A quantum computing method and apparatus for structural instability problems

Abstract

The application discloses a quantum computing method and device for a structural instability problem. Firstly, a finite element control equation of a compression beam instability is established. Then, a target matrix of the compression beam instability is calculated according to the Euler beam property and the established finite element control equation, and the target matrix of the compression beam instability is converted into a linear combination of a Pauli matrix tensor product through data transformation. Next, a parameterized electronic circuit is constructed on a classical computer. Finally, the parameterized quantum circuit is run on a quantum computer, a loss function is constructed on the classical computer based on an expected value, and the parameters of the loss function are adjusted by an optimizer so that the corresponding eigenvalue converges. The application provides a new idea for solving the characteristic equation by virtue of the powerful parallel computing capability and quantum superposition characteristics of the quantum computer, and exponentially reduces the computing complexity, thereby providing a new possibility for quickly and efficiently solving complex engineering instability problems.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of limit element simulation and quantum computing, and more particularly, to a quantum computing method and device for structural instability problems. BACKGROUND

[0002] Structural instability refers to the phenomenon that the equilibrium state of a structure changes suddenly when it is subjected to external loads, resulting in the loss of stability of the structure and the destruction or failure of the structure. Such phenomena are commonly found in bridges, buildings, aircraft and other thin-walled complex structures. In order to avoid structural instability, engineers need to perform stability analysis when designing structures to ensure that the structure can maintain stability under the expected load.

[0003] Compared with experimental research, numerical simulation method can greatly save time and cost. At present, eigenvalue analysis based on finite element method is the most commonly used stability analysis method. The main idea of this method is to generate the stiffness matrix of the structure by finite element method, and then to calculate the eigenvalues and eigenvectors of the structure to determine the stability of the structure. If there is a zero value in the eigenvalue, it means that the structure has instability phenomenon.

[0004] Solving the characteristic equation by determinant equal to zero is the most direct method. However, there are two shortcomings: (1) for large sparse matrices, the calculation amount of calculating eigenvalues by directly expanding the determinant is huge, and even it is difficult to implement. For complex matrix structure and large-scale problems, the application of determinant method is greatly limited; (2) in the calculation process, the determinant method does not fully utilize the sparsity of the matrix, and a large amount of calculation resources is wasted on zero elements, and the calculation is easily affected by numerical errors, resulting in inaccurate results.

[0005] Compared with the direct determinant method, the iterative method is more widely used to solve the eigenvalue of matrix, such as QR algorithm, power method, inverse power method, Jacobi method, etc. Among them, the QR algorithm is the main algorithm for solving the eigenvalue in the large matrix calculation software MATLAB. This method converts the matrix into an upper triangular matrix or a quasi-upper triangular matrix through a series of orthogonal transformations, and then uses the properties of these matrices to calculate the eigenvalue and eigenvector. Compared with the sharp increase in computational complexity of the determinant method in processing large-scale matrices, the QR algorithm can usually effectively solve the eigenvalue, and has good stability in numerical calculation process, can more reliably handle various complex matrix cases, and reduce the accumulation of numerical errors. Under appropriate conditions, it has a faster convergence speed and can approach the eigenvalue faster. Therefore, the QR algorithm is often used in the instability problem of computational mechanics. However, the computational complexity of the QR algorithm is relatively high, especially for complex engineering structures, the stiffness matrix established based on the finite element is large (million or even billion), resulting in huge calculation amount. Moreover, the convergence speed of this method is slow, and usually multiple iterations are required to achieve good accuracy, and the convergence depends on the properties of the initial matrix. Therefore, it is difficult to meet the demand for computing power of large-scale engineering structure calculation. SUMMARY

[0006] In view of the problems of high complexity and large calculation amount existing in the existing method for solving the eigenvalue of matrix, the present application provides a quantum computing method for structural instability problem, first establishes the finite element control equation of the instability of the compressed beam, and then develops a quantum algorithm based on the variational quantum eigenvalue solver.

[0007] To solve the above technical problems, the first aspect of the present application provides a quantum computing method for structural instability problem, comprising:

[0008] A quantum computing method for structural instability problem, characterized in that it comprises:

[0009] Establishing the finite element control equation of the instability of the compressed beam;

[0010] According to the properties of the Euler beam and the established finite element control equation, the target matrix of the instability of the compressed beam is calculated, and the target matrix of the instability of the compressed beam is converted into a linear combination of Pauli matrix tensor product through data transformation;

[0011] Constructing a parameterized electronic circuit on a classical computer;

[0012] Running the parameterized quantum circuit on a quantum computer, constructing a loss function based on the expected value on a classical computer, and adjusting the parameters of the loss function by an optimizer to make the corresponding eigenvalue converge.

