Quantum State Reconstruction Method, Device, Medium and Product for Flow Field Evolution Prediction

Abstract

The present invention relates to the field of quantum computing technology, and discloses a quantum state reconstruction method, device, medium and product for predicting the evolution of a flow field. The training process of the quantum neural network adopted by the method includes: designing a quantum circuit containing adjustable parameters; after encoding the two-dimensional flow field matrix in the hydrodynamic data set into a target flow field quantum state, inputting the quantum state into the quantum circuit to generate an orthogonal basis quantum state; by using the least squares fitting method, calculating a set of coefficients for projecting the target flow field quantum state into the orthogonal basis state space; using a linear combination unit to superpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and 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. By deeply integrating the dimensionality reduction characteristics of orthogonal polynomials with the adaptive learning ability of quantum neural networks, the present invention achieves higher accuracy and fidelity in high-dimensional and complex quantum state reconstruction.

Description

Technical Field

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

[0002] Quantum State Reconstruction is a core task in quantum information science, aiming to accurately restore the quantum state of a system through limited measurement data, and is widely applied in multiple fields such as quantum computing, quantum communication, quantum physical experiments, and quantum chemical simulations. However, quantum state reconstruction faces significant challenges in high-dimensional quantum systems. Traditional Quantum State Tomography (QST) methods rely on comprehensive quantum measurements and need to obtain all the information of the system through multiple independent measurements. As the number of qubits increases, the number of measurements and computational complexity required by Quantum State Tomography (QST) increase exponentially, limiting its application in high-dimensional systems.

[0003] To address the above challenges, Compressed Sensing technology has been introduced into the field of quantum state reconstruction (see New Journal of Physics, 2012, 14(9): 095022). Compressed Sensing utilizes the sparsity of quantum states and achieves efficient reconstruction through a small number of random measurements, significantly reducing the required number of measurements and computational resources (see Physicalreview 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 the quantum state, construct an observation matrix that satisfies the isometry criterion, and design an optimized reconstruction algorithm for high-dimensional quantum states. These problems make the Compressed Sensing method still face challenges of high computational complexity and large 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 (RBM) and Generative Adversarial Networks (GAN) have been widely applied to the representation and reconstruction of quantum states. These models achieve efficient state reconstruction by learning the probability distribution of quantum states, and significantly improve the reconstruction accuracy and efficiency, especially when dealing with pure states and low-rank mixed states.

[0005] Although these machine learning methods have made significant progress in quantum state reconstruction, they still face problems such as high computational resource consumption, high training difficulty, and sensitivity to noise when dealing with high-dimensional complex quantum states. First, when generative models such as restricted Boltzmann machines perform effective sampling in high-dimensional quantum systems, due to the fully connected structure, the number of model parameters is huge, and the sampling efficiency is low, which affects the reconstruction speed and accuracy. Second, classical neural networks consume a huge amount of computational resources when dealing with high-dimensional quantum states. Especially in the case of high dimensions and complex mixed states, the requirements for computational power in the training and inference processes are further increased. Finally, these methods are highly sensitive to noise and decoherence effects in quantum systems, resulting in serious impacts on the reliability and robustness of the reconstruction results in the actual quantum computing environment.

[0006] In classical computing, orthogonal polynomials have been 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. By projecting high-dimensional data onto low-dimensional orthogonal bases, orthogonal polynomials achieve efficient dimensionality reduction and compression of data, providing an important theoretical basis for quantum state reconstruction.

