A quantum error mitigation neural network training method guided by physical prior structures.

Abstract

This invention provides a training method for a quantum error mitigation neural network based on a priori physical structure, applicable to the fields of quantum information processing and quantum machine learning. The method includes: sequentially performing real amplitude random assignment and normalization operations on computational ground states satisfying even Hamming weights to obtain quantum circuit input data; designing a parameterized quantum circuit based on a one-dimensional transverse field Ising model through Trotter decomposition to obtain a quantum circuit with structurally evolvable functionality; sampling the processing results of the quantum circuit on the quantum circuit input data under multiple measurement basis conditions to obtain noiseless training output data and noisy training output data with pairing relationships; using the noiseless training output data as training labels, training the quantum error mitigation neural network using the noisy training output data, and using the trained quantum error mitigation neural network to obtain the error mitigation mapping relationship of the target quantum circuit.

Description

Technical Field

[0001] This invention relates to the fields of quantum information processing and quantum machine learning, specifically to the fields of quantum computing and quantum error mitigation, and more specifically to a training method for quantum error mitigation neural networks based on parity structure guidance. Background Art

[0002] Existing quantum computing systems are generally affected by non-ideal noise (including incoherent noise and readout noise), leading to significant deviations between actual measured outputs and theoretical predictions. While some research has utilized neural networks to mitigate errors in noisy quantum circuit outputs, these methods typically rely on unstructured random-state data, treating the output distribution of quantum circuits as statistical data lacking physical structure. This ignores the symmetry information that quantum circuits may retain during evolution, resulting in AI models lacking symmetry perception capabilities, poor generalization ability, and poor physical consistency. Furthermore, existing quantum error mitigation techniques using AI models generally rely on training data generated from random states, lacking specific coverage of the physical priors of actual quantum circuits. This results in weak expressive power of the training data, inability to adapt to different application scenarios, and a lack of adaptability to different measurement bases, causing the effectiveness of quantum error mitigation to fluctuate with the measurement method. Summary of the Invention

[0003] In view of the above problems, the present invention provides a method, apparatus, electronic device and storage medium for training quantum error mitigation neural networks based on physical prior structure guidance.

[0004] According to a first aspect of the present invention, a method for training a quantum error mitigation neural network guided by a physical prior structure is provided, comprising:

[0005] The computational ground state with even Hamming weights is subjected to random real amplitude assignment and normalization operations in sequence to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with even parity structure;

[0006] Based on the one-dimensional transverse field Ising model, parameterized quantum circuits are designed through Trotter decomposition operations to obtain quantum circuits with structurally evolvable functions.

[0007] The processing results of the quantum circuit input data are sampled under multiple measurement bases to obtain noiseless training output data and noisy training output data with pairing relationship.

[0008] The noiseless training output data is used as training labels. The quantum error mitigation neural network is trained using the noisy training output data. The trained quantum error mitigation neural network is then used to obtain the error mitigation mapping relationship between the output data of the noisy quantum circuit and the output data of the noiseless quantum circuit in the target quantum circuit.

[0009] According to embodiments of the present invention, the above-described quantum error mitigation neural network training method based on physical prior structure guidance further includes:

[0010] The error mitigation capability of the trained quantum error mitigation neural network is evaluated using preset evaluation indicators, and the evaluation results are obtained. The preset evaluation indicators include root mean square error, parity fidelity, KL divergence, and Z-direction imbalance difference.

[0011] According to embodiments of the present invention, the above-described parameterized quantum circuit design based on the one-dimensional transverse field Ising model, through Trotter decomposition operation, to obtain a quantum circuit with structurally evolvable functionality includes:

[0012] The Hamiltonian of the one-dimensional transverse field Ising model is determined based on the nearest neighbor coupling strength, the transverse field strength, and the Pauli-X and Pauli-Z operators acting on each qubit. The nearest neighbor coupling strength is randomly selected based on a uniform distribution.

[0013] By decomposing the Hamiltonian through the Trotter decomposition operation, the time evolution operator can be approximated as a realizable quantum gate operation, resulting in a quantum circuit with structurally evolvable functionality.

[0014] According to an embodiment of the present invention, the above-described decomposition of the Hamiltonian through the Trotter decomposition operation to approximate the time evolution operator as a realizable quantum gate operation, resulting in a quantum circuit with structurally evolvable functionality, includes:

[0015] The qubit is rotated using the Rx rotation gate to obtain the rotated qubit;

[0016] The rotated even-number quantum bits and the rotated odd-number quantum bits are cross-coupled through CNOT gates and Rz rotation gates to obtain coupled quantum bits;

[0017] By adding barriers to separate different quantum circuit layers, quantum circuits with structurally evolving capabilities are obtained.

[0018] According to an embodiment of the present invention, the above-described method of processing the quantum circuit input data by the quantum circuit and performing multi-measurement basis output sampling to obtain noiseless training output data and noisy training output data with paired relationships includes:

[0019] Under the X-measurement basis, the processing results of the quantum circuit are subjected to Hadamard gate basis transformation to obtain paired noiseless training output data and noisy training output data under the X-measurement basis.

[0020] According to an embodiment of the present invention, the above-mentioned sampling of the output of the quantum circuit input under multiple measurement bases to obtain noiseless training output data and noisy training output data with pairing relationship further includes:

[0021] Under the Y-measurement basis, the processing result of the quantum circuit is transformed from the Z-measurement basis to the superposition state of the Y-measurement basis through the Hadamard gate basis transformation;

[0022] By applying superposition states to the complex conjugate of the T-gate The gate performs phase modulation to convert the superposition state to the Y measurement basis, thereby obtaining paired noiseless training output data and noisy training output data under the X measurement basis.

[0023] According to an embodiment of the present invention, the input of the above-mentioned quantum error mitigation neural network includes device error parameters, quantum circuit gate structure design information, rotation angle histogram, and noisy measurement distribution;

[0024] Among them, the noisy measurement distribution is obtained by modeling the counting distribution of the noisy training output data;

[0025] In the process of constructing the quantum error mitigation neural network, the expected value encoding of the input to the quantum error mitigation neural network is changed to a counting distribution.

[0026] According to a second aspect of the present invention, a quantum error mitigation neural network training device guided by physical prior structures is provided, comprising:

[0027] The input data construction module is used to perform real amplitude random allocation and normalization operations on the computational ground state that satisfies the Hamming weight being even, to obtain the quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure.

