Quantum state reconstruction method and device for flow field evolution prediction, medium and product

Abstract

The invention relates to the technical field of quantum computing, and discloses a quantum state reconstruction method and device for flow field evolution prediction, a medium and a product, and the training process of a quantum neural network adopted by the method comprises the steps: designing a quantum circuit containing adjustable parameters; encoding a two-dimensional flow field matrix in a fluid mechanics data set into a target flow field quantum state, inputting the target flow field quantum state into the quantum circuit, and generating an orthogonal basis quantum state; calculating a group of coefficients for projecting the quantum state of the target flow field to an orthogonal ground state space through a least square fitting method; and superposing the orthogonal basis quantum states according to the coefficients by adopting a linear combination unit to generate a reconstructed flow field quantum state, and adjusting parameters of a quantum circuit based on fidelity loss of the reconstructed flow field quantum state and the target flow field quantum state. According to the method, the dimension reduction characteristic of the orthogonal polynomial and the adaptive learning capability of the quantum neural network are deeply fused, so that higher precision and fidelity are realized in high-dimensional and complex quantum state reconstruction.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a quantum state reconstruction method, device, medium and product for flow field evolution prediction. Background Art

[0002] Quantum state reconstruction is a core task in quantum information science. It aims to accurately restore the quantum state of the system through limited measurement data. It is widely used in many fields such as quantum computing, quantum communication, quantum physics experiments and quantum chemistry simulation. However, quantum state reconstruction faces major challenges in high-dimensional quantum systems. Traditional quantum state tomography (QST) methods rely on comprehensive quantum measurements and require multiple independent measurements to obtain all the information of the system. As the number of quantum bits increases, the number of measurements and computational complexity required for quantum state tomography (QST) increase exponentially, limiting its application in high-dimensional systems.

[0003] To address the above challenges, compressed sensing technology was introduced into the field of quantum state reconstruction (see New Journal of Physics, 2012, 14(9): 095022). Compressed sensing uses the sparsity of quantum states to achieve efficient reconstruction through a small number of random measurements, significantly reducing the number of measurements and computing resources required (see Physical review letters, 2010, 105(15): 150401). However, there are still many problems in the application of compressed sensing in quantum state reconstruction: for example, how to select a sparse basis suitable for quantum states, construct an observation matrix that satisfies the isometry criterion, and design an optimized reconstruction algorithm for high-dimensional quantum states. These problems make compressed sensing methods still face the challenges of high computational complexity and high resource consumption when dealing with high-dimensional complex quantum states.

[0004] In recent years, machine learning, especially deep learning methods, have shown great potential in quantum state reconstruction. Neural network models such as restricted Boltzmann machines (RBMs) and generative adversarial networks (GANs) are widely used in the representation and reconstruction of quantum states. These models achieve efficient state reconstruction by learning the probability distribution of quantum states, especially when dealing with pure states and low-rank mixed states, which significantly improves the reconstruction accuracy and efficiency.

[0005] Although these machine learning methods have made significant progress in quantum state reconstruction, they still face problems such as high consumption of computing resources, high training difficulty, and sensitivity to noise when dealing with high-dimensional complex quantum states. First, when generative models such as restricted Boltzmann machines are effectively sampled in high-dimensional quantum systems, the fully connected structure leads to a large number of model parameters and low sampling efficiency, which affects the reconstruction speed and accuracy. Secondly, classical neural networks consume huge computing resources when dealing with high-dimensional quantum states, especially in high-dimensional and complex mixed states, and the demand for computing power in the training and inference processes is further increased. Finally, these methods are highly sensitive to noise and decoherence effects in quantum systems, which seriously affects the reliability and robustness of the reconstruction results in actual quantum computing environments.

[0006] In classical computing, orthogonal polynomials are widely used in the field of data reconstruction due to their good mathematical properties and dimensionality reduction characteristics. Orthogonal polynomials such as Chebyshev polynomials, Legendre polynomials and Hermite polynomials perform well in signal processing, data fitting and dimensionality reduction. Orthogonal polynomials achieve efficient dimensionality reduction and compression of data by projecting high-dimensional data onto a low-dimensional orthogonal basis, providing an important theoretical basis for quantum state reconstruction.

