are then input into the trained Transformer structure encoder. In the self-attention weight matrix of the last layer of the trained Transformer structure encoder, the row and column are used as the corresponding positions of the pairs of variables, and the attention weights are used as the variable dependency strength scores. A threshold is set to retain high-weight association pairs, and an undirected variable dependency graph is constructed.

[0066] In some specific embodiments of this application, step S126 above can also be implemented by extracting a dependency graph from the equivalence dependency score: Based on the final layer output of the trained Transformer encoder, the correlation dependency score is calculated for each input variable one by one through methods such as gradient attribution, feature perturbation or SHAP to quantify the pairwise dependence between variables. After thresholding, a variable dependency graph is constructed.

[0067] This variable dependency graph is used to obtain the candidate related position ranking for each target position. It is not directly equivalent to physical constraints, but serves as heuristic information for subsequent support set search.

[0068] The embodiments described above in this application, by randomly masking quantum observation samples and driving the Transformer encoder to perform mask position prediction tasks, combined with binary cross-entropy loss to optimize network parameters, force the model to deeply explore the contextual relationships and conditional dependencies between qubits; and then directly extract the dependency graph between variables from the self-attention weights of the last layer of the encoder after training, which can intuitively and efficiently characterize the potential interactions and higher-order correlations of multiple qubits under constrained observation. This method can accurately model local and global dependency structures without complete quantum state reconstruction, and has both strong nonlinear feature capture capabilities and topological interpretability, providing a high-confidence structural prior for subsequent support set search and constraint discovery, significantly improving the accuracy of dependency extraction, model generalization ability and computational efficiency.

[0069] In some specific embodiments of this application, for S13, the support set of the target position is extracted according to the dependency graph between variables, and the support set of each target position is determined. This can be done by S131 to S134.

[0070] S131, Based on the dependency graph between variables, determine the candidate position sequence for each target position, sorted in descending order of dependency.

[0071] Specifically, the candidate positions of each target are sorted from high to low according to their dependency to obtain the candidate position sequence for each target position.

[0072] S132, according to the candidate position sequence of each target position, the greedy variable addition strategy is executed sequentially on the candidate positions, and the trained Transformer structure encoder is input to determine the predicted value of the target position.

[0073] Specifically, for each target position t, all other positions in the sequence are initially set to a masked state, and the target position t remains masked and awaits prediction. Based on the candidate position sequence of each target position, a greedy variable addition strategy is adopted to remove the mask of highly correlated candidate positions one by one / batch by batch, and gradually input them into the trained Transformer structure encoder to output the predicted value of the target position.

[0074] S133, Determine the prediction accuracy of the target location based on the predicted value and the actual value of the target location.

[0075] Specifically, determine the accuracy of the target location prediction: Real label: y=[+1, 1,+1,+1, 1] ; The predicted value output by the model (can be score / logit): s=[2.3, 0.7, [0.2, 1.1, 0.4] ; If score > 0, predict +1; if score < 0, predict -1. 1; Convert the model's predicted values ​​into predicted labels: s=[+1,-1,-1,+1,+1] Therefore, 3 predictions were correct, out of a total of 5: Accuracy = 3 / 5 = 60% S134, according to the candidate position sequence of each target position, determine the candidate position sequence before the candidate position corresponding to the candidate position whose prediction accuracy is not less than the preset accuracy threshold as the support set of the target position, and determine the support set of each target position.

[0076] Specifically, based on the above steps S133 to S134, when the prediction accuracy of the target location first reaches the preset accuracy threshold... When the target position t is reached, stop adding new candidate positions and use the set of candidate positions that have been unmasked as the support set for the target position t. .

[0077] Based on the above steps S131 to S134, all bit target positions are traversed to complete the support set search for all target positions.

[0078] The above embodiments of this application, through the descending candidate sorting and greedy variable addition strategy guided by the dependency graph, combined with the Transformer prediction accuracy threshold judgment, realize the adaptive and accurate screening of the target position support set, effectively avoid the exponential search overhead of the full variable combination, and use the model representation to automatically truncate weakly correlated and redundant variables, while ensuring high prediction accuracy and obtaining a compact and complete minimum variable subset. The determined support set provides a high-confidence structural prior for subsequent cross-sample verification and GF(2) constraint reduction, significantly reducing the computational complexity and improving the data efficiency and noise robustness of the constraint discovery process.

[0079] In some specific embodiments of this application, for S14, parity check verification and GF(2) Gaussian elimination are performed on the support set of each target location to determine the set of linear constraints of the qubit, which can be done using S141 to S142.

