Quantum error mitigation neural network training method based on physical prior structure guidance

Abstract

The invention provides a quantum error mitigation neural network training method based on physical prior structure guidance, which can be applied to the technical field of quantum information processing and quantum machine learning. The method comprises the steps that real amplitude random distribution operation and standardization operation are sequentially carried out on calculation ground states meeting the even number of Hamming weights, and quantum circuit input data are obtained; based on a one-dimensional transverse field Ising model, designing a parameterized quantum circuit through Trotter decomposition operation to obtain a quantum circuit with a structure evolvable function; performing output sampling under multiple measurement bases on a processing result of the quantum circuit on the input data of the quantum circuit to obtain noise-free training output data and noise-containing training output data which have a pairing relationship; and taking the noise-free training output data as a training label, training the quantum error mitigation neural network by using the noise-containing training output data, and obtaining an error mitigation mapping relation of the target quantum circuit by using the trained quantum error mitigation neural network.

Description

Technical Field

[0001] The present 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 quantum error mitigation neural network training method 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), resulting in significant deviations between actual measured outputs and theoretical predictions. Although some studies have used neural networks to mitigate errors in noisy quantum circuit outputs, these studies generally 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 may be retained during the evolution of quantum circuits, resulting in artificial intelligence models lacking symmetry perception, generalization ability, and physical consistency. In addition, the training data for existing quantum error mitigation technology solutions for artificial intelligence models is generally based on random state generation, lacking targeted coverage of the physical priors of actual quantum circuits. This results in weak expressiveness of the training data, an 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 quantum error mitigation neural network training method, device, electronic device and storage medium based on physical prior structure guidance.

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

[0005] Performing random real amplitude distribution and normalization operations on the computational basis state satisfying the even Hamming weight in sequence to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure;

[0006] Based on the one-dimensional transverse field Ising model, a parameterized quantum circuit is designed through Trotter decomposition operation, and a quantum circuit with structural evolution function is obtained;

[0007] The processing result of the quantum circuit on the quantum circuit input data is sampled in multiple measurement bases to obtain noise-free training output data and noisy training output data with a paired relationship;

[0008] The noise-free training output data is used as the training label, and the noisy training output data is used to train the quantum error mitigation neural network. 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 noise-free quantum circuit output data in the target quantum circuit.

[0009] According to an embodiment of the present invention, the above-mentioned 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 to obtain evaluation results. The preset evaluation indicators include root mean square error, parity fidelity, KL divergence, and Z-direction imbalance gap.

[0011] According to an embodiment of the present invention, the above-mentioned parameterized quantum circuit is designed based on the one-dimensional transverse field Ising model through the Trotter decomposition operation to obtain a quantum circuit with structural evolvability, including:

[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, where the nearest neighbor coupling strength is randomly selected based on a uniform distribution.

[0013] The Hamiltonian is decomposed through the Trotter decomposition operation and the time evolution operator is approximated as a realizable quantum gate operation, resulting in a quantum circuit with structural evolvability.

[0014] According to an embodiment of the present invention, the above-mentioned decomposition of the Hamiltonian by the Trotter decomposition operation and the approximation of the time evolution operator into a realizable quantum gate operation to obtain a quantum circuit with structural evolutionary function includes:

[0015] Use the Rx rotation gate to rotate the quantum bit to obtain the rotated quantum bit;

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

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

[0018] According to an embodiment of the present invention, the above-mentioned output sampling of the processing result of the quantum circuit on the quantum circuit input data under multiple measurement bases to obtain noise-free training output data and noisy training output data with a paired relationship includes:

[0019] In the X measurement basis, the processing results of the quantum circuit are transformed into a Hadamard gate basis to obtain paired noise-free training output data and noisy training output data in the X measurement basis.

[0020] According to an embodiment of the present invention, the above-mentioned performing output sampling under multiple measurement bases on the processing result of the quantum circuit on the quantum circuit input to obtain noise-free training output data and noisy training output data with a paired relationship further includes:

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

[0022] By applying the superposition state to the complex conjugate of the T gate The gate performs phase modulation and then converts the superposition state into the Y measurement basis to obtain paired noise-free training output data and noisy training output data in the X measurement basis.

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

[0024] The noisy measurement distribution is obtained by modeling the count distribution of noisy training output data;

[0025] 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 count distribution.

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

[0027] An input data construction module is used to perform real amplitude random distribution operations and normalization operations on the calculation basis states that satisfy the Hamming weight being an even number in sequence to obtain 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 structural evolution capabilities.

[0029] A multi-measurement basis sampling module is used to perform output sampling on the processing results of the quantum circuit on the quantum circuit input data under multiple measurement bases to obtain noise-free training output data and noisy training output data with a paired relationship;

[0030] The neural network training module is used to use the noise-free training output data as training labels, use the noisy training output data to train the quantum error mitigation neural network, 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 noise-free quantum circuit output data in the target quantum circuit.