[0028] The circuit construction module is used to design parameterized quantum circuits based on the one-dimensional transverse field Ising model through Trotter decomposition operations, thereby obtaining quantum circuits with structurally evolvable functions.

[0029] The multi-measurement basis sampling module is used to sample the output of the quantum circuit's processing result of the quantum circuit's input data under multiple measurement basis conditions, so as to obtain noiseless training output data and noisy training output data with pairing relationship;

[0030] The neural network training module is used to use the noiseless training output data as training labels, train the quantum error mitigation neural network using the noisy training output data, and use the trained quantum error mitigation neural network to obtain the error mitigation mapping relationship between the output data of the noisy quantum circuit and the output data of the noiseless quantum circuit in the target quantum circuit.

[0031] A third aspect of the present invention provides an electronic device comprising: one or more processors; and a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method described above.

[0032] A fourth aspect of the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, wherein the computer program or instructions, when executed by a processor, implement the steps of the above-described method.

[0033] This invention provides a quantum error mitigation neural network training method guided by physical prior structures. By constructing an initial state with parity symmetry (limited to even-numbered excitations), it preserves the conserved structure in ideal dynamics, overcoming the unpredictable error patterns under traditional random initial states and effectively avoiding hardware parameter drift caused by random-state training. Based on a one-dimensional Ising model of the transverse field, a parameterized quantum circuit is designed to guide the measurement output to naturally exhibit physical consistency, unlike existing methods that rely on random or unstructured circuits to generate data. Furthermore, the quantum circuit designed based on the Ising model can effectively suppress crosstalk noise between qubits. Introducing multiple measurement bases and using the output count distribution as modeling input significantly improves the neural network's ability to distinguish error details and its generalization effect compared to using only the expected value. Simultaneously, the use of technical distribution accelerates the processing speed of the neural network and reduces hardware resource consumption. The method provided by this invention exhibits superior error mitigation capabilities in environments with incoherent noise and readout noise, outperforming previous methods in their local adaptation to specific noise or specific bases, demonstrating good hardware universality, and reducing hardware operating burden. Attached Figure Description

[0034] The above-described features, other objects, and advantages of the present invention will become clearer from the following description of embodiments of the invention with reference to the accompanying drawings, in which:

[0035] Figure 1 This is an application scenario diagram of quantum error mitigation neural network training based on physical prior structure according to an embodiment of the present invention;

[0036] Figure 2 This is a flowchart of a quantum error mitigation neural network training method based on physical prior structure guidance according to an embodiment of the present invention;

[0037] Figure 3 This is a circuit structure diagram of the Trotter evolution based on the Ising model according to an embodiment of the present invention;

[0038] Figure 4 This is a schematic diagram of training data samples according to an embodiment of the present invention;

[0039] Figure 5 This is a schematic diagram of single-qubit error mitigation under incoherent noise in Z-based measurement according to an embodiment of the present invention;

[0040] Figure 6 This is a schematic diagram illustrating the mitigation of single-qubit error after further introducing readout noise under the Z measurement basis according to an embodiment of the present invention;

[0041] Figure 7 This is a comparison chart of KL divergence index and root mean square error index under Z-basis measurement according to an embodiment of the present invention;

[0042] Figure 8 This is a schematic diagram illustrating single-qubit error mitigation under the X-measurement basis according to an embodiment of the present invention;

[0043] Figure 9 This is a schematic diagram illustrating single-qubit error mitigation under the Y-measurement basis according to an embodiment of the present invention;

[0044] Figure 10 This is a comparison chart of KL divergence index and root mean square error index under different measurement bases according to embodiments of the present invention;

[0045] Figure 11 This is a schematic diagram illustrating the mitigation of single-qubit errors in a generalization experiment under different noise conditions according to an embodiment of the present invention;

[0046] Figure 12 This is a comparison chart of the KL divergence index and root mean square error index in a generalization experiment under different noise levels according to an embodiment of the present invention.

[0047] Figure 13 This is a schematic diagram of a quantum error mitigation neural network training device based on a physical prior structure guided by an embodiment of the present invention.

[0048] Figure 14 This is a block diagram of an electronic device suitable for implementing a quantum error mitigation neural network training method guided by physical prior structures according to an embodiment of the present invention. Detailed Implementation

[0049] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the invention. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the invention for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0050] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0051] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0052] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0053] In the field of quantum computing, the outputs of certain conserved quantum systems exhibit residual structure in terms of parity, particle number, or symmetry distribution. If this structure can be effectively captured and incorporated into the learning process, it is expected to improve the physical consistency and generalization ability of the model. How to construct datasets with structural priors and enhance the mitigation effect of neural networks on measurement errors has become a key technical problem in current quantum error mitigation.

[0054] This invention addresses the technical problems existing in current quantum error mitigation methods, such as lack of physical priors, weak input representation capabilities, and poor adaptability to different measurement bases. It provides a quantum error mitigation solution with a structure prior injection mechanism, a data generation function driven by physical evolution, multi-measurement base coverage and distribution-level modeling characteristics, and robust modeling capabilities for multi-noise scenarios.

[0055] Figure 1 This is an application scenario diagram of quantum error mitigation neural network training based on physical prior structure guided by an embodiment of the present invention.

[0056] like Figure 1 As shown, application scenario 100 according to this embodiment may include quantum computing and quantum machine learning. Network 104 serves as a medium for providing a communication link between the first terminal device 101, the second terminal device 102, the third terminal device 103, and the server 105. Network 104 may include various connection types, such as wired or wireless communication links or fiber optic cables, etc.

[0057] Users can use the first terminal device 101, the second terminal device 102, and the third terminal device 103 to interact with the server 105 via the network 104 to receive or send messages, etc. Various communication client applications can be installed on the first terminal device 101, the second terminal device 102, and the third terminal device 103, such as shopping applications, web browser applications, search applications, instant messaging tools, email clients, social media platform software, etc. (for example only).

[0058] The first terminal device 101, the second terminal device 102, and the third terminal device 103 can be various electronic devices with displays and support web browsing, including but not limited to smartphones, tablets, laptops, and desktop computers.

