Flow field evolution method and device based on quantum computing and vortex characterization

Abstract

The application provides a flow field evolution method and device based on quantum computing and vortex characterization, which comprises the following steps: defining a complex scalar field, constructing an Hermite matrix based on an initial velocity field, and converting a vortex filament positioning problem into a quantum ground state solving problem; solving the minimum eigenvalue of the matrix through a quantum algorithm, and outputting an initial vortex quantum state; constructing a Hamiltonian through discretization processing according to a fluid dynamics control equation; constructing a quantum circuit of the Hamiltonian, and driving the initial vortex quantum state to evolve into a target quantum state; measuring the evolved quantum state, obtaining discrete numerical values of the complex scalar field at the center points of grid cells, positioning zero contour points through discrete winding numbers and interpolation, and reconstructing the vortex filament structure of the evolved flow field. The application fully utilizes the parallel computing advantage of quantum computing in high-dimensional data processing, significantly improves the computing efficiency of flow field simulation, speeds up the data processing speed, and effectively relieves the high demand for storage resources.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing technology and relates to a flow field evolution method and device, particularly a flow field evolution method and device based on quantum computing and vortex characterization. Background Technology

[0002] Vortex filaments, which can be viewed as extremely fine vortex tubes, are an effective tool for studying the mechanisms of fluid motion and evolution. The vortex filament method offers high flexibility, providing a convenient and effective framework for capturing the multi-scale characteristics of turbulence by controlling the morphology, spatial distribution, and thickness of the vortex filaments. Simultaneously, vortex filaments form a coherent structure within turbulent flow that dominates nonlinear dynamics, and their motion is driven by their induced velocities, laying a theoretical foundation for studying vortex dynamics processes such as vortex extension, twisting, and reconnection. Considering the importance of vortex filaments, methods such as the Lagrange vortex particle method have achieved good results by using vortices as basic units to calculate flow field evolution.

[0003] However, in complex flow fields such as turbulence, the density of vortex filaments is very high, and the topology undergoes complex changes. Explicitly calculating vortex filament evolution faces multiple limitations, including the enormous storage burden of explicitly storing vortex filaments and the difficulty in accurately describing and simulating interactions such as vortex filament reconnection. Compared to directly storing the positions of vortex filaments, implicit representation methods use the zeros of complex scalar functions to represent vortex filaments, transforming the solution of the evolution of each vortex element into the solution of the evolution of a complex scalar field. This method significantly reduces storage requirements and the computational burden of vortex structure evolution, while also providing more flexible representation of vortex interactions and topological changes. However, when dealing with large-scale flow field calculations, the high computational cost and complexity still pose challenges, placing demands on the computational methods.

[0004] Quantum computing is a promising solution to this problem. Based on quantum mechanical processes such as superposition, entanglement, and interference, quantum computing offers exponential speedup and demonstrates the potential to surpass traditional methods when dealing with complex problems. Although current flow field evolution techniques, such as quantum linear system algorithms and variational quantum algorithms that utilize Hamiltonian simulations to solve the lattice Boltzmann equation and the Navier-Stokes equation, are available, most methods are limited by initial state preparation and quantum measurement, and struggle to fully address the complex nonlinear interactions in real turbulence. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a flow field evolution method and device based on quantum computing and vortex characterization.

[0006] The technical solution adopted in this invention is as follows:

[0007] A flow field evolution method based on quantum computing and vortex characterization includes the following steps:

[0008] S1. For the flow field to be predicted, a complex scalar field is defined, and a Hermite matrix is ​​constructed based on the initial velocity field, transforming the vortex filament localization problem into a quantum ground state solution problem;

[0009] S2. Solve for the minimum eigenvalue of the Hermitian matrix using a quantum algorithm and output the initial vortex quantum state;

[0010] S3. Based on the fluid dynamics control equations, a Hamiltonian for quantum evolution is constructed through spatial discretization.

[0011] S4. Construct a Hamiltonian quantum circuit to drive the initial vortex quantum state to evolve into the target quantum state;

[0012] S5. Measure the evolved quantum state to obtain the discrete values ​​of the complex scalar field at the center point of the grid cell. Based on the grid topology, locate the zero isopleths by the discrete winding number and interpolation, reconstruct the vortex wire structure after the flow field evolution, and obtain the flow field evolution result.