[0031] A third aspect of the present invention provides an electronic device, comprising: one or more processors; 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 above method.

[0032] The fourth aspect of the present invention further provides a computer-readable storage medium having a computer program or instructions stored thereon, which implements the steps of the above method when the computer program or instructions are executed by a processor.

[0033] The quantum error mitigation neural network training method based on physical prior structure guidance provided by the present invention, by constructing an initial state with parity symmetry (limited to even excitations), retaining the conservation structure in ideal dynamics, overcoming the problem of unpredictable error patterns under traditional random initial states, and effectively avoiding the hardware parameter drift problem caused by random state training; designing a parameterized quantum circuit based on the transverse field one-dimensional Ising model, guiding the measurement output to naturally present physical consistency, which is different from the existing method of relying on random or unstructured circuits to generate data. At the same time, the quantum circuit designed based on the Ising model can effectively suppress the crosstalk noise between quantum bits; introducing multiple measurement bases and using the output count distribution as the modeling input, compared with the method of using only expected values, significantly improves the neural network's ability to resolve error details and generalization effect. At the same time, the use of technology distribution can accelerate the processing speed of the neural network and reduce the consumption of hardware resources. The method provided by the present invention shows better error mitigation ability in environments such as incoherent noise and readout noise, and is superior to the local adaptation of previous methods to specific noise or specific bases, showing good hardware universality and reducing the hardware operation burden. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The above contents and other objects, features and advantages of the present invention will become more apparent through the following description of the embodiments of the present invention with reference to the accompanying drawings, in which:

[0035] Figure 1 This is a diagram of an application scenario of quantum error mitigation neural network training guided by physical prior structures according to an embodiment of the present invention;

[0036] Figure 2 is a flow chart 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 is a circuit structure diagram of Trotter evolution based on the Ising model according to an embodiment of the present invention;

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

[0039] Figure 5 2 is a schematic diagram of single quantum bit error mitigation under incoherent noise and Z-basis measurement according to an embodiment of the present invention;

[0040] Figure 6 2 is a schematic diagram of single-qubit error mitigation after further introduction of readout noise in the Z measurement basis according to an embodiment of the present invention;

[0041] Figure 7 3. This is a comparison diagram of the KL divergence index and the root mean square error index under the Z-basis measurement according to an embodiment of the present invention;

[0042] Figure 8 2. This is a schematic diagram of single quantum bit error mitigation under the X measurement basis according to an embodiment of the present invention;

[0043] Figure 9 2. This is a schematic diagram of single quantum bit error mitigation in the Y measurement basis according to an embodiment of the present invention;

[0044] Figure 10 3. This is a comparison diagram of the KL divergence index and the root mean square error index under different measurement bases according to an embodiment of the present invention;

[0045] Figure 11 2. This is a schematic diagram of single-qubit error mitigation in a generalized experiment under different noises according to an embodiment of the present invention;

[0046] Figure 12 3. This is a comparison chart of the KL divergence index and the root mean square error index of the generalization experiment under different noises according to an embodiment of the present invention;

[0047] Figure 13 2 is a schematic structural diagram of a quantum error mitigation neural network training device guided by a physical priori structure according to an embodiment of the present invention;

[0048] Figure 14 4 is a block diagram of an electronic device suitable for implementing a quantum error mitigation neural network training method guided by a physical priori structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[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 present invention. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of embodiments of the present invention. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concept of the present invention.

[0050] The terms used herein are only for describing specific embodiments and are not intended to limit the present invention. The terms "comprise", "include", etc. used herein indicate the presence of the 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 should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

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

[0053] In quantum computing, the outputs of certain conserved quantum systems exhibit residual structure in parity, particle populations, or symmetry distributions. Effectively capturing this structure and incorporating it into the learning process could potentially improve the physical consistency and generalization capabilities of the model. Key technical challenges in quantum error mitigation include constructing datasets with structured priors and enhancing the effectiveness of neural networks in mitigating measurement errors.

[0054] The present invention addresses the technical problems in existing quantum error mitigation methods, such as lack of physical priors, weak input expression capabilities, and poor adaptability to different measurement bases, by providing a quantum error mitigation technology solution with a structural prior injection mechanism, a physical evolution-driven data generation function, multi-measurement basis coverage and distributed-level modeling characteristics, and robust modeling capabilities for multi-noise scenarios.

[0055] Figure 1 This is a diagram of an application scenario of quantum error mitigation neural network training guided by physical prior structures according to an embodiment of the present invention.