[0013] In one embodiment, the finite element control equation of the instability of the compressed beam is established, comprising:

[0014] For the problem of a centrally compressed bar, the classical incremental equilibrium equation is obtained:

[0015] ([K e ]-[K g (σ)]){Δu}={ΔF}

[0016] The classical incremental equilibrium equation is transformed into:

[0017] ([K e ]-λ1[K g (σ)]){Δu}={ΔF}

[0018] Where [Ke] is the elastic stiffness matrix, K g (σ) is the initial stress matrix under a certain stress condition, λ1 is a coefficient, {Δu} represents the displacement matrix, and ΔF represents the increment.

[0019] In an embodiment, the parameterized quantum circuit is run by a quantum computer, a loss function is constructed based on the expected value on a classical computer, and the parameters of the loss function are adjusted by an optimizer to make the corresponding eigenvalue converge, comprising:

[0020] The parameterized quantum circuit is run by a quantum computer, and the quantum state is generated by the parameterized quantum circuit and the expected value of the Hamiltonian under different quantum states is calculated by the quantum part;

[0021] The loss function is constructed based on the expected value on a classical computer, and the total expected value of the Hamiltonian is estimated based on the expected value of each Hamiltonian term by the classical computing part, and the variational parameters are adjusted to minimize the energy.

[0022] In an embodiment, the quantum state is generated by the parameterized quantum circuit and the expected value of the Hamiltonian under different quantum states is calculated by the quantum part, comprising:

[0023] Initialize and prepare the variational quantum state;

[0024] Execute multiple different quantum circuits to measure different Hamiltonians;

[0025] Calculate the expected value of each Hamiltonian term.

[0026] In an embodiment, the total expected value of the Hamiltonian is estimated based on the expected value of each Hamiltonian term by the classical computing part, and the variational parameters are adjusted to minimize the energy, comprising:

[0027] Sum all the measured expected values to estimate the total expected value of the Hamiltonian;

[0028] Based on the optimization algorithm, the variational parameters are adjusted to minimize the energy.

[0029] In an embodiment, the parameterized quantum circuit used is EfficientSU2.

[0030] In an embodiment, the optimization algorithm used is SPSA.

[0031] Based on the same inventive concept, the second aspect of the present application provides a quantum computing device for a structural instability problem, comprising:

[0032] a finite element control equation establishing module for establishing a finite element control equation of a buckling of a compressed beam;

[0033] a target matrix calculating and converting module for calculating a target matrix of the buckling of the compressed beam according to the properties of the Euler beam and the established finite element control equation, and converting the target matrix of the buckling of the compressed beam into a linear combination of Pauli matrix tensor products through data transformation;

[0034] a quantum circuit constructing module for constructing a parameterized quantum circuit on a classical computer;

[0035] a quantum computing module for running the parameterized quantum circuit through a quantum computer, constructing a loss function based on an expected value on the classical computer, and adjusting parameters of the loss function through an optimizer so that corresponding eigenvalues converge.

[0036] Based on the same inventive concept, the third aspect of the present application provides a computer readable storage medium having a computer program stored thereon, the program being executed by a processor to implement the quantum computing method for a structural instability problem of the first aspect.

[0037] Based on the same inventive concept, the fourth aspect of the present application provides an electronic device, comprising: at least one processor; and a memory communicatively connected with the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the quantum computing method for a structural instability problem of the first aspect.