[0059] Server 105 can be a server that provides various services, such as a backend management server that supports websites browsed by users using the first terminal device 101, the second terminal device 102, and the third terminal device 103 (this is just an example). The backend management server can analyze and process data such as received user requests, and feed back the processing results (such as web pages, information, or data obtained or generated according to user requests) to the terminal devices.

[0060] It should be noted that the quantum error mitigation neural network training method based on physical prior structure guided by the embodiments of the present invention can generally be executed by server 105. Correspondingly, the quantum error mitigation neural network training device based on physical prior structure guided by the embodiments of the present invention can generally be located in server 105. The quantum error mitigation neural network training method based on physical prior structure guided by the embodiments of the present invention can also be executed by a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105. Correspondingly, the quantum error mitigation neural network training device based on physical prior structure guided by the embodiments of the present invention can also be located in a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105.

[0061] It should be understood that Figure 1The number of terminal devices, networks, and servers shown is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be included.

[0062] The following will be based on Figure 1 The described scene, through Figures 2-12 The disclosed embodiments of the quantum error mitigation neural network training method based on physical prior structure guidance are described in detail.

[0063] This invention proposes a quantum error mitigation neural network training method guided by physical prior structure, aiming to improve the error mitigation performance of neural networks on noisy quantum measurement outputs. This method utilizes parity symmetry injection, structure-preserving evolution, multi-base measurement sampling, and neural network modeling to achieve a data-driven error mitigation strategy with both structure fidelity and generalization capabilities.

[0064] Figure 2 This is a flowchart of a quantum error mitigation neural network training method based on physical prior structure guided by an embodiment of the present invention.

[0065] like Figure 2 As shown, the above-mentioned quantum error mitigation neural network training method based on physical prior structure guidance includes operations S210 to S240.

[0066] In operation S210, the computational ground state satisfying the Hamming weight of an even number is subjected to real amplitude random assignment operation and normalization operation in sequence to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure.

[0067] Hamming weights are parameters that measure the number of times a "1" appears in a binary sequence.

[0068] Operation S210 involves the construction of the parity structure initial state: In order to introduce the influence of structural prior on the mitigation of quantum errors, this invention designs a type of quantum circuit input for calculating the ground state with even Hamming weights. The above quantum circuit input satisfies formula (1):

[0069] (1),

[0070] Where span represents the Hilbert subspace spanned by the computational ground state with even Hamming weights. Representing a vector space, This represents the corresponding computational ground state in binary form, and mod represents the modulo operation.

[0071] By enumerating all ground states that satisfy the even parity constraint and randomly assigning real amplitudes, the results are then standardized. These physically meaningful initial states are expected to exhibit intrinsic robustness to some quantum noise, thus providing physically driven prior information for error mitigation research.

[0072] In operating S220, based on the one-dimensional transverse field Ising model, parameterized quantum circuits are designed through Trotter decomposition operations to obtain quantum circuits with structurally evolvable functions.

[0073] The Ising model is a classic statistical model in physics used to study phase transitions of matter.

[0074] Trotter decomposition is an algorithmic technique used in quantum simulations to approximate the evolution of complex Hamiltonians.

[0075] In operation S230, the processing result of the quantum circuit on the quantum circuit input data is sampled under multiple measurement basis to obtain noiseless training output data and noisy training output data with pairing relationship.

[0076] In operation S240, the noiseless training output data is used as the training label, the noisy training output data is used to train the quantum error mitigation neural network, and the trained quantum error mitigation neural network is used to obtain the error mitigation mapping relationship between the noisy quantum circuit output data and the noiseless quantum circuit output data in the target quantum circuit.

[0077] This invention provides a quantum error mitigation neural network training method guided by physical prior structures. By constructing an initial state with parity symmetry (limited to even-numbered excitations), it preserves the conserved structure in ideal dynamics, overcoming the unpredictable error patterns under traditional random initial states and effectively avoiding hardware parameter drift caused by random-state training. Based on a one-dimensional Ising model of the transverse field, a parameterized quantum circuit is designed to guide the measurement output to naturally exhibit physical consistency, unlike existing methods that rely on random or unstructured circuits to generate data. Furthermore, the quantum circuit designed based on the Ising model can effectively suppress crosstalk noise between qubits. Introducing multiple measurement bases and using the output count distribution as modeling input significantly improves the neural network's ability to distinguish error details and its generalization effect compared to using only the expected value. Simultaneously, the use of technical distribution accelerates the processing speed of the neural network and reduces hardware resource consumption. The method provided by this invention exhibits superior error mitigation capabilities in environments with incoherent noise and readout noise, outperforming previous methods in their local adaptation to specific noise or specific bases, demonstrating good hardware universality, and reducing hardware operating burden.

[0078] According to an embodiment of the present invention, the above-described parameterized quantum circuit design based on the one-dimensional transverse field Ising model, through Trotter decomposition operation, to obtain a quantum circuit with structurally evolvable functionality includes: determining the Hamiltonian of the one-dimensional transverse field Ising model based on the nearest neighbor coupling strength, the transverse field strength, and the Pauli-X and Pauli-Z operators acting on each qubit, wherein the nearest neighbor coupling strength is randomly selected based on a uniform distribution; decomposing the Hamiltonian through Trotter decomposition operation, thereby approximating the time evolution operator as a realizable quantum gate operation, to obtain a quantum circuit with structurally evolvable functionality.

[0079] Pauli operators are tools in quantum mechanics for describing the intrinsic angular momentum of spin-1 / 2 particles.

[0080] According to an embodiment of the present invention, the above-described decomposition of the Hamiltonian through Trotter decomposition operation to approximate the time evolution operator as a realizable quantum gate operation to obtain a quantum circuit with structurally evolvable functionality includes: rotating the qubit using an Rx rotation gate to obtain rotated qubits; cross-coupling the rotated even-number qubits and the rotated odd-number qubits through a CNOT gate and an Rz rotation gate to obtain coupled qubits; and separating different quantum circuit layers by adding barriers to obtain a quantum circuit with structurally evolvable functionality.

[0081] The following describes specific implementation methods in conjunction with appendices. Figure 3 The design of structure evolution quantum circuits is explained in further detail.

[0082] Figure 3 This is a diagram of the Trotter evolution circuit structure based on the Ising model according to an embodiment of the present invention.