[0080] S141, perform parity check verification on the support set of each target location, remove candidate locations where the proportion of samples with an actual verification parity product of 1 is less than the weight-aware verification threshold, and determine the stable support set for each target location.

[0081] Specifically, during the verification process, a preset number of samples are collected based on the location of the support set. A parity test is then performed based on the number of locations in the support set, which involves multiplying the samples at the support set locations together to obtain the parity of that sample.

[0082] The preset number of samples can be 128.

[0083] In the noisy verification phase, we apply a weight-aware verification threshold to each candidate position (c), and the neural network extractor does not need to know the weights of the real stabilizer in advance.

[0084] Once a candidate position (c) is proposed, its support size can be calculated, which is the number of qubits actually affected by the candidate position (c), denoted as weight (w(c)). This weight (w(c)) is only related to the structure of the candidate position (c) itself and is independent of noise.

[0085] When bit-flip noise occurs independently in each qubit, and the noise rate is (p), the expected amplitude of the parity measurement for the true stable sub-c will decrease to... The essence of decay is that noise disrupts the "conservation" of the stabilizer, and the more factors that interact (the larger the weight (w(c))), the more severe the impact of noise, and the faster the decay.

[0086] To distinguish between "true stables" and "false stables" under noise, a weight-aware verification threshold is set, taking into account both statistical significance and weight-related decay caused by noise, to avoid misjudging coincidental results caused by random noise as true stables. The larger the weight of a stable, the more it is affected by noise, so we need to set a more lenient threshold for its expected amplitude (because it decays more naturally).

[0087] Measure the parity magnitude of the candidate position (c) and compare it with the weighted perception threshold; If the measured amplitude is higher than the threshold, c is considered a true stable component; otherwise, it is rejected.

[0088] The specific formula is as follows: in, Indicates the weight-aware threshold. This indicates the number of candidate positions tested in the current round. This indicates the number of samples used for validation. This represents the allowed overall false acceptance probability. This represents the probability of single-qubit bit-flip noise. Indicates candidate position The size or weight of the support. This represents the safety margin under a finite sample size.

[0089] For example, on different quantum observation samples, a support set for each target position is obtained. This support set is characterized as the set of candidate bits that can determine the target position t under that quantum observation sample.

[0090] Iterate through the candidate positions of each target position and multiply the samples of the candidate positions in the support set to obtain the parity of that sample. Based on the weight-aware verification threshold, remove the candidate positions that are not greater than the weight-aware verification threshold, thereby filtering out unstable dependencies and false dependencies and determining the stable support set for each target position.

[0091] S142, Gaussian elimination is performed sequentially on the stable support set of each target location to determine the set of linear constraints for the qubit.

[0092] Specifically, the GF(2) Gaussian elimination process is as follows: The stable support set for each target location is written as an augmented matrix, with each row representing a modulo 2 linear equation.

[0093] Select the pivot column in the order of variables, and find the row with a value of 1 in the current column as the pivot row; if the current row is not the pivot row, swap the two rows.

[0094] Subsequently, for all other rows that have a value of 1 in the pivot column, perform a row XOR operation, which involves XORing the row bit by bit with the pivot row, thereby eliminating the other 1s in the column.

[0095] Repeat the above process until all optional pivot columns have been processed.

[0096] Since addition and subtraction in GF(2) are equivalent to XOR, only two types of operations, "row swap" and "row XOR", are needed in the elimination process.

[0097] After elimination, if a row appears where all elements on the left are 0 and all elements on the right are 1, then the constraint set has no solution; otherwise, by back-substituting the principal variables and free variables, a solution that satisfies the constraint set is obtained, which is the set of linear constraints for the qubit.

[0098] For the stable support set problem, 1 in the solution corresponds to the position selected into the support set, and 0 corresponds to the position not selected.

[0099] In some specific embodiments of this application, step S143 may also involve sequentially performing row minimum form reduction on each target stable support set to obtain a set of linear constraints for qubits.

[0100] The embodiments described above in this application, through parity check verification, effectively eliminate redundant variables affected by noise or random correlation, significantly improving the statistical stability and noise robustness of the support set; further, Gaussian elimination is performed on the stable support set to achieve algebraic normalization, automatically eliminating linear correlation and repetition constraints, and extracting a set of mutually independent and structurally compact qubit linear constraints; the statistical screening and rigorous algebraic reduction are deeply integrated, which greatly compresses the search space and computational overhead while ensuring the mathematical rigor and physical interpretability of the constraint set, providing a high-confidence algebraic prior for the accurate discovery of subsequent stable subgenerators.