[0038] Compared with the prior art, the present application has the following advantages and beneficial technical effects:

[0039] The application provides a quantum computing method for structural instability problems, first, a finite element control equation of instability of a compression beam is established; according to the Euler beam property and the established finite element control equation, a target matrix of instability of the compression beam is calculated, and the target matrix of instability of the compression beam is converted into a linear combination of a Pauli matrix tensor product through data transformation; then a parameterized electronic circuit is constructed on a classical computer; finally, the parameterized quantum circuit is run on a quantum computer, a loss function is constructed based on an expected value on the classical computer, and the parameters of the loss function are adjusted by an optimizer to make the corresponding eigenvalue converge, and the final eigenvalue is obtained. By constructing a parameterized electronic circuit and running the parameterized quantum circuit on a quantum computer, the powerful parallel computing capability and quantum superposition characteristics of quantum computing are used to exponentially reduce the computational complexity, which provides a new idea for solving the characteristic equation and provides a new possibility for quickly and efficiently solving complex engineering instability problems. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings described below are some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0041] Figure 1 The overall flowchart of the quantum computing method for structural instability problems in the embodiments of the present application;

[0042] Figure 2 The detailed flowchart and framework of the quantum computing method for structural instability problems in the embodiments of the present application;

[0043] Figure 3 The iteration optimization process diagram for solving the eigenvalue in the embodiments of the present application;

[0044] Figure 4 The comparison diagram of the reference value and the quantum-classical hybrid algorithm solution value in the embodiments of the present application;

[0045] Figure 5 The eigenvalue matrix diagram generated by the target matrix [K] in the embodiments of the present application;

[0046] Figure 6 The diagram of the final target matrix [K] in the present application. DETAILED DESCRIPTION

[0047] When analyzing the stability of complex structures, the dimension of the matrix used in traditional numerical simulation methods increases dramatically. However, existing eigenvalue algorithms have high computational complexity, especially when dealing with high-dimensional problems, requiring a large amount of computational resources and time, leading to a bottleneck in the upgrade of classical computers.

[0048] In the 1980s, Feynman proposed the concept of quantum computing. In a quantum computer, a qubit can represent the superposition of both 0 and 1 states at the same time. Based on this superposition property, multiple possible solutions can be searched in parallel on a quantum computer, so quantum computers are expected to exponentially reduce the computational complexity, providing a new solution for the upgrade of computing power in the post-Moore era. In 1994, Shor proposed a quantum algorithm for large number factorization, marking the beginning of the practical application of quantum computing. In recent years, with the continuous improvement of quantum computer hardware and the continuous enrichment of quantum algorithms, quantum computing has shown great potential in information, materials, chemistry, and mechanics.

[0049] The VQE (Variational Quantum Eigensolver) algorithm was proposed by Aspuru-Guzik et al. in 2014. This algorithm uses a classical optimizer to train a parametric quantum circuit to solve matrix eigenvalues and eigenvectors. It is the first variational quantum algorithm proposed, suitable for quantum computing of chemical systems on near-term noisy intermediate-scale quantum simulators. The basic idea is to select a parametric trial wave function and initial parameters, measure the energy expectation using a quantum computer, and then update the parameters using a classical optimizer, repeating the process until convergence. Compared with traditional computing methods, VQE has potential quantum advantages, especially when dealing with large-scale or high-dimensional problems. It can use quantum superposition and entanglement to search for multiple possible solutions in parallel on a quantum computer, achieving exponential speedup in some cases. In addition, quantum algorithms can reduce the sensitivity to problem size when dealing with optimization problems, which is particularly important for solving large-scale optimization problems that are difficult for traditional computers.

[0050] Based on this, the application explores a quantum computing method and program design for structural instability problems. The key to applying quantum computing and VQE algorithm to structural stability problems is to process large sparse symmetric matrices through the characteristics of quantum computing, meet the real-time and accuracy requirements of engineering, and solve the minimum eigenvalue (critical instability load) specifically. The technical difficulties include Hamiltonian construction, quantum resource limitation, noise and error control, and quantum state preparation method suitable for structural problems. Compared with other fields (such as quantum chemistry), structural instability problems involve stronger sparsity, nonlinear mechanical behavior and higher reliability requirements. The application takes advantage of the powerful parallel computing capability and quantum superposition characteristics of quantum computing to exponentially reduce the computational complexity, providing a new idea for solving eigenvalue equations and a new possibility for quickly and efficiently solving complex engineering instability problems.

[0051] To make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0052] Embodiment one

[0053] The present embodiment discloses a quantum computing method for structural instability problems, please refer to Figure 1 , comprising:

[0054] S1: establishing a finite element control equation of a compression beam instability;

[0055] S2: calculating a target matrix of the compression beam instability according to the Euler beam properties and the established finite element control equation, and converting the target matrix of the compression beam instability into a linear combination of Pauli matrix tensor product through data transformation;

[0056] S3: constructing a parameterized quantum circuit (EfficientSU2);

[0057] S4: running the parameterized quantum circuit through a quantum computer, constructing a loss function based on an expected value on a classical computer, and adjusting the parameters of the loss function through an optimizer to make the corresponding eigenvalue converge.