[0083] In constructing physically interpretable quantum circuits, this invention chooses to design parameterized quantum circuits based on the one-dimensional Transverse Field Ising Model (TFIM). The Hamiltonian of TFIM is shown in equation (2):

[0084] (2),

[0085] in, Indicates the nearest neighbor coupling strength. For transverse field intensity, and They are the first Pauli operators in the X and Z directions of each qubit. The time evolution operator is approximated as a series of realizable quantum gate operations through the Trotter decomposition operation: rotation of each qubit (Rx gate), cross-coupling between even and odd qubits (CZ gate implemented by CNOT+Rz+CNOT), and separation of each layer through quantum barriers to maintain the structural clarity of the quantum circuit.

[0086] Specifically, if Figure 3 As shown, each Trotter step consists of three main parts: first, an Rx gate implements the rotation of each qubit; then, even and odd qubits are cross-coupled via a CNOT gate and a rotated Rz gate; finally, barriers are added to separate different quantum circuit layers. This design preserves the physical evolution of each step while ensuring the realizability and operability of the quantum circuit. The depth of the quantum circuit is proportional to the number of Trotter steps, meaning that the depth and complexity of the circuit increase with the number of time-evolving steps. In the circuit example of this invention, the coupling strength J is randomly drawn from a uniform distribution of U(0,1), exhibiting randomness, which provides a basis for circuit diversity. TFIM, as a natural evolution model, naturally preserves parity symmetry under short-time evolution or weak transverse field conditions. This allows it to serve as a structural prior, helping to construct more physically interpretable quantum circuits. In this way, this invention can introduce physical constraints to ensure that the structure of the quantum circuit is consistent with the characteristics of the physical system, thereby improving the efficiency and robustness of the quantum algorithm.

[0087] Furthermore, TFIM is a standard test platform for quantum circuit design and error simulation. It is widely used in the verification of quantum algorithms, the construction of error models, and quantum error correction research, possessing excellent physical interpretability and scalability. Therefore, using TFIM as the basis for the dataset can effectively test and verify the quantum circuit design and error mitigation methods proposed in this invention.

[0088] According to an embodiment of the present invention, the above-mentioned sampling of the output of the quantum circuit input data processing result of the quantum circuit under multiple measurement basis to obtain noiseless training output data and noisy training output data with pairing relationship includes: under the X measurement basis, performing Hadamard gate basis transformation on the quantum circuit processing result to obtain noiseless training output data and noisy training output data paired under the X measurement basis.

[0089] The Hadamard gate, mentioned above, is a single-qubit logic gate, mainly used to prepare quantum superposition states and realize quantum state transitions.

[0090] According to an embodiment of the present invention, the above-described method of sampling the output of the quantum circuit input to the quantum circuit under multiple measurement bases to obtain noiseless training output data and noisy training output data with a pairing relationship further includes: under the Y measurement base, converting the processing result of the quantum circuit from the Z measurement base to a superposition state of the Y measurement base through a Hadamard gate basis transformation; and applying the superposition state to the complex conjugate of the T gate. The gate performs phase modulation to convert the superposition state to the Y measurement basis, thereby obtaining paired noiseless training output data and noisy training output data under the X measurement basis.

[0091] The following detailed explanation of the quantum circuit output sampling mechanism under multiple measurement bases will be provided through specific implementation methods.

[0092] After state initialization and circuit evolution, the final measurement result will undergo different basis transformations depending on the selected measurement basis. In particular, when dealing with different measurement bases, the qubits need to be subjected to corresponding basis transformation operations to ensure that the measurement result correctly corresponds to the projection value of the selected basis.

[0093] For the X-measurement basis, a basis transformation needs to be performed using the Hadamard gate. The Hadamard gate can transform the standard Z-basis states (e.g., ...) into a basis transformation. and The superposition state required to transform ) into the X basis is, i.e. and Mapped to ( )and ( This allows the measurement results to be reflected on the X basis.

[0094] For the Y measurement basis, it is necessary to apply The combination of a gate (i.e., the complex conjugate of a T-gate) and a Hadamard gate. First, a Hadamard gate is applied to transform the qubit from a Z-based to an X-based superposition state, and then... The gate performs phase modulation, thereby converting the qubit to the Y basis. Ultimately, this combination operation allows the measurement result to correspond to the projected value of the Y basis. Quantum output sampling under this mechanism can not only provide projected values ​​under different measurement bases, but also reveal the response characteristics of the quantum circuit under different bases, which is of great significance for quantum error mitigation and accurate reconstruction of quantum states. Each experiment generates a pair of measurement result distributions containing a noiseless ideal output and a noisy output after noise perturbation, which are used as supervision labels and neural network model inputs, respectively.

[0095] According to an embodiment of the present invention, the input of the above-mentioned quantum error mitigation neural network includes device error parameters, quantum circuit gate structure design information, rotation angle histogram, and noisy measurement distribution; wherein, the noisy measurement distribution is obtained by modeling the counting distribution of noisy training output data; wherein, in the process of constructing the quantum error mitigation neural network, the expected value encoding input to the quantum error mitigation neural network is changed to a counting distribution.

[0096] The following detailed description of the construction process of the neural network error mitigation model involved in this invention will be provided through specific implementation methods.

[0097] This invention employs a simple and highly deployable classical neural network model (such as a multilayer perceptron, MLP) to model the count distribution of quantum circuit outputs. The model input is:

[0098] Equipment error parameters (such as gate error, T1 / T2 time) (8 dimensions);

[0099] Statistical analysis of circuit gate structures (6-dimensional);

[0100] Histogram of rotation angles (40-dimensional);

[0101] Noisy measurement distribution (2) n dimension).

[0102] When constructing a neural network error mitigation model, replacing the expectation value encoding with an output count distribution can more accurately reflect the actual measurement results of the quantum circuit. This is because the output count distribution provides more comprehensive information than a single expectation value, which has significant advantages for error mitigation and model training. The output of a quantum circuit is usually based on a probability distribution, rather than a single expectation value. For example, the measurement result under a certain measurement basis is the count distribution of the results obtained from multiple independent measurements. Therefore, using the output count distribution as the input of the neural network can effectively capture the diversity and probabilistic characteristics of the quantum circuit output, which can more comprehensively express the actual performance of the circuit than the expectation value, especially under conditions of significant noise. Combining circuit parameters and noise parameters, the output count distribution can provide more detailed characteristics of circuit behavior. For example, parameters in a quantum circuit, such as rotation angle and coupling strength, directly affect the evolution of quantum states, while noise parameters (such as coherent noise and readout noise) can lead to deviations in measurement results. By incorporating this information into the training data of the neural network, the model can better identify and learn noise patterns and effectively correct them. Through this improvement, the neural network error mitigation model of this invention can more realistically reflect the dynamic evolution of the quantum system and more accurately compensate for noise and errors, thereby improving the accuracy and stability of quantum computing. The model output is a complete ideal measurement distribution. Supervised learning is used to train the model to complete the error mitigation mapping from noisy output to ideal output.