[0101] In some specific embodiments of this application, for S16, mapping the set of linear constraints of qubits to verified Pauli generators and determining the set of verified stable subgenerators can be achieved by: Based on the current measurement basis, fill in the corresponding X / Y / Z at the support positions and fill in I at other positions to obtain the candidate Pauli generator representation, which is used to uniformly describe the constraints and subsequent experimental design.

[0102] In some specific embodiments of this application, for S16, a new Pauli measurement basis is constructed based on the commutation space of the verified stable sub-generator set, and the model learning phase and statistical verification phase are repeatedly executed until the preset convergence condition is met, and the complete set of stable sub-generators is determined. This can be achieved using S161 to S165.

[0103] S161, during the model learning phase, based on the search pattern of the quotient space, a trained Transformer structure encoder is used to search for multiple potential constraints under the new Pauli measurement basis. The constraint structure learning is performed iteratively. The set of verified stable sub-generators determined in each iteration is subjected to physical consistency screening with the set of historical verified stable sub-generators to determine whether the set of verified stable sub-generators is a new constraint. The model parameters of the trained Transformer structure encoder in the previous round are reused as the initial model parameters of the Transformer structure encoder model in the next round. The constraint structure learning is performed iteratively until there are no new constraints for a consecutive preset number of rounds, and then the model is switched to the verification mode of the statistical verification phase.

[0104] Specifically, step S161 can refer to steps S11 to S15 above, generate a new Pauli measurement basis based on the search pattern of the easy quotient space, and execute steps S11 to S15 above to perform constraint structure learning, determine the set of verified stable sub-generators, until no new constraints are added for consecutive preset rounds.

[0105] Among them, the physical consistency screening process is performed on the set of verified stable subgenerators determined in each iteration and the set of historical verified stable subgenerators to determine whether the set of verified stable subgenerators is a new constraint. This process can be carried out using S101 to S105.

[0106] S101, normalize the verified Pauli generators in the set of verified stable sub-generators to determine the normalized verified Pauli generators.

[0107] Specifically, the normalization process for the verified Pauli generators includes: The verified Pauli operators are uniformly represented by removing the global phase (usually fixed at +1) and then normalizing them according to a fixed bit order.

[0108] S102, in the historical generator dictionary composed of the historical Pauli generator set, look up the normalized verified Pauli generator. If the normalized verified Pauli generator already exists, discard it. If it does not exist, determine it as the set of verified stable sub-generators after deduplication.

[0109] Specifically, the table lookup operation can be a hash lookup, and if a match is found, the match is discarded.

[0110] If a normalized verified Pauli generator exists in the historical generator dictionary, it indicates that the normalized verified Pauli generator is a duplicate and can be discarded. The normalized verified Pauli generators that do not exist in the historical generator dictionary are combined to form a set of deduplicated verified stable sub-generators.

[0111] S103. Based on the deduplicated set of verified stable generators, calculate the average parity expectation of the deduplicated set of verified stable generators on the corresponding quantum measurement dataset. If the average parity expectation is less than a preset expectation threshold, discard it. If the average parity expectation is not less than the preset expectation threshold, determine it as a set of verified stable generators that has been screened by physical characteristics.

[0112] Specifically, calculations are performed using a quantum measurement dataset: in, This represents the result of a single parity measurement. denoted as mean parity expectation, and N represents the number of measurements.

[0113] The preset expected threshold is 0.9.

[0114] Ideal stable substate satisfy Theoretical expectation =1, but the actual value will be attenuated due to readout error, gate noise, decoherence, etc. The preset expected threshold of 0.9 is an empirical value used to distinguish between "true stable sub-signals" and "random fluctuation / unstable sub-operators".

[0115] S104, the verified stable generator set and the historical generator set, which have been filtered by physical features, are encoded into symplectic vectors over the two source domains.

[0116] S105 performs incremental Gaussian elimination on the symplectic vectors in the two-source domain, identifying the verified Pauli generators whose rank changes as new constraints and eliminating the verified Pauli generators whose rank remains unchanged.

[0117] Specifically, the verified Pauli generators corresponding to rank invariant functions are determined to be linear combinations of known neurons and rejected.

[0118] Specifically, based on the above steps S104 to S105, the following is an example: Map the Pauli operator to binary vectors on : This indicates that the i-th qubit contains either X or Y; Indicates the presence of Z or Y Add the symplectic vector corresponding to the verified Pauli generator to the historical Pauli generator matrix and perform modulo 2 Gaussian elimination.