[0007] In summary, the current quantum state reconstruction technology still has significant technical bottlenecks in the processing of high-dimensional complex quantum states. The traditional quantum state tomography (QST) method has high computational complexity, and the compressed sensing method faces problems such as high resource consumption in high-dimensional applications. Although the machine learning method has improved the reconstruction efficiency and accuracy to a certain extent, its application in high-rank mixed states and noisy environments still needs further optimization. Therefore, the efficient quantum state reconstruction method combining orthogonal polynomial fitting and quantum neural network has become an important research direction to solve the current bottleneck of quantum state reconstruction technology. Summary of the invention

[0008] In order to solve the above technical problems, the present invention provides a quantum state reconstruction method, device, medium and product for flow field evolution prediction.

[0009] In order to solve the above technical problems, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a quantum state reconstruction method for flow field evolution prediction, wherein the training process of the quantum neural network adopted comprises: Design a quantum circuit with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching the flow field characteristics by adjusting the parameters; After encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, the target flow field quantum state is input into the quantum circuit to generate k orthogonal basis quantum states; k is the number of basis functions of the orthogonal polynomial, and each orthogonal basis quantum state corresponds to a mode of the flow field; By using the least squares fitting method, a set of coefficients for projecting the target flow field quantum state into the orthogonal ground state space is calculated; the coefficients represent the weights of each mode in the flow field; Using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and inputting the reconstructed flow field quantum state into a quantum flow field prediction model to output the flow field distribution at the next time step; Based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, the parameters of the quantum circuit are adjusted until the flow field evolution prediction accuracy is met.

[0010] In one embodiment, the fluid mechanics data set includes a square cavity flow data set, a circular tube flow data set, a dam flow data set and a cylinder flow data set; a quantum neural network is trained for each data set; the square cavity flow data, the circular tube flow data, the dam flow data and the cylinder flow data are respectively input into the corresponding trained quantum neural networks to obtain the flow field distribution of the square cavity flow data, the circular tube flow data, the dam flow data and the cylinder flow data at the next time step.

[0011] In one embodiment, the design includes a quantum circuit with adjustable parameters, which can generate a quantum state corresponding to an orthogonal polynomial basis function matching the flow field characteristics by adjusting the parameters, specifically including: The adjustable parameters in the quantum circuit include a rotation gate; the orthogonal polynomial adopts a Chebyshev polynomial; the rotation gate is used to control the phase and weight of the Chebyshev polynomial basis function.

[0012] In one embodiment, the encoding of the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state is input into the quantum circuit to generate k orthogonal basis quantum states, specifically including: When the i-th target flow field quantum state is input into the quantum circuit, the quantum circuit will map the i-th target flow field quantum state into a quantum state corresponding to the i-th basis function of the Chebyshev polynomial, and obtain the i-th orthogonal basis quantum state; the value of k is dynamically adjusted according to the complexity of the spatiotemporal evolution of the flow field.

[0013] In one embodiment, the use of a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state specifically includes: Reconstructing the quantum state of the flow field for: ; in, For the coefficients, For the orthogonal basis quantum states.

[0014] In one embodiment, adjusting the parameters of the quantum circuit based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state specifically includes: The fidelity loss is: ; in, Represents the reconstructed flow field quantum state and the The fidelity between the quantum states of the target flow field; Represents the reconstructed flow field quantum state and the The inner product between the target flow field quantum states; the smaller the value of fidelity loss, the better the reconstruction effect; Based on the gradient information of fidelity loss, the gradient descent method is used to adjust the rotation gate in the adjustable parameter of the quantum circuit. Angle , to minimize fidelity loss.

[0015] In a second aspect, the present invention provides a quantum state reconstruction device for flow field evolution prediction, which is used to train a quantum neural network, comprising: Quantum circuit module: Design quantum circuits with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching flow field characteristics by adjusting parameters; Orthogonal basis quantum state preparation module: after encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, it is input into the quantum circuit to generate k orthogonal basis quantum states; k is the number of basis functions of the orthogonal polynomial, and each orthogonal basis quantum state corresponds to a mode of the flow field; Orthogonal polynomial fitting module: a set of coefficients for projecting the target flow field quantum state into the orthogonal ground state space is calculated by the least squares fitting method; the coefficients represent the weights of each mode in the flow field; Quantum state reconstruction module: using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and inputting the reconstructed flow field quantum state into a quantum flow field prediction model to output the flow field distribution at the next time step; Optimization module: Based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, adjust the parameters of the quantum circuit until the flow field evolution prediction accuracy is met.