[0103] According to an embodiment of the present invention, the above-mentioned quantum error mitigation neural network training method based on physical prior structure further includes: evaluating the error mitigation capability of the trained quantum error mitigation neural network using preset evaluation indicators to obtain evaluation results, wherein the preset evaluation indicators include root mean square error, parity fidelity, KL divergence and Z-direction imbalance difference.

[0104] The root mean squared error (RMSE) is the square root of the ratio of the square of the deviation between the predicted and the true value to the number of observations, n.

[0105] Parity Fidelity is used in data communication to ensure the validity of data.

[0106] The Z-direction imbalance gap is also known as the Z-direction Imbalance Gap.

[0107] The advantages of the method provided by this invention will be illustrated below through multiple noise models and generalization test design.

[0108] By utilizing noise model simulation platforms provided by IBM Qiskit (such as FakeLima), real hardware-level errors are accurately injected, making the generated samples more closely resemble the output of the physical system. In the experimental design, the training set circuit depth is set to shallow (e.g., layers 0–19), while the test set uses unseen deeper circuits (e.g., layers 20–29) to evaluate the model's cross-depth generalization ability. Furthermore, the model is trained and tested under different measurement bases and noise combinations. Indicators such as root mean square error, parity fidelity, KL divergence, and Z-direction imbalance difference are used to systematically evaluate the error mitigation ability of the constructed structured dataset under cross-scene transfer. All experimental results are clearly presented through figures and tables.

[0109] Among them, KL divergence measures the difference between two probability distributions. Parity fidelity is an indicator of a model's ability to preserve parity structure in its predictions. Imbalance gap measures the degree of loss of conservation of probability distributions in the Z-direction. FakeLima is a simulation backend provided by IBM, containing a real hardware noise model.

[0110] The following describes and verifies the above-mentioned quantum error mitigation neural network training method based on physical prior structure guidance provided by the present invention through specific experiments and in conjunction with the accompanying drawings.

[0111] The following describes the specific experimental setup, using the four-bit Ising model as an example:

[0112] (1) Set the parameters as J=0.15, h=1, dt=0.25, and the number of evolution steps as 0–29; the training circuit has 0–19 layers, and the testing circuit has 20–29 layers;

[0113] (2) Construct an initial state as a superposition of parity states and inject IBM hardware-level errors using a FakeLima noise backend;

[0114] (3) Collect ideal output and noise output under the three measurement bases of Z / X / Y respectively, and construct training samples;

[0115] (4) Use an MLP (Multilayer Perceptron) neural network to train a noisy-to-ideal mapping model;

[0116] (5) Evaluate the root mean square error, KL divergence, parity fidelity, and Z-direction imbalance gap of the model output.

[0117] All experimental results are recorded in the attached figures in the form of data tables and graphs. The experiments show that the parity structure training set outperforms the random structure in all metrics, especially in the generalization depth range, which verifies the comprehensive advantages of the method of the present invention in terms of structure preservation and generalization ability.

[0118] Figure 4 This is a schematic diagram of training data samples according to an embodiment of the present invention. Figure 4 In the example, (a) represents the parity training sample. Figure 4 In (b), the samples are random training samples; where sample index represents the sample number (the same below), idealcounts represents the ideal value count (the same below), noisy counts represents the noise count (the same below), and difference(noisy-ideal) represents the difference (noise-ideal) (the same below).

[0119] like Figure 4 As shown in (b), for random training samples, the distribution of the Hamming weight is relatively dispersed across all possible values ​​(0–4). After introducing noise ( Figure 4 (The middle plot of (b) in the figure) shows that the distribution of each Hamming weight becomes more uniform and the difference between even and odd weights is further weakened. This indicates that the random initial state itself lacks strong structural constraints and is prone to even and odd fluctuations under the influence of noise.

[0120] In comparison, such as Figure 4 As shown in (a), the parity training samples exhibit a clear bias towards even-numbered Hamming weights, particularly with the highest probability of distributions containing two 1s. The probability of one or three 1s is close to zero, clearly verifying the even-numbered structure of the initial state. After noise perturbation, although the parity constraint is weakened, the dominance of even-numbered 1s remains significant.

[0121] These results confirm that parity training samples have higher structural regularity and can be partially preserved under noisy conditions, thus providing favorable prior knowledge for neural network training and demonstrating better generalization ability and error mitigation performance in subsequent experiments.

[0122] Training phase (layers 0-19)

[0123] Table 1: Comparison of two structural indices under Z-measurement basis and incoherent noise

[0124]

[0125] Table 1 shows a comparison of performance metrics under incoherent noise and Z-basis measurements. The parity-structured dataset significantly outperforms the random-structured dataset. Specifically, the parity-structured dataset reduces the root mean square error (RMSE) by 22.53%, KL divergence by 23.13%, and parity fidelity by 17.20%. Furthermore, the Z-direction imbalance (imbalance gap) is improved by 64.9%, approaching the physically conserved ideal state. These metrics collectively indicate that the structure-guided dataset is more conducive to the model learning systematic biases during training, thus more effectively correcting measurement errors.

[0126] Figure 5 This is a schematic diagram illustrating single-qubit error mitigation under incoherent noise in Z-based measurement according to an embodiment of the present invention.

[0127] Figure 5 The above quantitative conclusions have been verified for random structures ( Figure 5 In (a) of the example, although the output distribution after error correction converges somewhat compared to the original noise, the parity structure ( Figure 5 The model predictions under (b) show stronger stability and accuracy, among which, Figure 5 In this context, dist_noisy_i represents the difference between the i-th qubit under noise and the ideal value (the same applies below), and dist_mitigated_i represents the difference between the i-th qubit and the ideal value after noise mitigation (the same applies below).

