Helmholtz equation quantum solving method, electromagnetic wave characteristic determination method and device

Abstract

The embodiment of the invention discloses a Helmholtz equation quantum solving method and an electromagnetic wave characteristic determination method and device, and the method comprises the steps: carrying out the series expansion of a solution and a source item of a Helmholtz equation according to a selected primary function, and discretizing a computational domain of the Helmholtz equation into grid points; substituting the solution and the series form of the source item into a margin function corresponding to the Helmholtz equation, and applying a weighted margin method at each network point to obtain a large linear equation set of which the dimension is consistent with the number of grid points; solving a linear equation set through a quantum linear solver to obtain a solution coefficient of the primary function, wherein the linear equation set is obtained by applying a weighted margin method to all grid points; and substituting the solution coefficient of the primary function into the series form of the solution to obtain the solution. By adopting the embodiment of the invention, the hardware resources of the computer can be saved, and the solving speed of the Helmholtz equation can be improved.

Description

Technical Field

[0001] This invention relates to the field of quantum computing technology, and in particular to a quantum solution method for the Helmholtz equation, a method and apparatus for determining electromagnetic wave characteristics. Background Technology

[0002] The Helmholtz equation is an important partial differential equation widely used in physics and engineering for wave phenomena and vibration analysis. The Helmholtz equation has the following form:

[0003]

[0004] in, is the Laplace operator, u is a solution to the Helmholtz equation, f is the source term of the Helmholtz equation, and k is the wave number. The Helmholtz equation has important applications in acoustics, electromagnetism, quantum mechanics, and other fields, such as describing sound wave propagation, light wave propagation, and the behavior of quantum particles.

[0005] Currently, classical computation typically employs the finite difference method to solve the Helmholtz equations. However, the finite difference method requires a sufficiently large number of grid points to achieve an accurate solution. An excessive number of grid points results in an excessively large dimensionality of the linear equations corresponding to the Helmholtz equations, necessitating a significant amount of Random Access Memory (RAM) to store intermediate and final results. The solution process may require megabytes or even gigabytes of data. Therefore, this method places excessive demands on computer hardware resources, making it unsuitable for simulating and solving real-world physical problems on classical computers. Summary of the Invention

[0006] This application provides a quantum solution method for the Helmholtz equation, a method and apparatus for determining electromagnetic wave characteristics, which can save computer hardware resources and improve the solution speed of the Helmholtz equation.

[0007] The first aspect of this application provides a quantum solution method for the Helmholtz equation, the method comprising:

[0008] The solutions and source terms of the Helmholtz equation are expanded into series based on the selected basis functions, and the computational domain of the Helmholtz equation is discretized into grid points.

[0009] Substituting the series form of the solution and source terms into the residual function corresponding to the Helmholtz equation, and applying the weighted residual method at each grid point, a large linear system of equations with the same dimension as the number of grid points is obtained.

[0010] The solution coefficients of the basis functions are obtained by solving the system of linear equations using a quantum linear solver. The system of linear equations is obtained by applying the weighted residual method to all grid points.

[0011] The solution is obtained by substituting the solution coefficients of the basis functions into the series form of the solution.

[0012] Unlike the existing finite difference method, which uses difference quotients instead of partial derivatives to obtain the corresponding difference equations and solves them to obtain approximate solutions to the differential equations, this scheme expands the solutions and source terms of the Helmholtz equations using selected basis functions. Then, it solves the linear equations corresponding to the discretized grid points using the collocation method to obtain the solution coefficients of the basis functions. This scheme requires less computation than the finite difference method, thus requiring less RAM to store intermediate and final results. Furthermore, using a quantum linear solver to solve the linear equations further reduces the number of bits required and accelerates the solution speed. Therefore, this scheme can improve the solution speed of the Helmholtz equations while saving computer hardware resources.