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

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

[0058] The first terminal device 101 , the second terminal device 102 , and the third terminal device 103 may be various electronic devices having display screens and supporting web browsing, including but not limited to smart phones, tablet computers, laptop computers, desktop computers, and the like.

[0059] The server 105 may be a server that provides various services, such as a background management server (for example only) that supports websites browsed by users using the first terminal device 101, the second terminal device 102, and the third terminal device 103. The background management server may analyze and process received data such as user requests, and feed back processing results (e.g., web pages, information, or data obtained or generated based on 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 guidance provided in the embodiment of the present invention can generally be executed by the server 105. Accordingly, the quantum error mitigation neural network training device based on physical prior structure guidance provided in the embodiment of the present invention can generally be set in the server 105. The quantum error mitigation neural network training method based on physical prior structure guidance provided in the embodiment of the present invention can also be executed by a server or server cluster that is different from the server 105 and can communicate with the first terminal device 101, the second terminal device 102, the third terminal device 103 and / or the server 105. Accordingly, the quantum error mitigation neural network training device based on physical prior structure guidance provided in the embodiment of the present invention can also be set in a server or server cluster that is different from the server 105 and can communicate with the first terminal device 101, the second terminal device 102, the third terminal device 103 and / or the server 105.

[0061] It should be understood that Figure 1The number of terminal devices, networks and servers in the embodiment is merely illustrative. Any number of terminal devices, networks and servers may be provided as required.

[0062] The following will be based on Figure 1 The scene described by Figures 2 to 12 The quantum error mitigation neural network training method based on physical prior structure guidance of the disclosed embodiment is described in detail.

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

[0064] Figure 2 This is a flow chart of a quantum error mitigation neural network training method based on physical prior structure guidance according to 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 , a real amplitude random distribution operation and a normalization operation are sequentially performed on a calculation basis state satisfying an even Hamming weight to obtain quantum circuit input data, wherein the quantum circuit input data is a quantum state with an even parity structure.

[0067] Hamming weight is a parameter that measures the number of times "1" appears in a binary sequence.

[0068] Operation S210 involves the construction of the initial state of the parity structure: in order to introduce the influence of the structural prior on the mitigation of quantum errors, the present invention designs a quantum circuit input of a computing ground state with an even Hamming weight, and the quantum circuit input satisfies formula (1):

[0069] (1),

[0070] Among them, span represents the Hilbert subspace spanned by the calculation basis state with an even Hamming weight. represents a vector space, It represents the corresponding calculation basis state in binary form, and mod represents the remainder operation.

[0071] By enumerating all ground states that satisfy even-parity constraints and randomly assigning real amplitudes, followed by normalization, these physically meaningful initial states are expected to be inherently robust to some quantum noise, thus providing physically driven prior information for error mitigation studies.

[0072] In operation S220 , a parameterized quantum circuit is designed based on a one-dimensional transverse field Ising model through a Trotter decomposition operation to obtain a quantum circuit with a structurally evolvable function.

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

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

[0075] In operation S230 , output sampling is performed on a result of processing the quantum circuit input data by the quantum circuit under multiple measurement bases to obtain noise-free training output data and noisy training output data having a paired relationship.

[0076] In operation S240, the noise-free training output data is used as a training label, and the quantum error mitigation neural network is trained using the noisy training output data. The trained quantum error mitigation neural network is used to obtain an error mitigation mapping relationship between the noisy quantum circuit output data and the noise-free quantum circuit output data in the target quantum circuit.

[0077] The quantum error mitigation neural network training method based on physical prior structure guidance provided by the present invention, by constructing an initial state with parity symmetry (limited to even excitations), retaining the conservation structure in ideal dynamics, overcoming the problem of unpredictable error patterns under traditional random initial states, and effectively avoiding the hardware parameter drift problem caused by random state training; designing a parameterized quantum circuit based on the transverse field one-dimensional Ising model, guiding the measurement output to naturally present physical consistency, which is different from the existing method of relying on random or unstructured circuits to generate data. At the same time, the quantum circuit designed based on the Ising model can effectively suppress the crosstalk noise between quantum bits; introducing multiple measurement bases and using the output count distribution as the modeling input, compared with the method of using only expected values, significantly improves the neural network's ability to resolve error details and generalization effect. At the same time, the use of technology distribution can accelerate the processing speed of the neural network and reduce the consumption of hardware resources. The method provided by the present invention shows better error mitigation ability in environments such as incoherent noise and readout noise, and is superior to the local adaptation of previous methods to specific noise or specific bases, showing good hardware universality and reducing the hardware operation burden.