[0007] In summary, there are still significant technical bottlenecks in the current quantum state reconstruction technology for dealing with high-dimensional complex quantum states. Traditional quantum state tomography (QST) methods have high computational complexity, and compressive sensing methods face problems such as high resource consumption in high-dimensional applications. Although machine learning methods have improved the reconstruction efficiency and accuracy to a certain extent, their applications in high-rank mixed states and noisy environments still need to be further optimized. Therefore, an efficient quantum state reconstruction method combining orthogonal polynomial fitting and quantum neural networks has become an important research direction to solve the current technical bottlenecks of quantum state reconstruction technology. Summary of the Invention

[0008] 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] To solve the above technical problems, the present invention adopts the following technical solutions:

[0010] In the first aspect, the present invention provides a quantum state reconstruction method for flow field evolution prediction. The training process of the adopted quantum neural network includes:

[0011] Design a quantum circuit with adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions that match the flow field characteristics by adjusting the parameters;

[0012] After encoding the two-dimensional flow field matrix in the hydrodynamic dataset into the target flow field quantum state, input it 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.

[0013] By using the least squares fitting method, calculate a set of coefficients for projecting the target flow field quantum state onto the orthogonal basis state space; these coefficients represent the weights of each mode in the flow field.

[0014] Use a linear combination unit to superpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and input the reconstructed flow field quantum state into the quantum flow field prediction model to output the flow field distribution at the next time step.

[0015] 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 satisfied.

[0016] In one embodiment, the hydrodynamic dataset includes a square cavity flow dataset, a circular pipe flow dataset, a dam flow dataset, and a circular cylinder wake dataset; train a quantum neural network for each dataset; input the square cavity flow data, circular pipe flow data, dam flow data, and circular cylinder wake data into the corresponding trained quantum neural network respectively to obtain the flow field distributions at the next time step for the square cavity flow data, circular pipe flow data, dam flow data, and circular cylinder wake data.

[0017] In one embodiment, the designed quantum circuit with adjustable parameters can generate quantum states corresponding to orthogonal polynomial basis functions that match the flow field characteristics by adjusting the parameters, specifically including:

[0018] The adjustable parameters in the quantum circuit include rotation gates; the orthogonal polynomial uses Chebyshev polynomials; the rotation gates are used to control the phase and weight of the Chebyshev polynomial basis functions.

[0019] In one embodiment, after encoding the two-dimensional flow field matrix in the hydrodynamic dataset into the target flow field quantum state and inputting it into the quantum circuit to generate k orthogonal basis quantum states, it specifically includes:

[0020] When inputting the i-th target flow field quantum state into the quantum circuit, the quantum circuit maps the i-th target flow field quantum state to a quantum state corresponding to the i-th basis function of the Chebyshev polynomial to obtain the i-th orthogonal basis quantum state; the value of k is dynamically adjusted according to the complexity of the flow field spatio-temporal evolution.

[0021] In one embodiment, the use of a linear combination unit to superpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state specifically includes:

[0022] Reconstructed flow field quantum state is:

[0023] ;

[0024] wherein, is the th coefficient, is the th orthogonal basis quantum state.

[0025] 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:

[0026] The fidelity loss is:

[0027] ;

[0028] wherein, represents the fidelity between the reconstructed flow field quantum state and the th target flow field quantum state; represents the inner product between the reconstructed flow field quantum state and the th target flow field quantum state; the smaller the value of the fidelity loss, the better the reconstruction effect;

[0029] According to the gradient information of the fidelity loss, use the gradient descent method to adjust the angle of the rotation gate in the adjustable parameters of the quantum circuit to minimize the fidelity loss.

[0030] 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, including:

[0031] Quantum circuit module: Design a quantum circuit containing adjustable parameters, which can generate quantum states corresponding to orthogonal polynomial basis functions matching the flow field characteristics by adjusting the parameters;

[0032] Orthogonal basis quantum state preparation module: After encoding the two-dimensional flow field matrix in the hydrodynamic data set into the target flow field quantum state, input it 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;

[0033] Orthogonal polynomial fitting module: Calculate a set of coefficients for projecting the target flow field quantum state onto the orthogonal basis state space by the least squares fitting method; the coefficients represent the weights of each mode in the flow field;

[0034] Quantum state reconstruction module: The orthogonal basis quantum states are superimposed according to the coefficients by using a linear combination unit to generate a reconstructed flow field quantum state, and the reconstructed flow field quantum state is input into a quantum flow field prediction model to output the flow field distribution at the next time step;

[0035] 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 prediction accuracy of the flow field evolution is satisfied.