[0013] Furthermore, the definition of the complex scalar field, the construction of the Hermitian matrix based on the initial velocity field, and the transformation of the vortex filament localization problem into a quantum ground state solution problem specifically include:

[0014] Define a complex scalar field and use the zero contour lines of the complex scalar field to represent the positions of the vortex filaments; construct a normalized velocity field by setting the vortex strength constant, and establish a unit modulus functional optimization problem for the complex scalar field and the dimensionless velocity field.

[0015] The functional is discretized on an interlaced grid, wherein the complex scalar field is stored at the center of the grid cell and the dimensionless velocity field is stored at the center of the adjacent grid surface.

[0016] Constructing a Hermitian matrix transforms the discrete functional optimization problem into a minimum eigenvalue problem.

[0017] Furthermore, the quantum algorithm employs a quantum variational eigensolver (VQE), and the specific solution steps are as follows:

[0018] Construct a parametric quantum circuit, input an initial state, and obtain the target quantum state based on the parameter evolution;

[0019] The energy expectation value of the Hermitian matrix is ​​calculated based on the target quantum state using quantum measurement techniques.

[0020] The parameters of the parametric quantum circuit are iteratively optimized using a classical optimizer until the energy expectation value converges, and the target quantum state corresponding to the optimal parameters is output as the initial vortex quantum state.

[0021] Furthermore, the parametric quantum circuit is composed of multiple repeating basic modules connected in series, and each basic module includes a parameterized rotating gate layer that acts sequentially on each quantum bit.

[0022] Furthermore, the specific steps for calculating the expected energy value of the Hermitian matrix using quantum measurement technology are as follows:

[0023] The Hermitian matrix is ​​decomposed into a linear combination of Pauli operators. The Pauli operators are sorted in descending order according to the absolute value of their coefficients, and a predetermined proportion of Pauli operators are truncated. The expected energy value of the Hermitian matrix in the target quantum state output by the parametric quantum circuit is calculated based on the truncated Pauli operators.

[0024] Furthermore, the governing equations of the fluid dynamics are the Gross–Pitaevskii (GP) equations:

[0025]

[0026] in, For the complex standard quantity field, For time, For spatial divergence operators, It is the imaginary unit.

[0027] The spatial discretization process includes:

[0028] The Laplace and nonlinear terms of the governing equations are discretized using the second-order central difference method to obtain the discrete form:

[0029]

[0030] Where G is the discretized Hamiltonian.

[0031] Furthermore, step S4 specifically includes:

[0032] The Hamiltonian is decomposed into a linear combination of Pauli operators;

[0033] The time evolution operator is obtained from the decomposed Hamiltonian. The time evolution operator is approximately decomposed into a product of multi-step evolution operators using Trotter decomposition.

[0034] Based on the properties of each evolution operator, the decomposed evolution operators are mapped to the corresponding quantum gates to obtain the corresponding evolution quantum circuits;

[0035] The initial vortex quantum state is input into the evolving quantum circuit, and the evolved target state is output.

[0036] Furthermore, the method of locating zero isopleths based on the mesh topology through discrete winding number and interpolation specifically includes:

[0037] For a cell surface formed by the centers of four adjacent grid cells, the sum of the argument differences between the complex scaling values ​​of adjacent cells is calculated sequentially, and the number of windings is obtained after normalization.

[0038] For elements with a non-zero winding number, the local normalized coordinates of the vortex wire passing through the element surface are determined by solving the bilinear interpolation equation.

[0039] Connecting the locally normalized coordinates obtained from adjacent grid cells forms the vortex filament structure after the flow field evolution.

[0040] A computer device, the computer device comprising:

[0041] One or more processors;

[0042] Memory, used to store one or more programs;

[0043] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-described flow field evolution method based on quantum computing and vortex characterization.

[0044] A computer-readable storage medium storing computer instructions that, when executed by one or more processors, cause the one or more processors to perform the steps in the method described above.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] This invention reduces the difficulty of characterizing vortices in complex topologies by using complex scalar functions to represent them. Simultaneously, it transforms the velocity field encoding process into an eigenvalue problem, which can be solved using quantum algorithms to accelerate encoding and reduce storage pressure. When solving the eigenvalue problem, a truncation strategy is employed for measuring the energy expectation, reducing measurement costs. The evolution of the vortex filament is simulated using quantum circuits, fully utilizing the acceleration effect of quantum computing to significantly reduce computational resource consumption and accelerate flow field simulation. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method in an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram of the evolutionary quantum circuit obtained by Trotter decomposition in an embodiment of the present invention, showing the first 40 layers.