[0078] According to an embodiment of the present invention, the above-mentioned parameterized quantum circuit is designed based on the one-dimensional transverse field Ising model through the Trotter decomposition operation to obtain a quantum circuit with structural evolvability, including: 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 operator and the Pauli-Z operator acting on each quantum bit, wherein the nearest neighbor coupling strength is randomly selected based on a uniform distribution; decomposing the Hamiltonian through the Trotter decomposition operation and then approximating the time evolution operator as a realizable quantum gate operation, thereby obtaining a quantum circuit with structural evolvability.

[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-mentioned decomposition of the Hamiltonian by the Trotter decomposition operation and then approximation of the time evolution operator as a realizable quantum gate operation to obtain a quantum circuit with structural evolvability includes: rotating the quantum bit using the Rx rotation gate to obtain a rotated quantum bit; cross-coupling the rotated even quantum bit and the rotated odd quantum bit through the CNOT gate and the Rz rotation gate to obtain a coupled quantum bit; and separating different quantum circuit layers by adding barriers to obtain a quantum circuit with structural evolvability.

[0081] The following is a specific implementation method and combined with the attached Figure 3 The design of structure evolution quantum circuit is further explained in detail.

[0082] Figure 3 4 is a structural diagram of a Trotter evolution circuit based on an Ising model according to an embodiment of the present invention.

[0083] When constructing a quantum circuit with physical interpretability, the present invention chooses to design a parameterized quantum circuit based on the one-dimensional transverse field Ising model (TFIM). The Hamiltonian of TFIM is shown in formula (2):

[0084] (2),

[0085] in, represents the nearest neighbor coupling strength, is the transverse field strength, and They are The Pauli operators in the X and Z directions of the qubits are represented by the time evolution operator. Through Trotter decomposition, the time evolution operator is approximated as a series of implementable quantum gate operations, namely, rotation of each qubit (Rx gate), cross-coupling between even and odd bits (CZ gate implemented by CNOT+Rz+CNOT), and separation of each layer by 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 components: first, the Rx gate implements the rotation of each qubit; then, cross-coupling between even and odd bits is achieved via CNOT gates and rotating Rz gates; finally, barriers are added to separate different quantum circuit layers. This design preserves the physical evolution of each step while ensuring the feasibility and operability of the quantum circuit. The depth of the quantum circuit is proportional to the number of Trotter steps, meaning that as the number of time evolution steps increases, the depth and complexity of the circuit also increase. In the circuit example designed by the present invention, the coupling strength J is randomly drawn from a uniform distribution U(0,1), which provides a randomness that provides a basis for circuit diversity. As a natural evolution model, TFIM can naturally preserve parity symmetry under short-time evolution or weak transverse field conditions. This makes it suitable as a structural prior to help construct quantum circuits with greater physical interpretability. In this way, the present 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 quantum algorithms.

[0087] Furthermore, TFIM is a standard testing platform for quantum circuit design and error simulation. It is widely used in quantum algorithm verification, error model construction, and quantum error correction research, and possesses excellent physical interpretability and scalability. Therefore, using TFIM as the foundation for the dataset effectively tests and verifies the quantum circuit design and error mitigation methods proposed in this paper.

[0088] According to an embodiment of the present invention, performing output sampling on a result of processing quantum circuit input data by a quantum circuit in multiple measurement bases to obtain paired noise-free training output data and noisy training output data includes performing a Hadamard gate basis transformation on the result of processing the quantum circuit in an X measurement basis to obtain paired noise-free training output data and noisy training output data in the X measurement basis.

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

[0090] According to an embodiment of the present invention, the above-mentioned processing result of the quantum circuit on the quantum circuit input is subjected to output sampling under multiple measurement bases to obtain noise-free training output data and noisy training output data with a paired relationship, further comprising: in the Y measurement basis, converting the processing result of the quantum circuit from the Z measurement basis to the superposition state of the Y measurement basis through the Hadamard gate basis transformation; applying the superposition state to the complex conjugate of the T gate The gate performs phase modulation and then converts the superposition state into the Y measurement basis to obtain paired noise-free training output data and noisy training output data in the X measurement basis.

[0091] The quantum circuit output sampling mechanism under the above-mentioned multi-measurement basis is described in detail below through a specific implementation method.

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

[0093] For the X measurement basis, a Hadamard gate is required to transform the basis. The Hadamard gate can transform the standard Z basis state (e.g. and ) is converted into the superposition state required by the X basis, that is, and Mapped to ( )and ( ), so that the measurement results can be reflected in the X basis.

[0094] For the Y measurement basis, you need to apply The combination of gate (i.e., the complex conjugate of T gate) and Hadamard gate. First, the Hadamard gate is applied to convert the qubit from the Z basis to the superposition state of the X basis, and then the The gate performs phase modulation, converting the qubit to the Y basis. Ultimately, this combined operation enables the measurement result to correspond to the projection value of the Y basis. Quantum output sampling performed under this mechanism not only provides projection values in different measurement bases but also reveals the response characteristics of quantum circuits in 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 consisting of a noise-free ideal output and a noisy output after noise perturbation, which serve 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 count 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 the count distribution.