[0013] In conjunction with the first aspect, in some descriptions of the first aspect, the residual function is:

[0014] R(x) = Lu(x) - f(x),

[0015] Where R(x) is the residual function, u(x) and f(x) are the solution and source term, respectively, and L is the matrix operator, L = D. 2 +k 2 I (N+1)×(N+1) D is the derivative matrix, I is the identity matrix, k is the wave number, and N is the number of terms in the series, which is equal to the number of grid points.

[0016] In conjunction with the first aspect, in some descriptive methods of the first aspect, the coordinates of any grid point are... The value of i ranges from 0 to N.

[0017] In conjunction with the first aspect, in certain descriptions of the first aspect, determining the linear equation corresponding to each grid point using the collocation method includes:

[0018] Determine R(x) i When x is 0, each of the grid points x i The corresponding linear equation Lu(x) i )-f(x i ) = 0.

[0019] In conjunction with the first aspect, in certain descriptive methods of the first aspect, the series forms of the solution and the source term are respectively and At that time, among them, These are the solution coefficients and source term coefficients of the basis functions, respectively, φ. i (x) is a basis function.

[0020] A second aspect of this application provides a method for determining electromagnetic wave characteristics, the method comprising:

[0021] Obtain the Helmholtz equation characterizing the electromagnetic field. The source term of the Helmholtz equation characterizes the electromagnetic field distribution in the space where the conductor is located. The solution of the Helmholtz equation characterizes the magnetic vector potential of the charge in the conductor. The computational domain of the Helmholtz equation is determined according to the length and cross-sectional area of ​​the conductor.

[0022] The magnetic vector potential of the charge in the conductor is determined according to the method of any embodiment of the first aspect, and the characteristics of the electromagnetic wave are determined according to the magnetic vector potential.

[0023] Based on the above scheme, the source term of the Helmholtz equation characterizes the electromagnetic field distribution in the space where the conductor is located, and the solution characterizes the magnetic vector potential of the charge in the conductor. The computational domain is determined according to the length and cross-sectional area of ​​the conductor. Then, the magnetic vector potential of the charge in the conductor can be obtained by solving the Helmholtz equation according to the method of any embodiment of the first aspect. Furthermore, the characteristics of the electromagnetic wave can be quickly and accurately determined based on the magnetic vector potential.

[0024] A third aspect of this application provides a quantum solution device for the Helmholtz equation, the device comprising:

[0025] The preprocessing unit is used to perform series expansion of the solutions and source terms of the Helmholtz equation based on the selected basis functions, and to discretize the computational domain of the Helmholtz equation into grid points.

[0026] The equation determination unit is used to substitute the series form of the solution and source terms into the residual function corresponding to the Helmholtz equation, and to apply the weighted residual method at each grid point to obtain a large linear system of equations with the same dimension as the number of grid points.

[0027] The equation solving unit is used to solve the linear equation system by a quantum linear solver to obtain the solution coefficients of the basis functions. The linear equation system is obtained by applying the weighted residual method to all grid points.

[0028] The series solving unit is used to substitute the solution coefficients of the basis functions into the series form of the solution to obtain the solution.

[0029] A fourth aspect of this application provides an electromagnetic wave characteristic determination device, the device comprising:

[0030] The model acquisition unit is used to acquire the Helmholtz equation characterizing the electromagnetic field. The source term of the Helmholtz equation characterizes the electromagnetic field distribution in the space where the conductor is located. The solution of the Helmholtz equation characterizes the magnetic vector potential of the charge in the conductor. The computational domain of the Helmholtz equation is determined according to the length and cross-sectional area of ​​the conductor.

[0031] A characteristic determination unit is configured to determine the magnetic vector potential of the charge in the conductor according to the method of any embodiment of the first aspect, and to determine the characteristics of the electromagnetic wave based on the magnetic vector potential.

[0032] A fifth aspect of this application provides an electronic device, including: a processor and a memory;

[0033] The processor is connected to a memory, wherein the memory is used to store computer programs and the processor is used to invoke the computer programs to execute the methods as described in the first aspect of the embodiments of this application.