[0049] Figure 3 This is a diagram showing the evolution results at different time steps in an embodiment of the present invention. Detailed Implementation

[0050] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0051] like Figure 1 As shown, a flow field evolution method based on quantum computing and vortex characterization includes the following steps:

[0052] S1. For the flow field to be predicted, a complex scalar field is defined, and a Hermitian matrix is ​​constructed based on the initial velocity field, transforming the vortex filament localization problem into a quantum ground state solution problem.

[0053] S1.1 Defines the complex scalar field for the flow field to be predicted. The position of the vortex is represented by the zero contour lines of the complex scalar field;

[0054] For the input velocity field By setting the vortex strength constant Constructing a normalized velocity field :

[0055]

[0056] Establish a complex standard field With the unitized velocity field The unit modulus functional optimization problem:

[0057]

[0058] Where i is the imaginary unit.

[0059] S1.2 Discretizes the functional on an interlaced grid, where the complex scalar field Stored at the center of the grid cell, the unitized velocity field Stored at the centers of adjacent grid faces, the above problem can be discretized and written as:

[0060]

[0061] in represent The conjugate transpose of the matrix elements Defined as:

[0062] in, , All represent grid cells. For matrix row indices, For matrix column subscripts, , The distance between the center points of the two units. For unit With unit The speed on the grid surface between them The imaginary unit, It is with grid cells Number of adjacent units.

[0063] S1.3 Constructs the Hermitian matrix, transforming the discrete functional optimization problem into a minimum eigenvalue problem.

[0064] matrix It satisfies the properties of Hermitian matrices, therefore the discretized wavefunction can be... Treat as a quantum state At the same time, the matrix Treating it as a Hamiltonian, the problem can therefore be transformed into a ground state problem in quantum computing, i.e., minimizing... .

[0065] S2. Solve for the minimum eigenvalue of the Hermitian matrix using a quantum algorithm, and output the initial vortex quantum state. In this embodiment, the quantum algorithm uses a quantum variational eigenvalue solver, and the specific solution steps are as follows:

[0066] S2.1 Constructing a parametric quantum circuit ,in The parameterized quantum circuit is a set of circuit parameters that can be determined based on the initial input state. The target quantum state is obtained through evolution:

[0067]

[0068] The parametric quantum circuit is composed of multiple repeating basic modules connected in series, each basic module including an independently controlled parameterized rotating gate layer that acts sequentially on each qubit. Its gate operation definition is as follows:

[0069]

[0070] in, These are the parameters for a single gate.

[0071] To enhance the expressive power of the circuit, the basic modules are repeated. Second-rate.

[0072] S2.2 The expected energy value of the Hermitian matrix is ​​calculated using quantum measurement techniques based on the target quantum state output by the parametric quantum circuit.

[0073] Decompose the Hermitian matrix into a linear combination of Pauli operators:

[0074]

[0075] in, For the subscript of the Pauli operator, For Pauli operators, The corresponding subscripts after Hermitian matrix decomposition Pauli operators.

[0076] Pauli operator coefficients Sort by absolute value in descending order and determine a cutoff ratio. Keep the one with the largest absolute value. Some Pauli operators and coefficients were used, and those with smaller contributions were removed.

[0077] Calculate the approximate energy expectation of the Hermitian matrix in the target quantum state output by the parametric quantum circuit based on the truncated Pauli operator:

[0078]

[0079] in, This indicates the number of the Pauli operators and their coefficients that have been retained.

[0080] S2.3 uses a classical optimizer to iteratively optimize the parameters of the parametric quantum circuit based on the measured energy expectation until the optimal parameters are obtained. With the target quantum state The initial flow field is encoded, and the target quantum state corresponding to the optimal parameters is output as the initial vortex quantum state.

[0081] S3. Based on the fluid dynamics control equations, a Hamiltonian for quantum evolution is constructed through spatial discretization.

[0082] S3.1 Construct the Gross-Pitajewski (GP) equations to describe the evolution of the flow field:

[0083]

[0084] in, For the complex standard quantity field, For time, For spatial divergence operators, It is the imaginary unit.

[0085] S3.2 The governing equations are spatially discretized using the second-order central difference method to discretize the Laplace and nonlinear terms, resulting in the discrete form:

[0086]

[0087] Where G is the discretized Hamiltonian.