[0096] The following is a further detailed description of the construction process of the neural network error mitigation model involved in the present invention through specific implementation methods.

[0097] This paper uses a simple and deployable classical neural network model (such as a multi-layer perceptron (MLP)) to model the count distribution (counts) output by the quantum circuit. The model input is:

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

[0099] Circuit gate structure statistics (6 dimensions);

[0100] Rotation angle histogram (40 dimensions);

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

[0102] When building neural network error mitigation models, switching from expected value encoding to output count distributions can more accurately reflect the actual measurement results of quantum circuits. This is because the output count distribution provides more comprehensive information than a single expected value, which has significant advantages for error mitigation and model training. The output of a quantum circuit is typically based on a probability distribution rather than a single expected 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 diverse and probabilistic characteristics of the quantum circuit output. This more comprehensively describes the actual circuit behavior than the expected value, especially in the presence of significant noise. By combining circuit parameters with noise parameters, the output count distribution can provide a more detailed characterization of circuit behavior. For example, parameters in the quantum circuit, such as rotation angle and coupling strength, directly affect the evolution of the quantum state, while noise parameters (such as coherence noise and readout noise) can lead to biased measurement results. By incorporating this information into the neural network training data, the model can better identify and learn noise patterns and effectively correct for them. Through this improvement, the neural network error mitigation model of the present invention can more realistically reflect the dynamic evolution of quantum systems 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. The error mitigation mapping from noisy output to ideal output is achieved through supervised learning training.

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

[0104] The root mean squared error (RMSE) is the square root of the ratio of the square of the deviation between the predicted value 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 called the Z-direction Imbalance Gap.

[0107] The advantages of the method provided by the present invention are illustrated below through multi-class noise models and generalization test design.

[0108] By invoking noise model simulation platforms (such as FakeLima) provided by IBM Qiskit, we accurately inject real hardware-level errors, ensuring that the generated samples more closely resemble the physical system output. In the experimental design, the training set circuit depth was set to shallow layers (e.g., 0–19 layers), while the test set used previously unseen deeper circuits (e.g., 20–29 layers) to evaluate the model's cross-depth generalization capabilities. Furthermore, the model was trained and tested under different measurement bases and noise combinations. Metrics such as root mean square error (RMS), parity fidelity, KL divergence, and Z-axis imbalance were used to systematically evaluate the error mitigation capabilities of the constructed structured dataset when transferring across scenarios. All experimental results are clearly presented in accompanying figures and data tables.

[0109] The KL divergence measures the difference between two probability distributions. Parity fidelity measures the ability of a model's predictions to preserve parity structure. Imbalance gap measures the lack of conservation in the probability distribution in the Z direction. FakeLima is a simulation backend provided by IBM that includes a realistic hardware noise model.

[0110] The quantum error mitigation neural network training method based on physical prior structure guidance provided by the present invention is described and verified through specific experiments and in combination with the accompanying drawings.

[0111] The following is the specific experiment setup, taking the four-bit Ising model as an example:

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

[0113] (2) Constructing the initial state as a parity state superposition and injecting IBM hardware-level errors using the FakeLima noise backend;

[0114] (3) Collect ideal output and noise output in three measurement bases (Z / X / Y) to construct training samples;

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

[0116] (5) Evaluate the model output indicators such as root mean square error, KL divergence, parity fidelity, and Z-direction Imbalance Gap;

[0117] All experimental results are recorded in the form of data tables and diagrams in the accompanying drawings. The experiments show that the parity structure training set outperforms the random structure in all indicators, especially in the generalization depth segment, which verifies the comprehensive advantages of the method of the present invention in structure preservation and generalization ability.

[0118] Figure 4 is a schematic diagram of a training data sample according to an embodiment of the present invention. Figure 4 (a) in is the parity training sample, Figure 4 (b) in the figure is a random training sample; 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 value) (the same below).

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

[0120] In contrast, Figure 4 As shown in (a), the parity training sample exhibits a clear bias toward even Hamming weights, with two 1s being the most likely. The probability of one or three 1s is close to zero, clearly demonstrating the even structure of the initial state. After noise perturbation, although the parity constraint is weakened, the dominance of even numbers of 1s remains evident.

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

[0122] Training phase (0-19 layers)

[0123] Table 1: Comparison of the two structural indicators 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%, the KL divergence by 23.13%, and the parity fidelity by 17.20%. The Z-direction imbalance (imbalance gap) improves by 64.9%, bringing it closer to the ideal state of physical conservation. These metrics demonstrate that structure-guided datasets help the model learn systematic biases during training, thereby more effectively correcting measurement errors.