[0016] In one embodiment, the quantum circuit module specifically includes: the adjustable parameters in the quantum circuit include a rotation gate; the orthogonal polynomial adopts a Chebyshev polynomial; and the rotation gate is used to control the phase and weight of the Chebyshev polynomial basis function.

[0017] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method of any one of the embodiments of the first aspect.

[0018] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, the steps of the method of any one of the embodiments of the first aspect are implemented.

[0019] Compared with the prior art, the beneficial technical effects of the present invention are: The present invention achieves higher accuracy and fidelity in high-dimensional and complex quantum state reconstruction by deeply integrating the dimensionality reduction characteristics of orthogonal polynomials with the adaptive learning ability of quantum neural networks. In addition, the versatility and scalability of the present invention make it suitable for interdisciplinary fields, including computational fluid dynamics, quantum chemistry, materials science, and medical data analysis, ultimately forming an efficient, accurate, and scalable quantum state reconstruction algorithm framework. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flow chart of a method in an embodiment of the present invention; Figure 2 Schematic diagram of the framework of a quantum neural network in an embodiment of the present invention; Figure 3 It is a schematic diagram of the implementation of discrete cosine transform (DCT) in a quantum circuit in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0022] The present invention aims to provide a quantum state reconstruction method of a quantum neural network based on orthogonal polynomial fitting. By introducing the mathematical advantages of orthogonal polynomials, the structure and training process of the quantum neural network (QNN) are optimized, the resource bottleneck problem in quantum state preparation and measurement is overcome, and efficient and accurate quantum state reconstruction is achieved.

[0023] like Figure 1 As shown, the present invention provides a quantum state reconstruction method for flow field evolution prediction, and the training process of the adopted quantum neural network includes the following steps: S1: Design a quantum circuit with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching the flow field characteristics by adjusting the parameters; S2: After encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, the target flow field quantum state is input into the quantum circuit to generate k orthogonal basis quantum states; k is the number of basis functions of the orthogonal polynomial, and each orthogonal basis quantum state corresponds to a mode of the flow field; S3: Calculate a set of coefficients for projecting the target flow field quantum state into the orthogonal ground state space by the least squares fitting method; the coefficients represent the weights of each mode in the flow field; S4: using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and inputting the reconstructed flow field quantum state into a quantum flow field prediction model to output the flow field distribution at the next time step; S5: Based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, adjust the parameters of the quantum circuit until the flow field evolution prediction accuracy is met.

[0024] In one embodiment, the fluid mechanics data set includes a square cavity flow data set, a circular tube flow data set, a dam flow data set and a cylinder flow data set; a quantum neural network is trained for each data set; the square cavity flow data, the circular tube flow data, the dam flow data and the cylinder flow data are respectively input into the corresponding trained quantum neural networks to obtain the flow field distribution of the square cavity flow data, the circular tube flow data, the dam flow data and the cylinder flow data at the next time step.

[0025] In one embodiment, the design in step S1 includes a quantum circuit with adjustable parameters, which can generate a quantum state corresponding to an orthogonal polynomial basis function matching the flow field characteristics by adjusting the parameters, specifically including: The adjustable parameters in the quantum circuit include a rotation gate; the orthogonal polynomial adopts a Chebyshev polynomial; the rotation gate is used to control the phase and weight of the Chebyshev polynomial basis function.

[0026] Specifically, the invention is designed to include a revolving door with adjustable parameters. The quantum circuit is shown in the following Figure 3 As shown, the paper [ / ISPA 2001. Proceedings of the 2nd International Symposium on Imageand Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat. IEEE, 2001: 464-468.] on the design of quantum circuits for discrete cosine transforms is referenced here, in which the adjustable parameter rotation gate The location in the unit , which represents the circuit form of quantum discrete Fourier transform. Figure 3 middle and Respectively represent the parameters The specific form of quantum gate, its matrix form is and ,in , , Represents the imaginary unit. represent The conjugate form of , according to the line, The values ​​of are 1, 2, ..., . The role is , represents the hadamard gate, The matrix form is , The matrix form is , The matrix form is .

[0027] The specific design idea of ​​the present invention is that the formulas of discrete cosine transform and discrete Chebyshev basis transform are extremely similar, so only by conducting subsequent experiments on the basis of this quantum circuit, the quantum discrete Chebyshev basis can be constructed using the quantum circuit. The remarkable feature of this circuit is that when a specific initial ground state is input (like ), the quantum circuit will map it into the Chebyshev polynomial The quantum states corresponding to the basis functions are obtained, thereby realizing the quantum representation of the orthogonal polynomial basis.