[0034] A sixth aspect of this application provides a computer-readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, perform the method as described in the first aspect of this application. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 An example system block diagram of quantum solving of the Helmholtz equations according to an embodiment of this application is shown;

[0037] Figure 2 This paper illustrates the overall architecture of a VQLS algorithm provided in one embodiment of this application.

[0038] Figure 3 A flowchart illustrating a quantum solution method for the Helmholtz equation provided in one embodiment of this application is shown.

[0039] Figure 4 A flowchart illustrating an embodiment of the electromagnetic wave characteristic determination method provided in this application is shown.

[0040] Figure 5 This invention provides a schematic diagram of the structure of a quantum solver for the Helmholtz equation according to an embodiment of the present application.

[0041] Figure 6A schematic diagram of the structure of an electromagnetic wave characteristic determination device provided in one embodiment of this application is shown;

[0042] Figure 7 A schematic diagram of the structure of a computer device provided in one embodiment of this application is shown. Detailed Implementation

[0043] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0044] Classical computers use transistors to encode information in binary data, such as bits, where each bit can represent a value of 1 or 0. These 1s and 0s act as switches to drive the functions of a classical computer. If there are n bits of data, there are 2^n possible classical states, and one state is represented at a time.

[0045] Quantum computers use quantum processors that operate on data represented by qubits, also known as quantum bits. A single qubit can represent the classical binary states "0" or "1", or a superposition of "0" and "1". Because it can represent a superposition of "0" and "1", a qubit can represent both "0" and "1" states simultaneously. For example, if there are n bits of data, then 2^n qubits can represent n bits of data. n A quantum state can be represented simultaneously. Furthermore, qubits in a superposition can be correlated with each other, a phenomenon known as entanglement, where the state of one qubit (whether 1, 0, or both) depends on the state of another qubit, and more information can be encoded within two entangled qubits. Based on the principles of superposition and entanglement, qubits enable quantum computers to perform functions that might be relatively complex and time-consuming for classical computers.

[0046] Please refer to Figure 1 This illustrates an example system block diagram for quantum solving of the Helmholtz equations according to one embodiment of this application. System 100 may be a hybrid computing system comprising a combination of one or more quantum computers, quantum systems, and / or classical computers. Figure 1In the example shown, system 100 may include a quantum system 110 and a classical computer 120. In one implementation, the quantum system 110 and the classical computer 120 may be configured to communicate via one or more wired and / or wireless connections (e.g., wireless networks). The quantum system 110 may include a quantum chipset consisting of one or more quantum chips, comprising various hardware components for processing data encoded in qubits. The quantum chipset may be a quantum computing core surrounded by infrastructure to protect the quantum chips from electromagnetic noise sources, mechanical vibration sources, heat sources, and other noise sources that can degrade the performance of the quantum chips. The classical computer 120 may be electronically integrated with the quantum system 110 via any suitable wired and / or wireless electronic connection.

[0047] exist Figure 1 In the example shown, quantum system 110 can be any suitable set of components capable of performing quantum operations on a physical system. Quantum operations, such as quantum gate operations, manipulate the quantum states of qubits to evolve and / or become entangled. Figure 1 In the illustrated example embodiment, the quantum system 110 may include a measurement and control unit 111, an interface 112, and a quantum chip 113. In some embodiments, all or part of each of the measurement and control unit 111, interface 112, and quantum chip 113 may be located in a cryogenic environment to facilitate the performance of quantum operations. The quantum chip 113 may be any hardware capable of processing information using quantum states. This hardware may include multiple qubits and means for coupling or entanglement of the qubits to process information using quantum states. Qubits may include, but are not limited to, charge qubits, flux qubits, phase qubits, spin qubits, and ion qubits. The quantum chip may include a set of quantum logic gates configured to perform quantum logic operations on the qubits stored in a quantum register. The quantum gates may include one or more single-qubit gates, two-qubit gates, and / or other multi-qubit gates.