[0126] Figure 5 2 is a schematic diagram of single quantum bit error mitigation under Z-based measurement and incoherent noise according to an embodiment of the present invention.

[0127] Figure 5 The above quantitative conclusions are verified. For random structures ( Figure 5 (a) in the figure), although the output distribution after error correction is converged compared to the original noise, the parity structure ( Figure 5 The model prediction under (b) shows stronger stability and closeness, where Figure 5 Where dist_noisy_i represents the difference between the i-th quantum bit and the ideal value under noise (the same below), and dist_mitigated_i represents the difference between the i-th quantum bit and the ideal value after mitigation (the same below).

[0128] Figure 6 Schematic diagram of single quantum bit error mitigation after further introduction of 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 structures in the Z measurement basis; Figure 6 (b) Schematic diagram of single-qubit error mitigation after readout noise of the parity structure in the Z measurement basis

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

[0130]

[0131] As shown in Table 2, after further noise introduction, the parity structure samples outperformed random structures in all four key metrics, demonstrating excellent error robustness and structural generalization. The root mean square error and KL divergence decreased by 34.17% and 40.92%, respectively, indicating a significant reduction in the gap between the output probability distribution and the ideal target. 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 the structured prior helps maintain the physical conservation of quantum states. Figure 6 This reflects the alleviation of the error of each quantum bit under this condition, further verifying the above quantitative conclusion.

[0132] Figure 7 : is a comparison chart of the KL divergence index and the root mean square error index under the Z-basis measurement according to an embodiment of the present invention. Figure 7 (a) represents the KL divergence index of random structure and odd-even structure under incoherent noise (incoherent, the same below) and composite noise (incoherent+readout, incoherent noise and readout noise, the same below); Figure 7 (b) in the figure shows the RMSE indicators of random structures and odd-even structures under incoherent noise and composite noise.

[0133] In the comparative experiments described above, the present invention systematically analyzed the impact of random structure samples and parity structure samples on error mitigation under different noise models (including readout noise and with readout noise removed). Key metrics included corrected root mean square error (RMS) and KL divergence. The experimental results showed that the model trained using the parity structure maintained a significant advantage, maintaining more stable output and stronger physical consistency, both in relatively noisy environments (such as those with readout noise) and in relatively ideal environments with readout noise removed.

[0134] These trends are mapped in the present invention Figure 7 This is particularly clear in the indicator curve diagram, which fully demonstrates that the parity structure training samples can not only enhance the fitting ability of the model, but also help improve its robustness and generalization ability in different noise scenarios.

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

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

[0137]

[0138] Under X-basis measurement conditions, this study also compared the performance of parity structure samples and random structure samples in the quantum error mitigation task. As shown in Table 3, the parity structure training samples outperformed the random structure in all indicators: its 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 increased by as much as 72.51%, indicating that under the Hadamard basis, the model can still better maintain the parity symmetry structure of the quantum state; the KL divergence decreased by 43.92%, reflecting that the output distribution of the model is more closely aligned with the ideal distribution; the absolute value of the Imbalance Gap in the Z direction decreased, further indicating that the model better preserves physical conservation. Figure 8 This reflects the alleviation of the error of each quantum bit under this condition, further verifying the above quantitative conclusion.

[0139] Figure 9 : is a schematic diagram of single quantum bit error mitigation under the Y measurement basis according to an embodiment of the present invention. Figure 9 (a) shows the schematic diagram of single-qubit error mitigation of random structure under Y measurement basis; Figure 9 (b) in the figure shows the schematic diagram of single quantum bit error mitigation of the parity structure under the Y measurement basis.

[0140] Table 4: Comparison of the two structural indicators 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 the accuracy of the expected value. Parity fidelity was improved by 74.47%, reflecting a significant improvement in alignment with the 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 was also reduced, further demonstrating that the model better preserves physical conservation. These results highlight that the parity structure still performs well under Y-basis measurements, with enhanced fidelity and improved noise resilience. Figure 9 This reflects the alleviation of the error of each quantum bit under this condition, further verifying the above quantitative conclusion.

[0143] Figure 10 3 is a comparison chart of the KL divergence index and the root mean square error index under different measurement bases according to an embodiment of the present invention.

[0144] Figure 10(a) in the equation represents the KL divergence index of random structure and odd-even structure under the X, Y and Z measurement basis. Figure 10 (b) in the figure represents the RMSE index of random structure and parity structure under the X, Y and Z measurement basis; among them, 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); by analyzing Figure 10 The root mean square error and KL divergence curves for different measurement bases show that the parity structure training data outperforms the random structure in all measurement bases, exhibiting lower root mean square error and smaller KL divergence. In particular, in the X and Y bases, the parity structure significantly enhances the neural network's ability to identify and fit the structure of quantum output distributions. These results demonstrate that the parity structure not only improves error mitigation during model training but also enhances the model's structural generalization capabilities across different measurement bases.