[0028] In one embodiment, after encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state in step S2, the target flow field quantum state is input into the quantum circuit to generate k orthogonal basis quantum states, which specifically includes: When the i-th target flow field quantum state is input into the quantum circuit, the quantum circuit will map the i-th target flow field quantum state into a quantum state corresponding to the i-th basis function of the Chebyshev polynomial, and obtain the i-th orthogonal basis quantum state; the value of k is dynamically adjusted according to the complexity of the spatiotemporal evolution of the flow field.

[0029] Using a simple H gate and the initial ground state, the target flow field quantum state can be constructed in sequence , , applying the quantum circuit to the above states in turn, we can get The corresponding orthogonal basis quantum states , .

[0030] The present invention uses the idea of ​​orthogonal polynomials (such as Chebyshev polynomials) to reduce the dimension and fit the target flow field quantum state. Specifically, the input of the quantum least squares method is the target flow field quantum state , the result is a set of fitting coefficients , That is, the reconstruction order of the selected orthogonal basis fitting, that is, several orthogonal bases are selected for reconstruction.

[0031] In one embodiment, the use of a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state specifically includes: Reconstructing the quantum state of the flow field for: ; in, is the jth coefficient, is the jth orthogonal basis quantum state.

[0032] Specifically, the present invention adopts a linear combination unit (LCU) and uses the calculated coefficients , for the orthogonal basis quantum state , Perform linear combination to generate the reconstructed flow field quantum state.

[0033] In one embodiment, adjusting the parameters of the quantum circuit based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state specifically includes: The fidelity loss is: ; in, Represents the reconstructed flow field quantum state and the The fidelity between the quantum states of the target flow field; Represents the reconstructed flow field quantum state and the The inner product between the target flow field quantum states; the smaller the value of fidelity loss, the better the reconstruction effect.

[0034] Use the gradient descent method to adjust the rotation gate in the adjustable parameter of the quantum circuit according to the gradient information of the fidelity loss Angle , to minimize fidelity loss.

[0035] Specifically, the present invention uses fidelity as a loss function to quantify the similarity between the reconstructed flow field quantum state and the target flow field quantum state. The smaller the value of the fidelity loss, the better the reconstruction effect. As a measurement indicator, fidelity can accurately reflect the similarity between quantum states and ensure the effectiveness of the reconstruction process.

[0036] Parameter optimization: Use gradient descent or other optimization algorithms to adjust the adjustable parameter revolving gate in the quantum circuit according to the gradient information of the loss function. Angle , in order to minimize the loss function and improve the reconstruction accuracy. The optimization process needs to consider the differentiability of quantum circuits to ensure the continuity and stability of the parameter update process.

[0037] Iterative training: Through multiple iterative training, the quantum circuit parameters are continuously optimized so that the reconstructed quantum state gradually approaches the target flow field quantum state, achieving a high-fidelity and high-accuracy reconstruction effect. Each iteration needs to evaluate the fidelity of the current reconstructed flow field quantum state, and adjust the parameters according to the optimization results to ensure the gradual convergence of the training process.

[0038] In one embodiment, the logical framework of the present invention is as follows Figure 2 The overall process from left to right includes the following parts: The left side of the image is the input target flow field quantum state set , Refers to the number of quantum states involved in training or testing, and can be any value. These are the original quantum state data that need to be reconstructed. The target flow field quantum state is sent to a rotating gate with adjustable parameters. In the quantum circuit of other quantum gates (such as CNOT gate), after parameterized quantum circuit processing, a set of orthogonal basis quantum states can be obtained , The value of will depend on the specific situation. The larger the value, the higher the reconstruction accuracy, but at the expense of reconstruction complexity. will be much smaller than any target flow field quantum state These orthogonal basis quantum states correspond to basis functions defined by specific orthogonal polynomials (such as Chebyshev polynomials), Figure 2 The distribution of these basis functions is shown in different curve shapes. Then, the target flow field quantum state is obtained by the least squares fitting method. A set of coefficients projected onto the orthogonal ground state space After obtaining the coefficients, these orthogonal ground states are superimposed according to the corresponding coefficients through the Linear Combination of Unitaries (LCU) to reconstruct the approximate quantum state. On the right, the fidelity loss is calculated by , to measure the similarity between the reconstructed flow field quantum state and the target flow field quantum state. Then, according to the calculated loss value, the information is fed back to the adjustable parameters of the quantum circuit (revolving gate From the perspective of the above, by continuously adjusting the line parameters through iterative optimization (such as gradient descent method), the reconstructed flow field quantum state can gradually approach the target flow field quantum state, thereby improving the accuracy of quantum state reconstruction.