[0058] Specifically, step S1 establishes the finite element control equation of the buckling of the compressed beam, and through the calculation of S2 and data transformation, the target matrix of the buckling of the compressed beam is obtained. In order to be able to efficiently calculate on the quantum device, the target matrix of the buckling of the compressed beam is converted into a linear combination of Pauli matrix tensor products through mathematical transformation. This representation enables the quantum device to efficiently evaluate the expectation value of different Pauli operators and ultimately calculate the required eigenvalue. Step S3 constructs a parameterized electronic circuit on a classical computer, and then S4 runs the parameterized quantum circuit on a quantum computer, and runs an optimization algorithm on a classical computer to obtain the eigenvalue of the target matrix.

[0059] In an embodiment, S1 can be implemented in the following way:

[0060] For the problem of a centrally compressed bar, the classical incremental equilibrium equation is obtained as follows:

[0061] ([K e ]-[K g (σ)]){Δu}={ΔF}

[0062] The classical incremental equilibrium equation is transformed into:

[0063] ([K e ]-λ1[K g (σ)]){Δu}={ΔF}

[0064] Where [Ke] is the elastic stiffness matrix, K g (σ) is the initial stress matrix under a certain stress condition, λ1 is a coefficient, {Δu} represents the displacement matrix, and ΔF represents the increment.

[0065] Specifically, the structural instability problem includes linear buckling analysis and nonlinear buckling analysis, and this embodiment only introduces linear buckling analysis, i.e., the eigenvalue problem of the classical algorithm.

[0066] For the classical eigenvalue problem, i.e., the centrally compressed bar, the classical incremental equilibrium equation can be obtained as follows:

[0067] ([K e ]-[K g (σ)]){Δu}={ΔF}

[0068] Let the external load, i.e. the vertical downward load, be {F0}, which is set to 1, indicating that there is only a vertical force on the beam, and the size is 1. The actual external load can be written as a linear function of {F0}, λ1{F0}, indicating that there is only a unit force on the beam. It is assumed that when the external force on the beam reaches the critical load of the beam, the size of the critical force can be written as λ1{F0}. The displacement matrix obtained at this time is λ1{U0}, and thus the initial stress at this time is λ1{σ0}. {U0} refers to the displacement matrix when the force at this time is a unit force. Therefore, when the external load is the critical load, the corresponding initial stress matrix is:

[0069] [K g (σ)]=λ1[K g (σ0)]

[0070] Therefore, we have:

[0071] {ΔF}=([K e ]-λ1[K g (σ0)]){Δu}

[0072] Assuming that the external load is the critical load, and given an increment ΔF, at this time ΔF≈0, since the system is disturbed, there will be a displacement Δu. The original equation becomes

[0073] ([K e ]-λ1[K g (σ)]){Δu}={ΔF};

[0074] Therefore

[0075] det([K e ]-λ1[K g (σ)])=0;

[0076] Therefore, the characteristic value λ1 is obtained, and at this time the critical load is:

[0077] P cr =λ1*1=λ1.

[0078] In one embodiment, S2 can be implemented in the following way:

[0079] First, according to the properties of Euler beam and the established finite element control equation, the target matrix of the instability of the compression beam is calculated,

[0080] According to the properties of Euler beam:

[0081]

[0082] w=w0.....................(2)

[0083] where u is the axial displacement, a function of x and z, w is the deflection, i.e. the longitudinal displacement, x is the axial coordinate, z is the section length, u0(x) is the initial displacement.