[0145] Figure 11 2 is a schematic diagram of single quantum bit error mitigation in a generalization experiment under different noises according to an embodiment of the present invention.

[0146] Figure 12 3 is a comparison chart of the KL divergence index and the root mean square error index of the generalization experiment under different noises according to an embodiment of the present invention.

[0147] Generalization stage (20-29 layers): 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 quantum bit system, such as Figure 11 As shown, Figure 11 (a) in the figure represents incoherent noise + readout noise + random structure. Figure 11 (b) in the figure represents incoherent noise + readout noise + odd-even structure. Figure 11 (c) in the figure represents incoherent noise + random structure. Figure 11 (d) in the figure represents incoherent noise plus parity structure. The results show that, in the presence of both incoherent noise and readout noise, introducing input states with parity structure significantly improves prediction accuracy after error mitigation. Compared to random structures, structured inputs not only make the distribution of expected values after mitigation more concentrated around the ideal value, but also demonstrate greater consistency and stability across multiple model instances.

[0148] Furthermore, the present invention uses the KL divergence and root mean square error to conduct a statistical quantitative analysis of the above conclusions (see Figure 12 ),in, Figure 12(a) in the figure represents the KL divergence index of random structure and odd-even structure under the conditions of incoherent noise and composite noise. Figure 12 (b) shows the RMSE metrics for random and even-odd structures under incoherent and composite noise conditions. In terms of KL divergence, the structured input exhibits lower distribution deviation under both types of noise, with the KL value dropping significantly under composite noise (from 0.285 to 0.242), indicating that the model is superior in preserving probabilistic structural information. Regarding the root mean square error (RMS) metric, the parity structure also demonstrates significant prediction error mitigation: the RMS error decreases from 0.203 to 0.086 in the case of incoherent noise alone and from 0.172 to 0.133 in the case of 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 above-mentioned quantum error mitigation neural network training method based on physical prior structure guidance provided by the present invention, compared with traditional random structure data sets, the parity structure training set samples significantly improve the prediction accuracy and fidelity in error mitigation tasks, with the root mean square error reduced by up to 55% and the KL divergence reduced by about 40-50%; the structure-guided samples effectively enhance the learning ability of the neural network model for physical conserved quantities, the output parity conservation is enhanced, and the imbalance gap is reduced by more than 60%; experimental results show that the parity structure training samples have excellent structural generalization capabilities in unseen deep circuits and different measurement basis scenarios; the network structure used in the method provided by the present invention is simple, and while keeping the model lightweight, it significantly improves the error mitigation effect, providing a feasible path for the future construction of lightweight error mitigation solutions with physical consistency and strong generalization capabilities; it is suitable for task scenarios such as VQE, quantum simulation, and quantum classifiers that require accurate retention of physical structure information.

[0151] Figure 13 3 is a structural diagram of a quantum error mitigation neural network training device guided by a physical priori structure according to an embodiment of the present invention.

[0152] like Figure 13 As shown, the above-mentioned 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] Input data construction module 1310 is configured to sequentially perform real amplitude random distribution and normalization operations on computational basis states satisfying an even Hamming weight to obtain quantum circuit input data, where the quantum circuit input data is a quantum state having an even parity structure. In one embodiment, input data construction module 1310 can be configured to perform operation S210 described above, which will not be further described herein.

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

[0155] The multi-measurement basis sampling module 1330 is configured to perform output sampling in a multi-measurement basis on the processing result of the quantum circuit on the quantum circuit input data, thereby obtaining noise-free training output data and noisy training output data that are paired. In one embodiment, the multi-measurement basis sampling module 1330 can be used to perform the operation S230 described above, which will not be further described here.

[0156] Neural network training module 1340 is configured to use the noise-free 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 an error mitigation mapping relationship between the noisy quantum circuit output data and the noise-free quantum circuit output data in the target quantum circuit. In one embodiment, neural network training module 1340 can be configured to perform operation S240 described above and will not be further described here.

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

[0158] Figure 14 4 is a block diagram of an electronic device suitable for implementing a quantum error mitigation neural network training method guided by a physical priori structure 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 based on a program stored in a read-only memory (ROM) 1402 or a program loaded from a storage unit 1408 into a random access memory (RAM) 1403. Processor 1401 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. Processor 1401 may also include onboard memory for caching purposes. 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 the programs in ROM 1402 and / or RAM 1403 to perform various operations according to the method flow of the embodiment of the present invention. 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 the programs stored in the one or more memories to perform various operations according to the method flow of the embodiment of the present invention.