[0039] The following is a detailed introduction to the application of quantum neural network (QNN) based on orthogonal polynomial fitting in flow field prediction: Dataset introduction: The CFDBench dataset is an important resource in the field of classical computational fluid dynamics (CFD). It contains data on four typical flow problems: square cavity flow, circular pipe flow, dam flow, and flow around a cylinder. In each flow field, different data sets are grouped according to different initial conditions. The dimensions of each data file are , where 64 is the dimension of the data in each dimension, and t is the time slice. The data at the previous moment is needed to predict the data at the next moment.

[0040] First, extract the two-dimensional data matrix of each time point of the data set and normalize it to facilitate the formation of quantum states. Each quantum state of each dimension needs to be encoded with 6 quantum bits, requiring a total of 12 quantum bits. Then randomly shuffle the data and divide it into 80% training set and 20% test set. Then train the training data with the quantum neural network proposed in the present invention to train a quantum neural network that can reconstruct various data. During the test, the test data is reconstructed using the quantum neural network, and the reconstructed quantum state is input into the flow field prediction model based on the quantum algorithm to test the results.

[0041] The experimental results of preliminary numerical experiments show that the orthogonal basis obtained by training the quantum neural network (QNN) is significantly better than the classical orthogonal basis in the fidelity of the reconstructed quantum state. The fidelity of the reconstructed quantum state and the original quantum state is significantly improved, which verifies the effectiveness and advantages of the quantum neural network (QNN) in quantum state reconstruction.

[0042] It should be understood that, although the steps in the flowcharts of the accompanying drawings of the specification are displayed in sequence as indicated by the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts of the accompanying drawings of the specification may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0043] Based on the description of the above method embodiment, the present invention also provides a device. The device may be a system (including a distributed system), software (application), module, component, server, client, etc. using the method described in the embodiment of this specification and combined with the necessary implementation hardware. Based on the same innovative concept, the device in one or more embodiments provided by the embodiment of the present invention is as described in the following embodiments. Since the implementation scheme of the device to solve the problem is similar to the method, the implementation of the specific device in the embodiment of this specification can refer to the implementation of the aforementioned method, and the repetitions will not be repeated. As used below, the term "module" or "module" is a combination of software and / or hardware that can implement a predetermined function. Although the device described in the following embodiments is preferably implemented in software, the implementation of hardware, or a combination of software and hardware, is also possible and conceived.

[0044] In one embodiment, a quantum state reconstruction device for flow field evolution prediction is used to train a quantum neural network, comprising: Quantum circuit module: Design quantum circuits with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching flow field characteristics by adjusting parameters; Orthogonal basis quantum state preparation module: after encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, it is input into the quantum circuit to generate k orthogonal basis quantum states; k is the number of basis functions of the orthogonal polynomial, and each orthogonal basis quantum state corresponds to a mode of the flow field; Orthogonal polynomial fitting module: a set of coefficients for projecting the target flow field quantum state into the orthogonal ground state space is calculated by the least squares fitting method; the coefficients represent the weights of each mode in the flow field; Quantum state reconstruction module: using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and inputting the reconstructed flow field quantum state into a quantum flow field prediction model to output the flow field distribution at the next time step; Optimization module: Based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, adjust the parameters of the quantum circuit until the flow field evolution prediction accuracy is met.

[0045] In one embodiment, the quantum circuit module specifically includes: the adjustable parameters in the quantum circuit include a rotation gate; the orthogonal polynomial adopts a Chebyshev polynomial; and the rotation gate is used to control the phase and weight of the Chebyshev polynomial basis function.

[0046] In an exemplary embodiment, the present invention also provides a computer-readable storage medium including instructions, such as a memory including instructions, and the above instructions can be executed by a processor to perform the above method. The storage medium can be a computer-readable storage medium, for example, the computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0047] In an exemplary embodiment, the present invention further provides a computer program product, comprising a computer program, wherein the computer program implements the steps of the above method when executed by a processor.