[0048] The measurement and control unit 111 can be any combination of digital computing devices capable of performing quantum computing (e.g., executing quantum circuits) in conjunction with interface 112. This digital computing device may include a digital processor and memory for storing and executing quantum instructions using interface 112. The digital computing device may also include a communication protocol device for receiving instructions and sending the results of the performed quantum computing to a classical computer. Additionally, the digital computing device may include a communication interface having interface 112. In one embodiment, the measurement and control unit 111 may be configured to receive classical instructions (e.g., from classical computer 120) and convert these classical instructions into measurement and control instructions for interface 112. The measurement and control instructions provided by the measurement and control unit 111 to interface 112 may be, for example, digital signals indicating which quantum gates in a quantum gate array need to be applied to the qubits to perform a specific function. Interface 112 may be configured to convert these digital signals into analog signals (e.g., analog pulses of microwave pulses), which can be used to apply quantum gates to the qubits to manipulate the interactions between the qubits.

[0049] Interface 112 may be a classical-quantum interface, comprising a combination of devices capable of receiving instructions from the integrated measurement and control unit 111 and converting those instructions into a means for implementing quantum operations. In one embodiment, interface 112 may convert instructions from the integrated measurement and control unit 111 into drive signals capable of driving or manipulating qubits, and / or applying quantum gates to qubits. Additionally, interface 112 may be configured to convert signals received from the quantum chip 113 into digital signals capable of being processed and transmitted by the integrated measurement and control unit 111. Devices included in interface 112 may include, but are not limited to, digital-to-analog converters, analog-to-digital converters, waveform generators, attenuators, amplifiers, optical fibers, lasers, and filters. Interface 112 may further include circuitry configured to measure multiple qubits after the application of quantum gates, wherein the measurements may produce results represented in classical bits. Each measurement performed by interface 112 may be read out to a device connected to the quantum system 110, such as a classical computer 120. The multiple measurement results provided by interface 112 may represent probabilistic results.

[0050] The classical computer 120 can include hardware components such as a processor and storage devices (e.g., including memory devices and classical registers) for processing data encoded in classical bits. In one embodiment, the classical computer 120 can be configured to provide the quantum system 110 with various control signals, instructions, and data encoded in classical bits. Further, quantum states measured by the quantum system 110 can be read out by the classical computer 120, and the classical computer 120 can store the measured quantum states as classical bits in classical registers. In one embodiment, the classical computer 120 can be any suitable combination of computer-executable hardware and / or computer-executable software capable of executing the preparation module 121 to perform quantum computation using data stored in the data storage module 122 as part of the construction and computation. The data storage module 122 can be a repository for data to be analyzed using quantum computing algorithms and the results of that analysis. The preparation module 121 can be a program or module capable of preparing classical data from the data storage module 122 as part of a quantum circuit implementation. Preparation module 121 can be instantiated as part of a larger algorithm, such as an application programming interface (API) function call, or by resolving hybrid classical-quantum computing into aspects of quantum and classical computing. For example, preparation module 121 can generate instructions for creating quantum circuits using quantum gates. In an embodiment, such instructions can be stored by the measurement and control unit 111 and can be instantiated by components of interface 112 to execute, enabling quantum operations of quantum gates to be performed on quantum chip 113.

[0051] The classic computer 120 may be a laptop computer, desktop computer, vehicle-integrated computer, smart mobile device, tablet device, and / or any other suitable classic computing device. Additionally or alternatively, the classic computer 120 may also operate as part of a cloud computing service model, such as Software as a Service (SaaS), Platform as a Service (PaaS), or Infrastructure as a Service (IaaS). The classic computer 120 may also reside in a cloud computing deployment model, such as a private cloud, community cloud, public cloud, or hybrid cloud.