[0036] In one embodiment, the quantum circuit module specifically includes: The adjustable parameters in the quantum circuit include rotation gates; The orthogonal polynomial uses Chebyshev polynomials; The rotation gates are used to control the phase and weight of the Chebyshev polynomial basis functions.

[0037] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method in any one of the embodiments of the first aspect are implemented.

[0038] A computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the method in any one of the embodiments of the first aspect are implemented.

[0039] Compared with the prior art, the beneficial technical effects of the present invention are:

[0040] The present invention deeply integrates the dimensionality reduction characteristics of orthogonal polynomials with the adaptive learning ability of quantum neural networks, achieving higher accuracy and fidelity in high-dimensional and complex quantum state reconstruction. In addition, the generality and scalability of the present invention make it applicable to interdisciplinary fields, including computational fluid dynamics, quantum chemistry, materials science, and medical data analysis, etc., and finally form an efficient, accurate, and scalable quantum state reconstruction algorithm framework. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flowchart of the method in the embodiment of the present invention;

[0042] Figure 2 It is a schematic diagram of the framework of the quantum neural network in the embodiment of the present invention;

[0043] Figure 3 It is a schematic diagram of the implementation manner of the discrete cosine transform (DCT) in the quantum circuit in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] A preferred embodiment of the present invention will be described in detail below with reference to the accompanying drawings.

[0045] The present invention aims to provide a quantum state reconstruction method for 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 to overcome the resource bottleneck problems in quantum state preparation and measurement, and to achieve efficient and accurate quantum state reconstruction.

[0046] As Figure 1 shown, the present invention provides a quantum state reconstruction method for predicting the evolution of a flow field. The training process of the adopted quantum neural network includes the following steps:

[0047] 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;

[0048] S2: After encoding the two-dimensional flow field matrix in the fluid mechanics dataset into the target flow field quantum state, input it 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;

[0049] S3: By using the least squares fitting method, calculate a set of coefficients for projecting the target flow field quantum state onto the orthogonal basis state space; the coefficients represent the weights of each mode in the flow field;

[0050] S4: Use a linear combination unit to superpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and input the reconstructed flow field quantum state into the quantum flow field prediction model to output the flow field distribution at the next time step;

[0051] 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 accuracy of flow field evolution prediction is satisfied.

[0052] In one embodiment, the fluid mechanics dataset includes a square cavity flow dataset, a circular pipe flow dataset, a dam flow dataset, and a circular cylinder wake flow dataset; a quantum neural network is trained for each dataset; the square cavity flow data, circular pipe flow data, dam flow data, and circular cylinder wake flow data are respectively input into the corresponding trained quantum neural network to obtain the flow field distributions at the next time step of the square cavity flow data, circular pipe flow data, dam flow data, and circular cylinder wake flow data.

[0053] In one embodiment, the design of the quantum circuit with adjustable parameters in step S1, which can generate quantum states corresponding to orthogonal polynomial basis functions matching the flow field characteristics by adjusting the parameters, specifically includes:

[0054] The adjustable parameters in the quantum circuit include rotation gates; the orthogonal polynomial uses Chebyshev polynomials; the rotation gates are used to control the phase and weight of the Chebyshev polynomial basis functions.