[0048] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

[0049] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A quantum state reconstruction method for flow field evolution prediction, characterized in that: The training process of the adopted quantum neural network includes: Design a quantum circuit with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching the flow field characteristics by adjusting the parameters; After encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, the target flow field quantum state is input into the quantum circuit to generate k orthogonal basis quantum states; k is the number of basis functions of the orthogonal polynomial, and each orthogonal basis quantum state corresponds to a mode of the flow field; By using the least squares fitting method, a set of coefficients for projecting the target flow field quantum state into the orthogonal ground state space is calculated; the coefficients represent the weights of each mode in the flow field; Using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and inputting the reconstructed flow field quantum state into a quantum flow field prediction model to output the flow field distribution at the next time step; Based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, the parameters of the quantum circuit are adjusted until the flow field evolution prediction accuracy is met.

2. The quantum state reconstruction method for flow field evolution prediction according to claim 1, characterized in that: The fluid mechanics data set includes a square cavity flow data set, a circular tube flow data set, a dam flow data set and a cylinder flow data set; a quantum neural network is trained for each data set; the square cavity flow data, the circular tube flow data, the dam flow data and the cylinder flow data are respectively input into the corresponding trained quantum neural networks to obtain the flow field distribution of the square cavity flow data, the circular tube flow data, the dam flow data and the cylinder flow data in the next time step.

3. The quantum state reconstruction method for flow field evolution prediction according to claim 1, characterized in that: The design includes a quantum circuit with adjustable parameters, which can generate a quantum state corresponding to an orthogonal polynomial basis function matching the flow field characteristics by adjusting the parameters, specifically including: The adjustable parameters in the quantum circuit include a rotation gate; the orthogonal polynomial adopts a Chebyshev polynomial; the rotation gate is used to control the phase and weight of the Chebyshev polynomial basis function.

4. The quantum state reconstruction method for flow field evolution prediction according to claim 3 is characterized in that: After encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, the target flow field quantum state is input into the quantum circuit to generate k orthogonal basis quantum states, which specifically includes: When the i-th target flow field quantum state is input into the quantum circuit, the quantum circuit will map the i-th target flow field quantum state into a quantum state corresponding to the i-th basis function of the Chebyshev polynomial, and obtain the i-th orthogonal basis quantum state; the value of k is dynamically adjusted according to the complexity of the spatiotemporal evolution of the flow field.

5. The quantum state reconstruction method for flow field evolution prediction according to claim 1, characterized in that: The method of using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state specifically includes: Reconstructing the quantum state of the flow field for: ； in, For the coefficients, For the orthogonal basis quantum states.

6. The quantum state reconstruction method for flow field evolution prediction according to claim 1, characterized in that: The adjusting of the parameters of the quantum circuit based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state specifically includes: The fidelity loss is: ； in, Represents the reconstructed flow field quantum state and the The fidelity between the quantum states of the target flow field; Represents the reconstructed flow field quantum state and the The inner product between the target flow field quantum states; the smaller the value of fidelity loss, the better the reconstruction effect; Based on the gradient information of fidelity loss, the gradient descent method is used to adjust the rotation gate in the adjustable parameter of the quantum circuit. Angle , to minimize fidelity loss.

7. A quantum state reconstruction device for flow field evolution prediction, used for training quantum neural networks, characterized in that: include: quantum Circuit module: Design quantum circuits with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching flow field characteristics by adjusting the parameters; Orthogonal basis quantum state preparation module: after encoding the two-dimensional flow field matrix in the fluid mechanics data set into the target flow field quantum state, it is input into the quantum circuit to generate k orthogonal basis quantum states; k is the number of basis functions of the orthogonal polynomial, and each orthogonal basis quantum state corresponds to a mode of the flow field; Orthogonal polynomial fitting module: calculates a set of coefficients that project the target flow field quantum state into the orthogonal ground state space through the least squares fitting method; The coefficients represent the weights of each mode in the flow field; Quantum state reconstruction module: using a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and inputting the reconstructed flow field quantum state into a quantum flow field prediction model to output the flow field distribution at the next time step; Optimization module: Based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, adjust the parameters of the quantum circuit until the flow field evolution prediction accuracy is met.

8. The quantum state reconstruction device for flow field evolution prediction according to claim 7, characterized in that: The quantum circuit module specifically includes: the adjustable parameters in the quantum circuit include a revolving gate; the orthogonal polynomial adopts a Chebyshev polynomial; and the revolving gate is used to control the phase and weight of the Chebyshev polynomial basis function.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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