[0052] The Variational Quantum Linear Solver (VQLS) is a variational quantum algorithm for solving systems of linear equations. It employs a classical-quantum hybrid approach and can run on recent noisy, medium-scale quantum computers. Please refer to [reference needed]. Figure 2 This diagram illustrates the overall architecture of the VQLS algorithm provided in one embodiment of this application. For a detailed explanation of the VQLS algorithm's working principle, please refer to [link / reference]. Figure 2The linear system of equations A·x=b, where A is the coefficient matrix, b is the constant vector, and x is the unknown quantity to be solved. Using the VQLS algorithm, a quantum state proportional to x can be obtained, i.e., a normalized vector.

[0053] Solving linear equations in a quantum scenario differs slightly from the usual approach because quantum computing requires applying unitary operators to quantum states. For an input coefficient matrix A, it needs to be decomposed into a linear combination of unitary operators, A = ∑ n C n A n , where each A n Both are unitary operators and can run on quantum circuits. For the input constant vector b, it needs to be assumed that it is a quantum state that can be prepared by some unitary operator U, i.e., U|0>=|b>.

[0054] As can be seen, the VQLS algorithm is a hybrid optimization algorithm, which can be divided into classical and quantum parts. It requires preparing a parameterized quantum circuit V(α) on a quantum computer and calculating the loss function C(α). Then, it optimizes the parameter α on a classical computer to minimize the loss function until the loss is below a certain threshold, finally outputting the target quantum state |x>. The parameterized circuit V(α) generates a quantum state |ψ(α)>, and the circuit F(A) calculates the approximation between A|ψ(α)> and |b>, i.e., the loss function C(α). When the quantum state A|ψ(α)> is close enough to |b>, it means that the quantum state |ψ(α)> is close enough to the target quantum state |x>, and the quantum state |ψ(α)> can be output as an approximation of the target quantum state |x>.

[0055] Please refer to Figure 3 This document illustrates a flowchart of a quantum solution method for the Helmholtz equation provided in one embodiment of this application. This method can be applied to computer devices, which refer to electronic devices capable of data computation and processing. The method may include the following steps:

[0056] Step 301: Perform a series expansion of the solutions and source terms of the Helmholtz equation based on the selected basis functions, and discretize the computational domain of the Helmholtz equation into grid points.

[0057] In mathematics and engineering, a basis function is a specific set of functions used to construct a function space. In many cases, basis functions are used to represent or approximate other functions, especially in fields such as numerical analysis, signal processing, image processing, and machine learning.

[0058] Specifically, the solutions and source terms of the Helmholtz equation are expanded into series based on the selected basis functions. The selected basis functions can be, for example, Fourier series, Chebyshev polynomials, Legendre polynomials, etc. The solutions and source terms are expanded using the same basis functions, but their coefficients to be determined are different. If the coefficients of the solutions (i.e., the series expansion coefficients of the solutions) can be determined, they can be substituted into their series expansion forms to determine the solutions.

[0059] Specifically, discretizing the computational domain of the Helmholtz equations into grid points includes:

[0060] The computational domain of the Helmholtz equation is mapped, and then the mapped domain is discretized into N+1 grid points.

[0061] For example, if the computational domain of the Helmholtz equation is [-5, 5], then [-5, 5] is mapped to [0, N], where N is a positive integer. For example, if N is 5, then 6 grid points (0, 1, 2, 3, 4, 5) can be obtained; if N is 10, then 11 grid points (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) can be obtained; if N is 15, then 16 grid points (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15) can be obtained. The above is an example of the one-dimensional case. The same applies to two-dimensional or higher-dimensional cases; refer to the specific example of the one-dimensional case above, which will not be repeated here.

[0062] In one specific embodiment of this application, Chebyshev polynomials are used for expansion, and the series forms of the solution and the source term are respectively... and At that time, among them, These are the solution coefficients and source term coefficients of the basis functions, respectively, φ. i (x) is a basis function.

[0063] The coordinates of any grid point are: The value of i ranges from 0 to N. At both endpoints, x0 = 1, x... N =-1.