[0055] Specifically, the quantum circuit designed by the present invention includes a rotatable gate with adjustable parameters as shown in the appendix Figure 3 . Here, reference is made to the quantum circuit design of the discrete cosine transform in the paper [ / ISPA 2001. Proceedings of the 2nd International Symposium on Imageand Signal Processing and Analysis. In conjunction with 23rd InternationalConference on Information Technology Interfaces (IEEE Cat. IEEE, 2001: 464-468.]. The position of the rotatable gate with adjustable parameters is in the unit , representing the circuit form of the quantum discrete Fourier transform Figure 3 In and respectively represent quantum gates in specific forms with parameters . Their matrix forms are and respectively, where , , represents the imaginary unit represents the conjugate form of . According to the circuit, the value of is 1, 2,..., The role of is . represents the hadamard gate. The matrix form of is The matrix form of is The matrix form of is

[0056] The specific design idea of the present invention is that the formulas of the discrete cosine transform and the discrete Chebyshev basis transform are extremely similar. Therefore, only by conducting subsequent experiments on the basis of this quantum circuit can a quantum discrete Chebyshev basis be constructed using the quantum circuit. The remarkable feature of this circuit is that when a specific initial basis state is input (such as ), the quantum circuit will map it to the quantum state corresponding to the th basis function of the Chebyshev polynomial, thereby realizing the quantum representation of the orthogonal polynomial basis ​

[0057] In one embodiment, after encoding the two-dimensional flow field matrix in the hydrodynamic data set into the target flow field quantum state in step S2 and inputting it into the quantum circuit, generating k orthogonal basis quantum states specifically includes:

[0058] When the i-th target flow field quantum state is input into the quantum circuit, the quantum circuit maps the i-th target flow field quantum state to a quantum state corresponding to the i-th basis function of the Chebyshev polynomial, obtaining the i-th orthogonal basis quantum state; the value of k is dynamically adjusted according to the complexity of the spatio-temporal evolution of the flow field.

[0059] Using simple H gates and the initial basis state, the target flow field quantum state can be constructed sequentially , , and by applying the quantum circuit to the above states sequentially, corresponding orthogonal basis quantum states can be obtained , .

[0060] 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 , and the result is a set of fitting coefficients , is the reconstruction order fitted by the selected orthogonal basis, that is, how many orthogonal bases are selected for reconstruction.

[0061] In one embodiment, using the linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate the reconstructed flow field quantum state specifically includes:

[0062] The reconstructed flow field quantum state is:

[0063] ;

[0064] where is the j-th coefficient, is the j-th orthogonal basis quantum state.

[0065] Specifically, the present invention uses a linear combination of unitaries (LCU), and uses the calculated coefficients to perform a linear combination on the orthogonal basis quantum states , to generate the reconstructed flow field quantum state.

[0066] In one embodiment, based on the fidelity loss between the reconstructed flow field quantum state and the target flow field quantum state, adjusting the parameters of the quantum circuit specifically includes:

[0067] The fidelity loss is:

[0068] ;

[0069] 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.

[0070] 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.

[0071] 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.

[0072] 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.

[0073] 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.

[0074] 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 greater the value, the higher the reconstruction accuracy, but at the cost of the complexity of reconstruction. will be much smaller than any target flow field quantum state The dimension of these orthogonal basis quantum states corresponds to the basis functions defined by specific orthogonal polynomials (such as Chebyshev polynomials). Figure 2 The distributions of these basis functions are schematically shown by different curve shapes in. Subsequently, a set of coefficients for projecting the target flow field quantum state onto the orthogonal basis state space are obtained by the least squares fitting method. After obtaining the coefficients, these orthogonal basis states are superimposed according to the corresponding coefficients through a Linear Combination of Unitaries (LCU), thereby reconstructing an approximate quantum state. On the right side, the similarity between the reconstructed flow field quantum state and the target flow field quantum state is measured by calculating the fidelity loss. Subsequently, according to the calculated loss value, the information is fed back to the adjustable parameters (the angles of the rotation gates ) of the quantum circuit. By continuously adjusting the circuit parameters through iterative optimization (such as the 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.