[0119] Where I represents no flip → (0,0); X represents bit flip only → (1,0); Z represents phase flip only → (0,1); Y represents bit + phase flip → (1,1).

[0120] A new generator is only accepted if the GF(2) rank of the matrix increases strictly.

[0121] S162, in the verification mode of the statistical verification stage, based on a preset number of measurement samples, perform a bitwise multiplication operation on all measurement positions corresponding to the verified stable subgenerator set to determine the odd-even product result of each measurement sample.

[0122] S163, Calculate the percentage of measurement samples with a parity product result of 1, and determine the average parity product result.

[0123] S164. If the average parity product result is not less than the preset verification threshold, the set of verified stable child generators is included in the set of stable child generators. If the average parity product result is less than the preset verification threshold, the set of verified stable child generators is discarded, and the verification result is determined.

[0124] Specifically, steps S162 to S164 can be referred to step S141 above, and will not be repeated here.

[0125] S165. Based on the verification results, determine the complete set of stable sub-generators.

[0126] Specifically, the set of verified stable child generators is updated to the complete set of stable child generators to determine the complete set of stable child generators.

[0127] The embodiments described above in this application achieve efficient mining of constraint structures by combining theoretical search of the quotient space with Transformer deep learning; the introduction of physical consistency screening and model parameter reuse mechanisms effectively avoids redundant search and significantly accelerates iterative convergence; at the same time, relying on the quantitative verification strategy of bitwise multiplication and parity product statistics, reliable verification of candidate constraints in noisy environments is achieved. This method significantly reduces measurement overhead and computational complexity while ensuring the rigor of quantum physics, and improves the convergence efficiency, noise robustness, and engineering feasibility of constructing the complete set of stable subgenerators.

[0128] Figure 2 This is a schematic diagram illustrating a complete quantum state reconstruction turning to latent structure learning according to an exemplary embodiment.

[0129] Reference Figure 2 As shown, Figure 2 In the diagram, (a) indicates that the complex quantum state has a potential global structure, which can be indirectly obtained through Pauli measurement.

[0130] Figure 2 (b) indicates that complete quantum state tomography is not feasible due to the exponential growth in the number of observations required; shadow tomography, while efficient in estimating specific physical quantities, cannot reveal the underlying structure.

[0131] Figure 2 (c) in this application indicates that quantum state analysis is formulated as a structure learning problem, directly extracting correlations and constraint structures from measurement data.

[0132] Reference Figure 2 As shown, the latent constraint structure learning method based on quantum measurement data proposed in this application provides a quantum state representation modeling method for implicit constraint structures. It is a classical representation of quantum states with interpretability and overall quantum state description, providing a new paradigm for quantum state learning.

[0133] Figure 3 This is a schematic diagram illustrating a closed-loop constraint structure learning process according to an exemplary embodiment.

[0134] Reference Figure 3 As shown, Figure 3 In this context, (a) represents training the MCM using a classic ±1 bit string under a fixed n-bit measurement basis, i.e. And a joint single-bit mask is used to predict the target.

[0135] Figure 3 In (b), it means that the structured attention mask restricts the information flow to the candidate support set. The ISP iteratively removes low-saliency paths and requires that the mask prediction accuracy be maintained after removal, thus obtaining the minimum candidate parity constraint.

[0136] Figure 3 In the diagram, (c) indicates that the updated measurement basis phase uses a validated generator Gr to compute the quotient space direction in the centralizer Z(Gr) / <Gr>. Phase A greedily packs compatible quotient space representatives into the same measurement setting to expose multiple new constraints to the MCM. Phase B samples a single quotient space anchor and validates it through direct parity statistics, thus avoiding the bias of the packing strategy on the remaining high-weight generators.

[0137] Reference Figure 3 As shown in the figure, this application realizes structural modeling of quantum states through the complete process depicted in the figure, thereby avoiding the cumbersome quantum state tomography process and realizing the expression of implicit constraint relations.

[0138] Figure 4 This is a schematic diagram illustrating a dependency graph and support set search results under local, global, and mixed constraint scenarios according to an exemplary embodiment.