[0064] Step 302: Substitute the series form of the solution and source terms into the residual function corresponding to the Helmholtz equation, and apply the weighted residual method to each grid point to obtain a large linear system of equations with the same dimension as the number of grid points.

[0065] The residual function is typically used to measure the difference between the actual and expected results, and is a key indicator for evaluating the goodness of fit of a model. In residual analysis, the quality of model fit is evaluated by analyzing the residual function.

[0066] In this scheme, the residual function can be, for example:

[0067] R(x) = Lu(x) - f(x),

[0068] Where R(x) is the residual function, u(x) and f(x) are the solution and source term, respectively, and L is the matrix operator, L = D. 2 +k 2 I (N+1)×(N+1) D is the derivative matrix, I is the identity matrix, k is the wave number, and N is the number of terms in the series, which is equal to the number of grid points.

[0069] The collocation method requires that the residual function be zero at selected grid points. This yields a set of algebraic equations concerning the unknown coefficients. By solving these equations, the coefficients of the approximate solution can be obtained, thus leading to the final approximate solution.

[0070] Specifically, determining the linear equation corresponding to each grid point using the collocation method includes:

[0071] Determine R(x) i When x is 0, each of the grid points x i The corresponding linear equation Lu(x) i )-f(x i ) = 0.

[0072] Step 303: Solve the linear equations using a quantum linear solver to obtain the solution coefficients of the basis functions. The linear equations are obtained by applying the weighted residual method to all grid points.

[0073] Among them, the Quantum Linear Solver (QLS) is a method that uses a quantum computer to solve linear system equations. Its main steps include quantum state encoding, quantum linear algorithms, and quantum state tomography. The quantum linear algorithm can be, for example, the HHL algorithm, or other algorithms. Figure 2 The VQLS algorithm is used in this example.

[0074] Step 304: Substitute the solution coefficients of the basis functions into the series form of the solution to obtain the solution.

[0075] As can be seen, unlike the existing finite difference method, which uses difference quotients to replace partial derivatives to obtain the corresponding difference equations and solves the difference equations to obtain approximate solutions to the differential equations, this scheme expands the solutions and source terms of the Helmholtz equations using selected basis functions, and then solves the linear equations corresponding to the discretized grid points using the collocation method to obtain the solution coefficients of the basis functions. This scheme requires less computation than the finite difference method; therefore, the RAM needed to store intermediate and final results is less than that required by the finite difference method. Furthermore, using a quantum linear solver to solve the linear equations further reduces the number of bits required and accelerates the solution speed. Therefore, the above scheme can improve the solution speed of the Helmholtz equations while saving computer hardware resources.

[0076] Signal transmission in conductors is a fundamental component of modern communication, electronic, and power systems. For example, in communications, studying the propagation characteristics of electromagnetic waves in conductors helps reduce signal distortion and interference; in power transmission, studying the propagation characteristics of electromagnetic waves helps reduce power loss and improve transmission efficiency; and in microwave detection, studying the propagation of electromagnetic waves in conductors helps improve radar detection capabilities and resolution. With the development and application of various electronic and power devices, the environment is becoming increasingly noisy, making it particularly important to quickly and accurately determine the propagation characteristics of electromagnetic waves in conductors in complex environments. To address this technical problem, this application also provides a method for determining electromagnetic wave characteristics.

[0077] Please refer to Figure 4 This illustration shows a flowchart of an electromagnetic wave characteristic determination method according to an embodiment of this application. The method can be applied to computer devices, which refer to electronic devices with data computing and processing capabilities. The method may include the following steps:

[0078] Step 401: Obtain the Helmholtz equation characterizing the electromagnetic field. The source term of the Helmholtz equation characterizes the electromagnetic field distribution in the space where the conductor is located. The solution of the Helmholtz equation characterizes the magnetic vector potential of the charge in the conductor. The computational domain of the Helmholtz equation is determined according to the length and cross-sectional area of ​​the conductor. The wave number is determined according to the conductivity, permeability and frequency of the electromagnetic wave in the space.