[0075] The following specifically introduces the application of a quantum neural network (QNN) based on orthogonal polynomial fitting in flow field prediction:

[0076] Dataset introduction: The CFDBench dataset is an important resource in the field of classical computational fluid dynamics (CFD). It contains data for four typical flow problems: cavity flow, pipe flow, dam flow, and flow around a circular cylinder. In each flow field, the data is grouped according to different initial conditions into different datasets. The dimension of each data file is , where 64 is the dimension of the data in each dimension, and t is the time slice. The data at the previous moment needs to be used to predict the data at the next moment.

[0077] First, the two-dimensional data matrices at each time point of the dataset are extracted and normalized to facilitate the formation of quantum states. Each dimension of the quantum state requires 6 qubits for encoding, for a total of 12 qubits. Then the data is randomly shuffled and divided into an 80% training set and a 20% test set. Then the training data is trained using the quantum neural network proposed in the present invention to train a quantum neural network that can reconstruct various data. During testing, the quantum neural network is used to reconstruct the test data, and the reconstructed quantum state is input into the flow field prediction model based on the quantum algorithm to obtain the test results.

[0078] The experimental results verified by preliminary numerical experiments show that the orthogonal basis obtained by training based on the quantum neural network (QNN) is significantly superior to the classical orthogonal basis in terms of the fidelity of the reconstructed quantum state. The fidelity between the reconstructed quantum state and the original quantum state has been significantly improved, verifying the effectiveness and advantages of the quantum neural network (QNN) in quantum state reconstruction.

[0079] It should be understood that although the steps in the flowchart of the accompanying drawings of the specification are shown in sequence according to the indication of the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowchart of the accompanying drawings of the specification may include multiple steps or multiple stages. These steps or stages are not necessarily executed at the same moment, but can be executed at different moments. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or steps or stages in other steps.

[0080] Based on the description of the above method embodiments, the present invention also provides a device. The device may be a system (including a distributed system), software (application), module, component, server, client, etc. that uses the method described in the embodiments of this specification and combines the necessary implementation hardware. Based on the same innovative concept, the devices in one or more embodiments provided by the embodiments of the present invention are as described in the following embodiments. Since the implementation solutions for the device to solve problems are similar to those of the method, the implementation of the specific device in the embodiments of this specification can refer to the implementation of the foregoing method, and the repeated parts will not be described again. As used hereinafter, the term "module" or "modular" is a combination of software and / or hardware that can implement a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, implementation in hardware, or a combination of software and hardware is also possible and contemplated.

[0081] In one of the embodiments, a quantum state reconstruction device for predicting the evolution of a flow field, used for training a quantum neural network, includes:

[0082] Quantum circuit module: Design a quantum circuit containing adjustable parameters, which can generate a quantum state corresponding to an orthogonal polynomial basis function matching the flow field characteristics by adjusting the parameters;

[0083] Orthogonal basis quantum state preparation module: After encoding the two-dimensional flow field matrix in the hydrodynamic data set into a target flow field quantum state, input it 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;

[0084] Orthogonal polynomial fitting module: By using the least squares fitting method, calculate a set of coefficients for projecting the target flow field quantum state onto the orthogonal basis state space; the coefficients represent the weights of each mode in the flow field.

[0085] Quantum state reconstruction module: Use a linear combination unit to superimpose the orthogonal basis quantum states according to the coefficients to generate a reconstructed flow field quantum state, and input the reconstructed flow field quantum state into the quantum flow field prediction model to output the flow field distribution at the next time step.

[0086] 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 prediction accuracy of the flow field evolution is satisfied.

[0087] In one embodiment, the quantum circuit module specifically includes: The adjustable parameters in the quantum circuit include rotation gates; the orthogonal polynomials use Chebyshev polynomials; the rotation gates are used to control the phase and weight of the Chebyshev polynomial basis functions.

[0088] 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 complete the above method. The storage medium can be a computer-readable storage medium. For example, the computer-readable storage medium can be ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage devices, etc.

[0089] In an exemplary embodiment, the present invention also provides a computer program product including a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0090] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention, and any reference signs in the claims should not be regarded as limiting the claims involved.

[0091] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only includes an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments 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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