[0128] Figure 6 This is a schematic diagram illustrating the mitigation of single-qubit error after further introducing readout noise under the Z-measurement basis according to an embodiment of the present invention. Figure 6 (a) Schematic diagram of single-qubit error mitigation after readout noise of random structure under Z measurement basis; Figure 6 (b) Schematic diagram of single-qubit error mitigation after parity structure readout noise under Z measurement basis.

[0129] Table 2: Comparison of two structural parameters under Z-measurement basis and incoherent noise + readout noise

[0130]

[0131] As shown in Table 2, in scenarios with further introduced noise, the parity-structured samples outperformed the random-structured samples in all four key metrics, demonstrating good error robustness and structural generalization ability. Specifically, the root mean square error and KL divergence decreased by 34.17% and 40.92%, respectively, indicating a significant reduction in the distance between the output probability distribution and the ideal target. The parity fidelity improved by 17.77%, further demonstrating that the model better preserves the structural information of the ideal output. Furthermore, the imbalance in the Z-basis direction decreased by 65.67%, indicating that structured priors help maintain the physical conservation of quantum states. Figure 6 This reflects the mitigation of error per qubit under this condition, further verifying the above quantization conclusions.

[0132] Figure 7 This is a comparison chart of the KL divergence index and root mean square error index under Z-basis measurement according to an embodiment of the present invention. Figure 7 In the text (a), KL divergence indexes for random and even structures are given under incoherent noise and combined noise (incoherent + readout). Figure 7 (b) in the figure represents the RMSE index of random structure and parity structure under incoherent noise and composite noise.

[0133] In the comparative experiments described above, this invention systematically analyzed the impact of random structure samples and parity structure samples on error mitigation under different noise models (including readout noise and readout noise removal). Key indicators included root mean square error after error correction and KL divergence. Experimental results show that, regardless of whether in a strong noise environment (e.g., with readout noise) or a relatively ideal environment with readout noise removed, the model trained on the parity structure still exhibits significant advantages, maintaining more stable output and stronger physical consistency.

[0134] These trends are illustrated in the present invention. Figure 7 The performance curves clearly demonstrate that parity structure training samples not only enhance the model's fitting ability but also help improve its robustness and generalization ability under different noise scenarios.

[0135] Figure 8 This is a schematic diagram illustrating single-qubit error mitigation under the X-measurement basis according to an embodiment of the present invention. Figure 8 (a) in the diagram represents a schematic of error mitigation for a single qubit in a random structure under the X measurement basis; Figure 8 (b) in the figure represents a schematic diagram of single-qubit error mitigation for parity structure under the X measurement basis.

[0136] Table 3: Comparison of two structural indices under X-measurement basis and incoherent noise

[0137]

[0138] Under X-basis measurement conditions, this study also compared the performance of parity-structured samples and random-structured samples in the quantum error mitigation task. As shown in Table 3, the parity-structured training samples outperformed the random-structured samples in all indicators: the root mean square error after error correction decreased by 52.21%, indicating that the model is more accurate in energy expectation estimation; the parity fidelity improved by as much as 72.51%, indicating that the model can still maintain the parity symmetry structure of the quantum state well under the Hadamard basis; the KL divergence decreased by 43.92%, reflecting a higher degree of fit between the model output distribution and the ideal distribution; the absolute value of the imbalance gap in the Z direction decreased, further indicating that the model better preserved physical conservation. Figure 8 This reflects the mitigation of error per qubit under this condition, further verifying the above quantization conclusions.

[0139] Figure 9 This is a schematic diagram illustrating single-qubit error mitigation under the Y-measurement basis according to an embodiment of the present invention. Figure 9 (a) in the diagram represents a schematic of error mitigation for a single qubit in a random structure under the Y measurement basis; Figure 9 (b) in the diagram represents a schematic of single-qubit error mitigation for parity structure under the Y measurement basis.

[0140] Table 4: Comparison of two structural indices under Y measurement basis and incoherent noise

[0141]

[0142] Under Y-basis measurements, the parity structure data consistently outperformed the random structure control group across all key metrics. Specifically, the root mean square error was reduced by 55.17%, demonstrating a significant improvement in expected value accuracy. Parity fidelity improved by 74.47%, reflecting a substantial increase in alignment with ideal physical constraints. Furthermore, the KL divergence decreased by 47.03%, indicating that the predicted output distribution is significantly closer to the ideal reference. The absolute value of the imbalance gap in the Z-direction also decreased, further illustrating that the model better preserves physical conservation. These results highlight that the parity structure continues to perform well under Y-basis measurements, enhancing fidelity and improving noise resilience. Figure 9 This reflects the mitigation of error per qubit under this condition, further verifying the above quantization conclusions.

[0143] Figure 10 This is a comparison chart of KL divergence index and root mean square error index under different measurement bases according to embodiments of the present invention.

[0144] Figure 10In the figure, (a) represents the KL divergence index for random and even structures under the X, Y, and Z measurement bases. Figure 10 (b) in the figure represents the RMSE indices for random structure and parity structure under the X, Y, and Z measurement bases; where Random-structured represents random structure (the same below), Parity-structured represents parity structure (the same below), incoherent represents incoherent noise (the same below), and incoherent+readout represents incoherent noise + readout noise (the same below); through analysis Figure 10 As can be seen from the root mean square error (RMSE) versus KL divergence curves under different measurement bases, the parity structure training data outperforms the random structure under all measurement bases, exhibiting lower RMSE and smaller KL divergence. Particularly under the X and Y bases, the parity structure significantly enhances the neural network's ability to identify and fit the quantum output distribution structure. These results indicate that the parity structure not only improves the error mitigation effect during model training but also enhances the model's structural generalization ability under different measurement base scenarios.

[0145] Figure 11 This is a schematic diagram illustrating the single-qubit error mitigation in a generalization experiment under different noise conditions according to an embodiment of the present invention.

[0146] Figure 12 This is a comparison chart of the KL divergence index and root mean square error index in generalization experiments under different noise levels according to an embodiment of the present invention.