[0139] Figure 4 In the diagram, (a) represents the global dependency graph learned under the global constraint structure. Figure 4 In the diagram, (b) represents the local dependency graph learned under the local constraint structure. Figure 4 In the diagram, (c) represents the mixed dependency graph learned under the mixed constraint structure; the diagonal shading represents the masked target variable. Figure 4 In the diagram, (d) represents the mask subset detection result under the global constraint structure. Figure 4 In the diagram, (e) represents the mask subset detection result under the local constraint structure. Figure 4 In the diagram, (f) represents the mask subset detection result under the hybrid constraint structure.

[0140] Reference Figure 4 As shown, the latent constraint structure learning method based on quantum measurement data provided in this application can accurately learn the dependencies between variables and detect the corresponding mask subsets with high confidence under three typical constraint structures: global, local, and hybrid. The dependency matrix clearly restores the structural features under different constraint scenarios, and the subset detection results achieve full confidence under key configurations. This verifies that the algorithm has high-precision recognition capability and strong robustness for multi-scale constraint scenarios under the parity check verification framework, and provides reliable structural prior support for the adaptive iterative update and convergence determination of subsequent stable subgenerators.

[0141] Figure 5 This is a schematic diagram illustrating the training loss and prediction accuracy of a pre-defined Transformer structure encoder under different constraint types, system sizes, and noise levels, according to an exemplary embodiment.

[0142] (a, b) represent the training loss and prediction accuracy under the local constraint mechanism, corresponding to the short-range dependency structure.

[0143] Reference Figure 5 As shown in (a, b), n The training dataset has a size of N_p = 1024 and a batch size of 128, with a probability of {6, 10, 20, 40}. To simulate a noisy experimental environment, a probability of 1 / 40 is added. Random bit-flipping noise.

[0144] (c, d) represent the training loss and prediction accuracy under the global constraint mechanism, characterized by a full pair and full dependency relationship. The results show that n For the case {6, 8, 10, 12}, the training dataset size is N_p = 2048, the batch size is 512, and the same noise level is used. The shaded area represents the interquartile range (IQR) of the results from 5 runs.

[0145] Reference Figure 5 As shown, the preset Transformer structure encoder has fast convergence capability and strong noise robustness under both local (short-range dependency) and global (all-total dependency) constraint mechanisms. Under experimental conditions with different system sizes (n=6~40) and the introduction of random bit flip noise, the training loss rapidly decreases to a stable low level, the prediction accuracy quickly approaches 1.0, and the convergence of the interquartile range shaded area in multiple independent runs is narrow, verifying the stability and repeatability of the algorithm under scale expansion.

[0146] The above results fully demonstrate that the pre-defined Transformer structure encoder can efficiently and accurately capture multi-scale quantum dependency structures in noisy environments, providing a reliable feature representation basis for subsequent dependency graph construction, high-confidence detection of mask subsets, and adaptive iteration of stable subgenerators.

[0147] Figure 6 This is a schematic diagram illustrating a comparison of the robustness of different models under varying noise and qubit size according to an exemplary embodiment.

[0148] Figure 6 In the diagram, (a) represents a performance comparison of Transformer, CNN, and MLP models under a global constraint learning task. Figure 6 (b) in the figure represents a performance comparison of Transformer, CNN, and MLP models under local constraint learning tasks.

[0149] Reference Figure 6 As shown, under a fair benchmark with uniform parameter quantity and two-layer architecture, the latent constraint structure learning method based on quantum measurement data provided in this application exhibits significantly better robustness than the comparative model under different qubit scale expansions and noise level perturbations. Its performance degradation is more gradual, and it can stably maintain high constraint capture accuracy in both global and local typical dependency structures. This verifies the strong generalization ability and scalability of the algorithm architecture in complex quantum environments, providing reliable benchmark support for constraint learning in practical noisy quantum systems.

[0150] The following examples and comparative examples will be used to further illustrate this application in order to better understand the above-mentioned technical solutions. It should be understood that the following are only some examples and are not intended to limit this application.

[0151] Figure 7This is a schematic diagram of the dynamic curve of adaptive constraint structure learning on GHZ, Ring Graph, and Star Graph structures according to an exemplary embodiment.

[0152] Example 1: Six-bit local + global hybrid constraint scenario Reference Figure 7 As shown, in the six-bit experiment, constraints can be artificially constructed: Q0=Q1, Q2=Q3, Q5=Q0⊕Q2⊕Q4. First, a batch of six-bit measurement bit strings are collected, the mask constraint model is trained, and then support set probing is performed on each target bit. Support set probing of target bit 5 yields approximate support {0,2,4}, while local support {0} and {2} are obtained for target bits 1 and 3, respectively. After GF(2) elimination, a hybrid constraint set with both local and global constraints can be recovered.