[0088] S4. Construct a Hamiltonian quantum circuit to drive the initial vortex quantum state to evolve into the target quantum state.

[0089] S4.1 decomposes the Hamiltonian into a linear combination of Pauli operators:

[0090]

[0091] in, For the subscript of the Pauli operator, For Pauli operators, The subscripts corresponding to the decomposition of the Hamiltonian Pauli operators.

[0092] S4.2 Obtain the time evolution operator based on the split Hamiltonian. The time evolution operator is analyzed using first-order Trotter decomposition. Perform approximate evolution:

[0093]

[0094] in, The set time interval for evolution, It is the imaginary unit.

[0095] S4.3 Based on the properties of each evolution operator, the decomposed evolution operators are mapped to the corresponding rotation gates or CNOT gates respectively, and finally the corresponding evolutionary quantum circuits are obtained;

[0096] S4.4 Input the initial vortex quantum state into the evolving quantum circuit and output the evolved target state.

[0097] S5. Measure the evolved quantum state to obtain the discrete values ​​of the complex scalar field at the center point of the grid cell. Based on the grid topology, locate the zero isovalue point by the discrete winding number and interpolation, and reconstruct the vortex wire structure after the flow field evolution.

[0098] S5.1 For a cell surface formed by the centers of four adjacent grid cells, the sum of the argument differences between the complex scaling values ​​of adjacent cells is calculated sequentially, and the winding number is obtained after normalization. :

[0099]

[0100] in, These are the numbers of the four grid cells.

[0101] S5.2 For element surfaces with non-zero winding numbers, solve the bilinear interpolation equation to determine the local normalized coordinates of the vortex wires passing through the element surface:

[0102]

[0103] in, Representing grid cells respectively The complex standard field.

[0104] S5.3 Connect the locally normalized coordinates obtained in adjacent units to form the vortex wire structure after the flow field evolution, and obtain the flow field evolution result.

[0105] In one specific embodiment of the present invention, a flow field induced by five two-dimensional point vortices is considered as a typical example, with the point vortex positions being... , , , , The point vortex intensity is ,exist The target velocity field is generated within the computational domain using the Biot-Savart law. and discretize it into Use the 2D mesh to extract the vortex positions by following these steps.

[0106] Step 1: Calculate the eddy current constant Construct a unitized velocity field List the optimization problems

[0107]

[0108] Using an interlaced grid, discretize the optimization problem according to the following expression, and assemble the matrix.

[0109]

[0110]

[0111] in , It is with grid cells Number of adjacent units, For unit With unit The velocity on the grid surface between them. The problem can therefore be transformed into a ground state solution problem in quantum computing, i.e., minimizing... .

[0112] Step 2: Solve the optimization problem using a quantum eigenvalue solver. Number of qubits The basic modules in a parametric quantum circuit are repeated. The Adam optimizer was used to optimize the parametric quantum circuit, with an initial learning rate of 0.01, which was reduced to 0.99 times the original rate at 10-step intervals, and the optimization was iterated 500 times. Measurements were retained. The Pauli operator and its constant are calculated. .

[0113] Step 3: Construct the Gross–Pitaevskii (GP) equations describing the flow field evolution, and discretize the equations using second-order central difference to obtain the Hamiltonian.

[0114] Step 4: Perform Trotter decomposition on the Hamiltonian, as shown in the attached figure. Figure 2 The evolutionary quantum circuit is shown, and the final quantum state is obtained. .

[0115] Step 5: Obtain the result using interpolation methods. The zero point, i.e., the position of the vortex at the evolution result point. The result is as follows... Figure 3 As shown, it demonstrates The evolution results and the corresponding induced velocity field streamlines are shown. It can be seen that this method simulates and calculates the velocity evolution process over time through quantum encoding and quantum circuits.