[0147] Generalization phase (layers 20-29): To evaluate the generalization ability of the neural network model under different input structures and noise types, the error mitigation effect was systematically tested on a single-qubit system, such as... Figure 11 As shown, where, Figure 11 In this context, (a) represents incoherent noise + readout noise + random structure. Figure 11 In the diagram, (b) represents incoherent noise + readout noise + parity structure. Figure 11 In this context, (c) represents incoherent noise plus random structure. Figure 11 In the diagram, (d) represents incoherent noise plus parity structure. The results show that, in the presence of both incoherent noise and readout noise, introducing an input state with parity structure significantly improves the prediction accuracy after error mitigation. Compared to random structures, structured inputs not only make the distribution of the mitigated expected value more concentrated near the ideal value, but also exhibit higher consistency and stability across multiple model instances.

[0148] Furthermore, this invention uses two indicators, KL divergence and root mean square error, to conduct a statistical quantitative analysis of the above conclusions (see...). Figure 12 ),in, Figure 12In the figure, (a) represents the KL divergence index for random and even structures under incoherent noise and complex noise conditions. Figure 12 (b) in the table represents the RMSE indices for random and even structures under incoherent and combined noise conditions. Regarding KL divergence, structured inputs exhibit lower distribution deviation under both types of noise, especially in the combined noise (incoherent + readout) scenario where the KL value decreases significantly (from 0.285 to 0.242), indicating that the model is superior in preserving probabilistic structure information. As for the root mean square error (RMSE), parity structure also demonstrates a significant ability to mitigate prediction errors: the RMSE decreases from 0.203 to 0.086 with only incoherent noise and from 0.172 to 0.133 with readout noise.

[0149] In summary, the experiments show that introducing parity structure as an input prior not only improves the noise resistance of the error mitigation neural network, but also significantly enhances its generalization performance under unseen input distributions, verifying the potential of structure-aware models in quantum error mitigation tasks.

[0150] The quantum error mitigation neural network training method based on physical prior structure provided by this invention significantly improves prediction accuracy and fidelity in error mitigation tasks compared to traditional random structure datasets. The root mean square error is reduced by up to 55%, and the KL divergence is reduced by approximately 40–50%. The structure-guided samples effectively enhance the neural network model's ability to learn physical conservation quantities, improving output parity conservation and reducing imbalance gaps by over 60%. Experimental results show that the parity structure training samples possess excellent structure generalization ability in scenarios without deep circuits and with different measurement bases. The network structure used in the method provided by this invention is simple, significantly improving error mitigation while maintaining model lightweightness. This provides a feasible path for future construction of lightweight error mitigation schemes with physical consistency and strong generalization ability. It is applicable to tasks requiring precise preservation of physical structure information, such as VQE, quantum simulation, and quantum classifiers.

[0151] Figure 13 This is a schematic diagram of a quantum error mitigation neural network training device based on a physical prior structure guided by an embodiment of the present invention.

[0152] like Figure 13 As shown, the quantum error mitigation neural network training device 1300 based on physical prior structure guidance includes an input data construction module 1310, a circuit construction module 1320, a multi-measurement basis sampling module 1330, and a neural network training module 1340.

[0153] The input data construction module 1310 is used to perform real amplitude random allocation and normalization operations sequentially on the computational ground state that satisfies the Hamming weight being even, to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure; in one embodiment, the input data construction module 1310 can be used to execute the operation S210 described above, which will not be repeated here.

[0154] The circuit construction module 1320 is used to design parameterized quantum circuits based on the one-dimensional transverse field Ising model through Trotter decomposition operations to obtain quantum circuits with structurally evolvable functions. In one embodiment, the circuit construction module 1320 can be used to perform the operation S220 described above, which will not be repeated here.

[0155] The multi-measurement basis sampling module 1330 is used to sample the output of the quantum circuit input data under multiple measurement basis to obtain noiseless training output data and noisy training output data with pairing relationship. In one embodiment, the multi-measurement basis sampling module 1330 can be used to perform the operation S230 described above, which will not be repeated here.

[0156] The neural network training module 1340 is used to train the quantum error mitigation neural network using the noisy training output data as training labels and the noisy training output data, and then uses the trained quantum error mitigation neural network to obtain the error mitigation mapping relationship between the noisy quantum circuit output data and the noisy quantum circuit output data in the target quantum circuit. In one embodiment, the neural network training module 1340 can be used to perform the operation S240 described above, which will not be repeated here.

[0157] According to embodiments of the present invention, any plurality of modules among the input data construction module 1310, circuit construction module 1320, multi-measurement basis sampling module 1330, and neural network training module 1340 can be combined into one module, or any one of these modules can be split into multiple modules. Alternatively, at least part of the functionality of one or more of these modules can be combined with at least part of the functionality of other modules and implemented in one module. According to embodiments of the present invention, at least one of the input data construction module 1310, circuit construction module 1320, multi-measurement basis sampling module 1330, and neural network training module 1340 can be at least partially implemented as hardware circuitry, such as field-programmable gate array (FPGA), programmable logic array (PLA), system-on-a-chip, system-on-a-substrate, system-on-package, application-specific integrated circuit (ASIC), or any other reasonable means of integrating or packaging the circuitry, or implemented in hardware or firmware, or in any one of software, hardware, and firmware implementations, or in a suitable combination of any of these. Alternatively, at least one of the input data construction module 1310, circuit construction module 1320, multi-measurement basis sampling module 1330, and neural network training module 1340 may be at least partially implemented as a computer program module, which can perform corresponding functions when the computer program module is run.

[0158] Figure 14 This is a block diagram of an electronic device suitable for implementing a quantum error mitigation neural network training method guided by physical prior structures according to an embodiment of the present invention.

[0159] like Figure 14 As shown, an electronic device 1400 according to an embodiment of the present invention includes a processor 1401, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1402 or a program loaded from a storage portion 1408 into a random access memory (RAM) 1403. The processor 1401 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1401 may also include onboard memory for caching purposes. The processor 1401 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present invention.

[0160] RAM 1403 stores various programs and data required for the operation of electronic device 1400. Processor 1401, ROM 1402, and RAM 1403 are interconnected via bus 1404. Processor 1401 executes various operations of the method flow according to embodiments of the present invention by executing programs in ROM 1402 and / or RAM 1403. It should be noted that the programs may also be stored in one or more memories other than ROM 1402 and RAM 1403. Processor 1401 may also execute various operations of the method flow according to embodiments of the present invention by executing programs stored in said one or more memories.