[0153] Example 2: Learning a 16-bit GHZ stable substructure Reference Figure 7 As shown, for a 16-bit GHZ structure, sampling begins with a random measurement basis. In early rounds, the algorithm prioritizes finding paired ZZ constraints and freezes the positions involved in the constraints as Z-basis; subsequently, after consecutive pauses, it switches to a commutative propagation mode to expose the global X^ with a higher probability. n constraints. Experimental results show that the number of frozen positions and the number of discovered independent constraints increase rapidly with each round, and approach the complete generator set within a few additional rounds.

[0154] Example 3: Learning Graph / Ring Graph Structures Reference Figure 7 As shown, for stable subfamilies of Ring Graph or Star Graph, the constraint support discovered in the current round can be mapped to the candidate graph structure. Then, the discovered boundaries are stabilized first through freeze-random exploration, and long-range dependencies are supplemented by easily propagating constraints. Since some constraints in Ring Graph involve three-body relationships, the algorithm can gradually recover its structure through a longer support set and multiple rounds of exploration; Star Graph converges faster due to the prominent constraints of the central node.

[0155] Example 4: Application in a Noisy Environment Even after injecting 10^-2 level random bit-flipping noise into the observation data, local constraint structure learning still exhibits strong robustness, while global constraint structure learning becomes more difficult.

[0156] The results demonstrate that this application is not only applicable to ideal simulations, but can also be used for coarse-grained discovery and experimental guidance of potentially stable structures under NISQ conditions.

[0157] Figure 8 This is a schematic diagram of a potential constraint structure learning system based on quantum measurement data, according to an exemplary embodiment.

[0158] Reference Figure 8 As shown, another embodiment of this application provides a latent constraint structure learning system 100 based on quantum measurement data, including: a data acquisition module 110, a model training module 120, a support set search module 130, a support set simplification module 140, a verified Pauli generator generation module 150, and an iterative optimization module 160.

[0159] The data acquisition module 110 is used to construct the Pauli measurement basis and the quantum measurement dataset. The samples of the quantum measurement dataset are ±1 bit strings measured under the Pauli measurement basis. The model training module 120 uses a quantum measurement dataset to train a pre-defined Transformer structure encoder, performs single-bit mask prediction for each target position, and extracts the inter-variable dependency graph under the mask condition through structure mask attention. The support set search module 130 extracts the support set for the target location based on the dependency graph between variables, and determines the support set for each target location. Support set simplification module 140 is used to perform parity check verification and GF(2) Gaussian elimination on the support set of each target location to determine the set of linear constraints of the qubit; The verified Pauli generator generation module 150 is used to map the set of linear constraints of qubits to verified Pauli generators and determine the set of verified stable subgenerators. The iterative optimization module 160 is used to construct a new Pauli measurement basis based on the commutation space of the verified stable sub-generator set, repeatedly execute the model learning phase and the statistical verification phase until the preset convergence condition is met, and determine the complete set of stable sub-generators.

[0160] The embodiments described above in this application construct a quantum measurement dataset and train a Transformer encoder to perform single-bit mask prediction for each target position. By extracting the inter-variable dependency graph under mask conditions through structural mask attention and combining it with support set search guided by the dependency graph, the decisive conditional dependencies can be accurately identified when only limited measurement results are available, effectively avoiding the exponential complexity brought about by the reconstruction of the complete quantum state. By performing parity check verification and GF(2) Gaussian elimination on the support set of each target position, a compact, interpretable and mutually independent set of potential linear constraints can be extracted from the high-dimensional quantum measurement bit string. The set of quantum bit linear constraints that has been screened for physical consistency is mapped to verified Pauli generators. Finally, based on the set of verified stable generators, an adaptive iterative strategy combining the model learning stage and the statistical verification stage is used for incremental exploration, reducing invalid measurement configurations round by round, which greatly improves the data efficiency of constraint discovery and can efficiently and accurately determine the complete set of stable generators.

[0161] Regarding the embodiments of the above system, the specific ways in which each module performs operations have been described in detail in the embodiments of the method, and will not be elaborated here.

[0162] Based on the same technical concept, in some specific embodiments of this application, a terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it can be used to execute a latent constraint structure learning method based on quantum measurement data.

[0163] Based on the same technical concept, in some specific embodiments of this application, a computer-readable storage medium is provided on which a computer program is stored, which, when executed by a processor, can be used to perform a latent constraint structure learning method based on quantum measurement data.