[0161] According to an embodiment of the present invention, electronic device 1400 may further include an input / output (I / O) interface 1405, which is also connected to bus 1404. Electronic device 1400 may also include one or more of the following components connected to I / O interface 1405: an input unit 1406 including a keyboard, mouse, etc.; an output unit 1407 including devices such as a cathode ray tube (CRT), liquid crystal display (LCD), and speakers; a storage unit 1408 including a hard disk; and a communication unit 1409 including a network interface card such as a LAN card or modem. Communication unit 1409 performs communication processing via a network such as the Internet. A drive 1410 is also connected to I / O interface 1405 as needed. Removable media 1411, such as a magnetic disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed in drive 1410 as needed, so that computer programs read from the removable media can be installed into storage unit 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 may exist independently and not incorporated 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 an embodiment of the present invention, a computer-readable storage medium may be a non-volatile computer-readable storage medium, and may include, for example, but not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to an embodiment of the present invention, a computer-readable storage medium may include ROM 1402 and / or RAM 1403 described above, and / or one or more memories other than ROM 1402 and RAM 1403.

[0164] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the above-mentioned module, program segment, or a part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

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

[0166] The above describes embodiments of the present invention. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention. Although each embodiment has been described separately above, this does not mean that the measures in each embodiment cannot be advantageously used in combination. Without departing from the scope of the present invention, those skilled in the art may make various substitutions and modifications, which should all fall within the scope of the present invention.

Claims

1. A quantum error mitigation neural network training method based on physical prior structure guidance, characterized in that: The method comprises: performing a real amplitude random distribution operation and a normalization operation on a calculation basis state satisfying an even Hamming weight 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, a parameterized quantum circuit is designed through Trotter decomposition operation, and a quantum circuit with structural evolution function is obtained; Performing output sampling on a multi-measurement basis on a result of processing the quantum circuit input data by the quantum circuit to obtain noise-free training output data and noisy training output data having a paired relationship; The noise-free training output data is used as a training label, the noisy training output data is used to train a quantum error mitigation neural network, and the trained quantum error mitigation neural network is used to obtain an error mitigation mapping relationship between the noisy quantum circuit output data and the noise-free quantum circuit output data in the target quantum circuit.

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 an evaluation result, wherein the preset evaluation indicators include root mean square error, parity fidelity, KL divergence, and Z-direction imbalance gap.

3. The method according to claim 1, characterized in that Based on the one-dimensional transverse field Ising model, we design parameterized quantum circuits through Trotter decomposition operations. The quantum circuits with structural evolutionary functions include: 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 operator and the Pauli-Z operator acting on each quantum bit, 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, thereby obtaining the quantum circuit with structural evolvability.

4. The method according to claim 3, characterized in that Decomposing the Hamiltonian by the Trotter decomposition operation and then approximating the time evolution operator into a realizable quantum gate operation, thereby obtaining the quantum circuit with structural evolutionary function, including: Use the Rx rotation gate to rotate the quantum bit to obtain the rotated quantum bit; The rotated even quantum bits and the rotated odd quantum bits are cross-coupled through the CNOT gate and the Rz rotation gate to obtain the coupled quantum bits; By adding barriers to separate different quantum circuit layers, the quantum circuit with structural evolvability is obtained.

5. The method according to claim 1, wherein Performing output sampling on a multi-measurement basis on a result of processing the quantum circuit input data by the quantum circuit to obtain noise-free training output data and noisy training output data having a paired relationship includes: In an X measurement basis, a Hadamard gate basis transformation is performed on the processing result of the quantum circuit to obtain paired noise-free training output data and noisy training output data in the X measurement basis.

6. The method according to claim 5, characterized in that Also includes: In the Y measurement basis, converting the processing result of the quantum circuit 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 into the Y measurement basis, thereby obtaining paired noise-free training output data and noisy training output data in the Y measurement basis.

7. The method according to claim 1, characterized in that The input of the 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 count 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 count distribution.

8. A quantum error mitigation neural network training device guided by physical prior structure, characterized in that: The device comprises: An input data construction module is used to sequentially perform real amplitude random distribution operations and normalization operations on a calculation basis state satisfying an even Hamming weight 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 structural evolution capabilities. a multi-measurement basis sampling module, configured to perform output sampling on a multi-measurement basis on a result of processing the quantum circuit input data by the quantum circuit, to obtain noise-free training output data and noisy training output data having a paired relationship; A neural network training module is configured to use the noise-free training output data as training labels, train a quantum error mitigation neural network using the noisy training output data, and obtain an error mitigation mapping relationship between noisy quantum circuit output data and noise-free quantum circuit output data in a target quantum circuit using the trained quantum error mitigation neural network.

9. An electronic device comprising: one or more processors; a memory for storing one or more computer programs, It is characterized in 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 7.

10. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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