[0079] Step 402: Determine the magnetic vector potential of the charge in the conductor according to the method of any embodiment of the first aspect, and determine the characteristics of the electromagnetic wave according to the magnetic vector potential.

[0080] Among them, the source terms of the Helmholtz equation μ represents magnetic permeability. Represents current density; solutions to the Helmholtz equation. Represents the magnetic vector potential; wave number k = μεω 2ε represents electrical conductivity, and ω represents the frequency of the electromagnetic wave.

[0081] The current density, conductivity, permeability, and angular frequency in the conductor are all known quantities. Therefore, the magnetic vector potential can be solved according to the equation, and then the characteristics of electromagnetic waves can be described based on the magnetic vector potential.

[0082] Based on the above scheme, the source term of the Helmholtz equation characterizes the electromagnetic field distribution in the space where the conductor is located, and the solution characterizes the magnetic vector potential of the charge in the conductor. The computational domain is determined according to the length and cross-sectional area of ​​the conductor. Then, the magnetic vector potential of the charge in the conductor can be obtained by solving the Helmholtz equation according to the method of any embodiment of the first aspect. Furthermore, the characteristics of the electromagnetic wave can be determined based on the fast and accurate magnetic vector potential.

[0083] Figure 5 A schematic diagram of a quantum solver for the Helmholtz equations according to an embodiment of this application is shown. The device includes:

[0084] The preprocessing unit 501 is used to perform series expansion on the solutions and source terms of the Helmholtz equation according to the selected basis functions, and to discretize the computational domain of the Helmholtz equation into grid points.

[0085] The equation determination unit 502 is used to substitute the series form of the solution and source terms into the residual function corresponding to the Helmholtz equation, and to apply the weighted residual method at each grid point to obtain a large linear system of equations with the same dimension as the number of grid points.

[0086] Equation solving unit 503 is used to solve the linear equation system to obtain the solution coefficients of the basis functions by using a quantum linear solver. The linear equation system is obtained by applying the weighted residual method to all grid points.

[0087] The series solving unit 504 is used to substitute the solution coefficients of the basis functions into the series form of the solution to obtain the solution.

[0088] Figure 6 This invention provides a schematic diagram of an electromagnetic wave characteristic determination device according to an embodiment of the present application. The device includes:

[0089] Model acquisition unit 601 is used to acquire the Helmholtz equation characterizing the electromagnetic field. The source term of the Helmholtz equation characterizes the electromagnetic field distribution in the space where the conductor is located. The solution of the Helmholtz equation characterizes the magnetic vector potential of the charge in the conductor. The computational domain of the Helmholtz equation is determined according to the length and cross-sectional area of ​​the conductor.

[0090] The characteristic determination unit 602 is used to determine the magnetic vector potential of the charge in the conductor according to the method of any embodiment of the first aspect, and to determine the characteristics of the electromagnetic wave according to the magnetic vector potential.

[0091] Figure 7 The diagram illustrates the structure of a computer device according to an embodiment of this application, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the functions of the computer system in any of the above embodiments, namely, the quantum solution method for the Helmholtz equation or the electromagnetic wave characteristic determination method.

[0092] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a computer, causes the computer to perform the functions of the computer system of the Helmholtz equation quantum solution method or electromagnetic wave characteristic determination method in any of the above embodiments.

[0093] This application also provides a computer program product containing instructions that, when executed by a computer, cause the computer to perform the functions of the computer system in any of the above embodiments: the quantum solution method for the Helmholtz equation or the method for determining electromagnetic wave characteristics.

[0094] It is understood that the specific examples in this application are only intended to help those skilled in the art better understand the implementation methods of this application, and are not intended to limit the scope of the invention.

[0095] It is understood that in the various embodiments of this application, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not limit the implementation process of the embodiments of this application in any way.

[0096] It is understood that the various implementation methods described in this application can be implemented individually or in combination, and the implementation methods in this application are not limited in this respect.