[0164] Optionally, the memory is used to store programs; the memory may include volatile memory, such as random-access memory (RAM), such as static random-access memory (SRAM), double data rate synchronous dynamic random-access memory (DDR SDRAM), etc.; the memory may also include non-volatile memory, such as flash memory. The memory is used to store computer programs (such as application programs and functional modules that implement the above methods), computer instructions, etc., and the aforementioned computer programs and computer instructions can be partitioned and stored in one or more memories. Furthermore, the aforementioned computer programs, computer instructions, data, etc., can be accessed by the processor.

[0165] The aforementioned computer programs, computer instructions, etc., can be stored in partitions within one or more memory locations. Furthermore, the aforementioned computer programs, computer instructions, data, etc., can be accessed by a processor.

[0166] A processor is used to execute a computer program stored in memory to implement the various steps of the methods involved in the above embodiments. For details, please refer to the relevant descriptions in the preceding method embodiments.

[0167] The processor and memory can be separate structures or integrated structures. When the processor and memory are separate structures, they can be coupled together via a bus.

[0168] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0169] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0170] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0171] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0172] The foregoing has described some specific embodiments of this application. It should be understood that this application is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the substantive content of this application. The above-described preferred features can be used in any combination without conflict.

Claims

1. A latent constraint structure learning method based on quantum measurement data, characterized in that, include: Construct a Pauli measurement basis and a quantum measurement dataset, wherein the samples in the quantum measurement dataset are ±1 bit strings measured under the Pauli measurement basis; The pre-defined Transformer structure encoder is trained using the quantum measurement dataset. Single-bit mask prediction is performed for each target position, and the dependency graph between variables under the mask condition is extracted through structure mask attention. Based on the variable dependency graph, support sets are extracted for the target locations to determine the support set for each target location; Parity check and GF(2) Gaussian elimination are performed on the support set of each target location to determine the set of linear constraints for the qubit. Map the set of linear constraints of the qubits to verified Pauli generators to determine the set of verified stable subgenerators. Based on the commutation space of the verified stable sub-generator set, a new Pauli measurement basis is constructed. The model learning phase and statistical verification phase are repeated until the preset convergence condition is met, and the complete set of stable sub-generators is determined.

2. The latent constraint structure learning method based on quantum measurement data according to claim 1, characterized in that, The construction of the Pauli measurement basis and quantum measurement dataset includes: Determine the number of multiple qubits; The Pauli measurement basis is constructed based on the number of qubits. Based on a preset number of samplings and preset noise parameters, repeated sampling is performed under the Pauli measurement basis to determine multiple quantum observation samples and construct the quantum measurement dataset.

3. The latent constraint structure learning method based on quantum measurement data according to claim 1, characterized in that, The process of training a pre-defined Transformer structure encoder using the quantum measurement dataset, performing single-bit mask prediction at each target position, and extracting the inter-variable dependency graph under mask conditions through structure mask attention includes: The quantum measurement dataset is divided into a training set and a constraint set according to a preset ratio; The quantum observation samples in the training set are randomly masked to determine the quantum observation samples after random masking. The quantum observation sample with random masking is input into the preset Transformer structure encoder, and the predicted value of the target position of the random mask is output to train the preset Transformer structure encoder. Based on the predicted value of the target position of the random mask and the actual value of the target position of the random mask, the binary cross-entropy loss is determined using the binary cross-entropy loss function. The binary cross-entropy loss is used to optimize the preset Transformer structure encoder to determine the trained Transformer structure encoder. The quantum observation samples in the constraint set are randomly masked and then input into the trained Transformer structure encoder. The dependency graph between variables under the masked conditions is extracted in the last layer of self-attention of the trained Transformer structure encoder.

4. The latent constraint structure learning method based on quantum measurement data according to claim 3, characterized in that, The step of extracting support sets for target locations based on the inter-variable dependency graph, and determining the support set for each target location, includes: Based on the dependency graph between variables, determine the candidate position sequence for each target position, sorted in descending order of dependency. According to the candidate position sequence of each target position, a greedy variable addition strategy is sequentially applied to the candidate positions, and the trained Transformer structure encoder is input to determine the predicted value of the target position. The prediction accuracy of the target location is determined based on the predicted value and the actual value of the target location. According to the candidate position sequence of each target position, the set of candidate positions where the prediction accuracy of the target position first reaches a preset accuracy threshold is determined as the support set of the target position, and the support set of each target position is determined.