[0116] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0117] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0118] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0119] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0120] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0121] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A flow field evolution method based on quantum computing and vortex characterization, characterized in that, Includes the following steps: S1. For the flow field to be predicted, a complex scalar field is defined, and a Hermitian matrix is ​​constructed based on the initial velocity field, transforming the vortex filament localization problem into a quantum ground state solution problem; S2. Solve for the minimum eigenvalue of the Hermitian matrix using a quantum algorithm and output the initial vortex quantum state; S3. Based on the fluid dynamics control equations, a Hamiltonian for quantum evolution is constructed through spatial discretization. S4. Construct a Hamiltonian quantum circuit to drive the evolution of the initial vortex quantum state to the target quantum state; specifically including: The Hamiltonian is decomposed into a linear combination of Pauli operators; The time evolution operator is obtained from the decomposed Hamiltonian. The time evolution operator is approximately decomposed into a product of multi-step evolution operators using Trout decomposition. Based on the properties of each evolution operator, the decomposed evolution operators are mapped to the corresponding quantum gates to obtain the corresponding evolution quantum circuits; The initial vortex quantum state is input into the evolving quantum circuit, and the evolved target state is output. S5. Measure the evolved quantum state to obtain the discrete values ​​of the complex scalar field at the center point of the grid cell. Based on the grid topology, locate the zero isopleths by the discrete winding number and interpolation, reconstruct the vortex wire structure after the flow field evolution, and obtain the flow field evolution results.

2. The flow field evolution method based on quantum computing and vortex characterization according to claim 1, characterized in that, The definition of the complex scalar field, based on the initial velocity field, constructs a Hermitian matrix, transforming the vortex filament localization problem into a quantum ground state solution problem, specifically including: Define a complex scalar field and use the zero contour lines of the complex scalar field to represent the positions of the vortex filaments; construct a normalized velocity field by setting the vortex strength constant, and establish a unit modulus functional optimization problem for the complex scalar field and the dimensionless velocity field. The functional is discretized on an interlaced grid, wherein the complex scalar field is stored at the center of the grid cell and the dimensionless velocity field is stored at the center of the adjacent grid surface. Constructing a Hermitian matrix transforms the discrete functional optimization problem into a minimum eigenvalue problem.

3. The flow field evolution method based on quantum computing and vortex characterization according to claim 1, characterized in that, The quantum algorithm employs a quantum variational eigenvalue solver, and the specific solution steps are as follows: Construct a parametric quantum circuit, input an initial state, and obtain the target quantum state based on the parameter evolution; The energy expectation value of the Hermitian matrix is ​​calculated based on the target quantum state using quantum measurement techniques. The parameters of the parametric quantum circuit are iteratively optimized using a classical optimizer until the energy expectation value converges, and the target quantum state corresponding to the optimal parameters is output as the initial vortex quantum state.

4. The flow field evolution method based on quantum computing and vortex characterization according to claim 3, characterized in that, The parametric quantum circuit is composed of multiple repeating basic modules connected in series, and each basic module includes a parameterized rotating gate layer that acts sequentially on each quantum bit.

5. The flow field evolution method based on quantum computing and vortex characterization according to claim 3, characterized in that, The specific steps for calculating the energy expectation value of the Hermitian matrix using quantum measurement technology are as follows: The Hermitian matrix is ​​decomposed into a linear combination of Pauli operators. The Pauli operators are sorted in descending order according to the absolute value of their coefficients, and a predetermined proportion of Pauli operators are truncated. The expected energy value of the Hermitian matrix in the target quantum state output by the parametric quantum circuit is calculated based on the truncated Pauli operators.

6. The flow field evolution method based on quantum computing and vortex characterization according to claim 1, characterized in that, The governing equations for the fluid dynamics are the Gross-Pitajewsky equations: ， in, For the complex standard quantity field, For time, For spatial divergence operators, The imaginary unit; The spatial discretization process includes: The Laplace and nonlinear terms of the governing equations are discretized using the second-order central difference method to obtain the discrete form: ， Where G is the discretized Hamiltonian.

7. The flow field evolution method based on quantum computing and vortex characterization according to claim 2, characterized in that, The method of locating zero isopleths based on grid topology through discrete winding number and interpolation specifically includes: For a cell surface formed by the centers of four adjacent grid cells, the sum of the argument differences between the complex scaling values ​​of adjacent cells is calculated sequentially, and the number of windings is obtained after normalization. For elements with a non-zero winding number, the local normalized coordinates of the vortex wire passing through the element surface are determined by solving the bilinear interpolation equation. Connecting the locally normalized coordinates obtained from adjacent grid cells forms the vortex filament structure after the flow field evolution.

8. A computer device, characterized in that, The computer device includes: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the flow field evolution method based on quantum computing and vortex characterization as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing computer instructions, characterized in that, When the computer instructions are executed by one or more processors, the one or more processors are caused to perform the steps of the method according to any one of claims 1 to 7.

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