[0161] According to an embodiment of the present invention, the electronic device 1400 may further include an input / output (I / O) interface 1405, which is also connected to a bus 1404. The electronic device 1400 may also include one or more of the following components connected to the input / output (I / O) interface 1405: an input section 1406 including a keyboard, mouse, etc.; an output section 1407 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1408 including a hard disk, etc.; and a communication section 1409 including a network interface card such as a LAN card, modem, etc. The communication section 1409 performs communication processing via a network such as the Internet. A drive 1410 is also connected to the input / output (I / O) interface 1405 as needed. A removable medium 1411, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 1410 as needed so that computer programs read from it can be installed into the storage section 1408 as needed.

[0162] The present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of the present invention.

[0163] According to embodiments of the present invention, a computer-readable storage medium may be a non-volatile computer-readable storage medium, such as including, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of the present invention, a computer-readable storage medium may include ROM 1402 and / or RAM 1403 and / or one or more memories other than ROM 1402 and RAM 1403 described above.

[0164] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0165] Those skilled in the art will understand that the features described in the various embodiments of the present invention can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in the present invention. In particular, the features described in the various embodiments of the present invention can be combined and / or combined in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or combinations fall within the scope of the present invention.

[0166] The embodiments of the present invention have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of the invention. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of the invention, and all such substitutions and modifications should fall within the scope of the invention.

Claims

1. A quantum error mitigation neural network training method based on physical prior structure guidance, characterized in that, The method includes: The computational ground state that satisfies an even Hamming weight is subjected to a real amplitude random assignment operation and a normalization operation in sequence to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure; Based on the one-dimensional transverse field Ising model, parameterized quantum circuits are designed through Trotter decomposition operations to obtain quantum circuits with structurally evolvable functions. The processing result of the quantum circuit on the input data of the quantum circuit is sampled under multiple measurement basis to obtain noiseless training output data and noisy training output data with pairing relationship; The noiseless training output data is used as training labels. The noisy training output data is used to train the quantum error mitigation neural network. The trained quantum error mitigation neural network is then used to obtain the error mitigation mapping relationship between the noisy quantum circuit output data and the noiseless quantum circuit output data in the target quantum circuit. Specifically, the process of sampling the output of the quantum circuit's input data under multiple measurement bases to obtain noiseless training output data and noisy training output data with paired relationships includes: Under the X measurement basis, the processing results of the quantum circuit are subjected to Hadamard gate basis transformation to obtain paired noiseless training output data and noisy training output data under the X measurement basis. Under the Y measurement basis, the processing result of the quantum circuit is transformed from the Z measurement basis to the superposition state of the X measurement basis through the Hadamard gate basis transformation; By applying the superposition state to the complex conjugate of the T-gate The gate performs phase modulation to convert the superposition state to the Y measurement basis, thereby obtaining paired noiseless training output data and noisy training output data under the Y measurement basis.

2. The method according to claim 1, characterized in that, Also includes: The error mitigation capability of the trained quantum error mitigation neural network is evaluated using preset evaluation indicators to obtain evaluation results. The preset evaluation indicators include root mean square error, parity fidelity, KL divergence, and Z-direction imbalance difference.

3. The method according to claim 1, characterized in that, Based on the one-dimensional transverse-field Ising model, parameterized quantum circuits are designed through Trotter decomposition operations, resulting in quantum circuits with structurally evolvable functions, including: The Hamiltonian of the one-dimensional transverse field Ising model is determined based on the nearest neighbor coupling strength, the transverse field strength, and the Pauli-X and Pauli-Z operators acting on each qubit, wherein the nearest neighbor coupling strength is randomly selected based on a uniform distribution. The Hamiltonian is decomposed by the Trotter decomposition operation, and the time evolution operator is approximated as a realizable quantum gate operation to obtain the quantum circuit with structurally evolvable function.

4. The method according to claim 3, characterized in that, The time evolution operator is approximated as a realizable quantum gate operation by decomposing the Hamiltonian through the Trotter decomposition operation, resulting in the quantum circuit with structurally evolvable functionality, comprising: The qubit is rotated using the Rx rotation gate to obtain the rotated qubit; The rotated even-number quantum bits and the rotated odd-number quantum bits are cross-coupled through CNOT gates and Rz rotation gates to obtain coupled quantum bits; By adding barriers to separate different quantum circuit layers, the quantum circuit with structurally evolvable functionality is obtained.

5. The method according to claim 1, characterized in that, The inputs to the quantum error mitigation neural network include device error parameters, quantum circuit gate structure design information, rotation angle histogram, and noisy measurement distribution; The noisy measurement distribution is obtained by modeling the counting distribution of the noisy training output data; In the process of constructing the quantum error mitigation neural network, the expected value encoding input to the quantum error mitigation neural network is changed to a counting distribution.

6. A quantum error mitigation neural network training device guided by physical prior structures, characterized in that, The device includes: The input data construction module is used to perform real amplitude random allocation and normalization operations on the computational ground state that satisfies the Hamming weight being even, to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure; The circuit construction module is used to design parameterized quantum circuits based on the one-dimensional transverse field Ising model through Trotter decomposition operations, thereby obtaining quantum circuits with structurally evolvable functions. The multi-measurement basis sampling module is used to sample the output of the quantum circuit input data under multiple measurement basis to obtain noiseless training output data and noisy training output data with pairing relationship; The neural network training module is used to use the noiseless training output data as training labels, train the quantum error mitigation neural network using the noisy training output data, and use the trained quantum error mitigation neural network to obtain the error mitigation mapping relationship between the noisy quantum circuit output data and the noiseless quantum circuit output data in the target quantum circuit. Specifically, the process of sampling the output of the quantum circuit's input data under multiple measurement bases to obtain noiseless training output data and noisy training output data with paired relationships includes: Under the X measurement basis, the processing results of the quantum circuit are subjected to Hadamard gate basis transformation to obtain paired noiseless training output data and noisy training output data under the X measurement basis. Under the Y measurement basis, the processing result of the quantum circuit is transformed from the Z measurement basis to the superposition state of the X measurement basis through the Hadamard gate basis transformation; By applying the superposition state to the complex conjugate of the T-gate The gate performs phase modulation to convert the superposition state to the Y measurement basis, thereby obtaining paired noiseless training output data and noisy training output data under the Y measurement basis.

7. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs. The characteristic feature is that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 5.

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