[0097] Unless otherwise stated, all technical and scientific terms used in the embodiments of this application have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The term "and / or" as used in this application includes any and all combinations of one or more of the associated listed items. The singular forms "a," "the," and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0098] It is understood that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0099] It is understood that the memory in the embodiments of this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Specifically, non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may be random access memory (RAM). It should be noted that the memory in the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0100] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0101] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the aforementioned method implementations, and will not be repeated here.

[0102] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0103] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0104] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0105] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0106] The above are merely specific embodiments of this application, but the scope of protection of this invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A Helmholtz equation quantum solution method characterized by, The method comprises: expanding the solution and the source term of the Helmholtz equation according to selected basis functions, and discretizing the calculation domain of the Helmholtz equation into grid points; substituting the series form of the solution and the source term into the corresponding residual function of the Helmholtz equation, and applying the weighted residual method at each grid point to obtain a large linear equation group with the same dimension as the number of grid points; solving the linear equation group by a quantum linear solver to obtain the solution coefficients of the basis functions, the linear equation group being obtained by applying the weighted residual method at all grid points; substituting the solution coefficients of the basis functions into the series form of the solution to obtain the solution.

2. The method of claim 1, wherein, The residual function is: R(x) = Lu(x) - f(x), Wherein, R(x) is the residual function, u(x), f(x) are the solution and source term respectively, L is the matrix operator, L=D 2 +k 2 I (N+1)×(N+1) , D is the derivative matrix, I is the unit matrix, k is the wave number, N+1 is the number of terms of the series, the number of terms of the series is equal to the number of grid points.

3. The method of claim 2, wherein, The coordinates of any one grid point are The value range of i is 0 to N.

4. The method of claim 2, wherein, The method comprises: determine R(x i ) as 0 when each of the grid points x i corresponding to the linear equation Lu(x i )-f(x i ) = 0.

5. The method of claim 2, wherein, The solution and the source term in series form are respectively and where, are the solution coefficients and the source term coefficients of the basis functions respectively, φ i (x) is the basis function.

6. A method of determining electromagnetic wave properties, characterized by, The method comprises: The device comprises: a preprocessing unit configured to expand the solution and the source term of the Helmholtz equation according to selected basis functions, and discretize the calculation domain of the Helmholtz equation into grid points; 7. A Helmholtz equation quantum solver apparatus, characterized by, an equation determination unit configured to substitute the series form of the solution and the source term into the corresponding residual function of the Helmholtz equation, and apply the weighted residual method at each grid point to obtain a large linear equation group with the same dimension as the number of grid points; an equation solving unit configured to solve the linear equation group by a quantum linear solver to obtain the solution coefficients of the basis functions, the linear equation group being obtained by applying the weighted residual method at all grid points; a series solving unit configured to substitute the solution coefficients of the basis functions into the series form of the solution to obtain the solution. The device comprises: a model acquisition unit configured to acquire the Helmholtz equation representing the electromagnetic field, the source term of the Helmholtz equation representing the electromagnetic field distribution in the space where the wire is located, the solution of the Helmholtz equation representing the magnetic vector potential of the charge in the wire, and the calculation domain of the Helmholtz equation being determined according to the length and cross-sectional area of the wire; 8. An electromagnetic wave property determining apparatus, characterized by comprising: a characteristic determination unit configured to determine the magnetic vector potential of the charge in the wire according to the method of any one of claims 1-5, and determine the characteristics of the electromagnetic wave according to the magnetic vector potential. comprise: a processor and a memory; 9. An electronic device, comprising: The processor and the memory are connected, wherein the memory is configured to store a computer program, and the processor is configured to invoke the computer program to execute the method of any one of claims 1-5 or claim 6. The computer readable storage medium stores a computer program, the computer program comprising program instructions, the program instructions being executed by a processor to execute the method of any one of claims 1-5 or claim 6. ​ 10. A computer-readable storage medium, characterized in that, ​

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