5. The latent constraint structure learning method based on quantum measurement data according to claim 1, characterized in that, The parity check and GF(2) Gaussian elimination processes are performed on the support set for each target location to determine the set of linear constraints for the qubit, including: For each target location, parity check is performed on the support set. Candidate locations with a sample ratio of actual verification parity product result of 1 that is less than the weight-aware verification threshold are removed to determine the stable support set for each target location. Gaussian elimination is performed sequentially on the stable support set of each target location to determine the linear constraint set of the qubit.

6. The latent constraint structure learning method based on quantum measurement data according to claim 1, characterized in that, The step of constructing a new Pauli measurement basis based on the commutation quotient space of the verified stable sub-generator set, repeatedly executing the model learning phase and the statistical verification phase until the preset convergence condition is met, and determining the complete set of stable sub-generators, includes: During the model learning phase, based on the search pattern of the quotient space, a trained Transformer structure encoder is used to search for multiple potential constraints under the new Pauli measurement basis. The constraint structure learning is performed iteratively. The set of verified stable sub-generators determined in each iteration is subjected to physical consistency screening with the set of historical verified stable sub-generators to determine whether the set of verified stable sub-generators is a new constraint. The model parameters of the trained Transformer structure encoder in the previous round are reused as the initial model parameters of the Transformer structure encoder model in the next round. The constraint structure learning is performed iteratively until there are no new constraints for a consecutive preset number of rounds, and then the model is switched to the verification mode of the statistical verification phase. In the verification mode of the statistical verification stage, based on a preset number of measurement samples, a bitwise multiplication operation is performed on all measurement positions corresponding to the verified stable subgenerator set to determine the odd-even product result of each measurement sample. The percentage of measurement samples with a parity product result of 1 is statistically analyzed to determine the average parity product result. If the average parity product result is not less than the preset verification threshold, the set of verified stable sub-generators is included in the complete set of stable sub-generators; if the average parity product result is less than the preset verification threshold, the set of verified stable sub-generators is discarded, and the verification result is determined. Based on the verification results, the complete set of stable subgenerators is determined.

7. The latent constraint structure learning method based on quantum measurement data according to claim 6, characterized in that, The step of performing a physical consistency screening process on the verified stable sub-generator set determined in each iteration and the historical verified stable sub-generator set to determine whether the verified stable sub-generator set is a new constraint includes: The verified Pauli generators in the set of verified stable sub-generators are normalized to determine the verified Pauli generators after normalization. In the historical generator dictionary composed of historical Pauli generator sets, the normalized verified Pauli generators are looked up. If the normalized verified stable sub-generator set already exists, it is discarded; otherwise, it is determined as the deduplicated verified stable sub-generator set. Based on the deduplicated verified stable generator set, the average parity expectation value of the deduplicated verified stable generator set on the corresponding quantum measurement dataset is calculated. If the average parity expectation value is less than a preset expectation threshold, it is discarded. If the average parity expectation value is not less than the preset expectation threshold, it is determined as a verified stable generator set that has been screened by physical characteristics. The verified stable sub-generator set filtered by physical features and the historical generator set are encoded as symplectic vectors over a two-source domain. Incremental Gaussian elimination is performed on the symplectic vectors in the two source domains. Verified Pauli generators whose rank changes are identified as new constraints, while verified Pauli generators whose rank remains unchanged are removed.

8. A latent constraint structure learning system based on quantum measurement data, characterized in that, include: The data acquisition module is used to construct the Pauli measurement base and the quantum measurement dataset, wherein the samples of the quantum measurement dataset are ±1 bit strings measured under the Pauli measurement base; The model training module uses the quantum measurement dataset to train a preset Transformer structure encoder, performs single-bit mask prediction for each target position, and extracts the inter-variable dependency graph under the mask condition through structure mask attention. The support set search module extracts the support set for the target location based on the dependency graph between variables, and determines the support set for each target location. Support set simplification module is used to perform parity check verification and GF(2) Gaussian elimination on the support set of each target location to determine the set of linear constraints of the qubit; A verified Pauli generator generation module is used to map the set of linear constraints of the qubits to verified Pauli generators and determine the set of verified stable subgenerators. The iterative optimization module is used to construct a new Pauli measurement basis based on the commutation space of the verified stable sub-generator set, repeatedly execute the model learning phase and the statistical verification phase until the preset convergence condition is met, and determine the complete set of stable sub-generators.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-7.

10. An electronic device, characterized in that, include: A memory on which computer programs are stored; A processor for executing the computer program in the memory to implement the steps of the method according to any one of claims 1-7.

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