[0084] According to Green's strain formula, we have

[0085]

[0086] Control equation: According to the principle of virtual work,

[0087] ∫ V δε x Eε x dV=δu T ·F………………(4)

[0088] Put (3) into (4) and integrate with respect to z, we have:

[0089] Original formula = [W]·[D]·[V]

[0090] [W], [D], [V] represent the matrix symbols of the three

[0091] where

[0092] [W] = [δε x0 δε x1 δε x2 ]

[0093]

[0094] Then transform the matrix [V] and let

[0095]

[0096]

[0097] Discretize by finite element method and let

[0098] u(ξ) = N a (ξ)u1+N b (ξ)u2

[0099] w(ξ) = N1(ξ)w1+N2(ξ)θ1+N3(ξ)w2+N4(ξ)θ2;

[0100] According to Hermit interpolation shape function, the coefficients of the two equations can be calculated, where ξ is a function of x: Non-dimensional, ξ range is [-1, 1];

[0101] Then we can get:

[0102] [Y] = [G] {u} (5)

[0103] Here we can get:

[0104]

[0105] L is the length of the beam of each unit, where

[0106]

[0107] Since

[0108]

[0109] Therefore, we know

[0110]

[0111] Then the boundary conditions are introduced, and the matrix diagonal element method is used to introduce the boundary conditions

[0112] Then assemble according to the stiffness matrix,

[0113] ∑[K e ]{u} = [F0]

[0114] The displacement {u} can be obtained, and then {u} is brought into (5) to obtain [Y];

[0115] Therefore, the initial stress

[0116]

[0117] Also

[0118] [A] T [S] = [S i ][Y]

[0119] Where we can get:

[0120]

[0121] Therefore

[0122]

[0123] Therefore

[0124]

[0125] Then assemble [K g ] to get the total initial stress stiffness matrix [K g (σ)]

[0126] [K g(σ)] = ∑ [K g ]

[0127] Here, [K g (σ)] needs to be Cholesky decomposed, where L is a lower triangular matrix

[0128] [K g (σ)] = LL T

[0129] Then the final target matrix [K]

[0130] [K] = L -1 [K e ]L -T

[0131] The problem is converted to finding the eigenvalue of the target matrix [K].

[0132] Then the target matrix of the buckling of the beam is converted into a linear combination of the tensor product of Pauli matrices through data transformation.

[0133] The object of the present application is to solve the eigenvalue in the buckling problem of the beam. First, the target matrix obtained by the buckling calculation of the beam is obtained. In order to be able to calculate efficiently on a quantum device, the matrix is converted into a linear combination of the tensor product of Pauli matrices through mathematical transformation. This representation enables the quantum device to efficiently evaluate the expectation value of different Pauli operators and finally calculate the required eigenvalue.

[0134] Run the parameterized quantum circuit on the quantum computer, construct the loss function based on the expectation value on the classical computer, and adjust the parameters of the loss function through the optimizer to make the corresponding eigenvalue converge.

[0135] Specifically, the present application adopts a quantum algorithm based on a variational quantum eigenvalue solver.

[0136] Its basic mathematical theory is:

[0137] Ax = λx

[0138] That is, given a specific matrix A, then solve the corresponding eigenvalue λ and eigenvector x of A.

[0139] Construct the characteristic equation: the characteristic equation is the key to solving the eigenvalue, and its form is |A-λI| = 0, where A is the characteristic matrix, I is the unit matrix, and λ is the eigenvalue;

[0140] Calculate the determinant: calculate the determinant in the characteristic equation to get a polynomial equation about λ.

[0141] Solving the polynomial equation: By solving this polynomial equation, we can obtain all the eigenvalues of the characteristic matrix.

[0142] The VQE (Variational Quantum Eigensolver) algorithm mainly consists of three parts: parameterized quantum circuit (Ansatz), measurement and expectation value estimation, and classical optimizer.

[0143] (1) Hamiltonian construction and representation

[0144] The target matrix of the buckling of the compressed beam is converted into a linear combination of Pauli matrix tensor products through data transformation.

[0145] (2) Ansatz design and state preparation

[0146] Once the matrix A is transformed into a form suitable for quantum computing, a parameterized quantum circuit Ansatz can be constructed to generate a trial state and used to measure the corresponding expectation values. The choice of Ansatz is crucial as it determines the accuracy and computational efficiency of the problem being solved.

[0147] Ansatz needs to have sufficient expressive power in the Hilbert space to ensure that it can approximate the eigenstate while avoiding excessive complexity that leads to optimization difficulties. Specifically, this includes the following points:

[0148] Expressibility: Measures the ability of Ansatz to cover the target state space, directly affecting the accuracy of the solution.

[0149] Trainability: Describes how to efficiently optimize Ansatz parameters, avoiding optimization difficulties such as gradient vanishing (Barren Plateau).

[0150] Circuit depth: Determines the consumption of computational resources and affects the computational efficiency of the algorithm. In recent NISQ (Noisy Intermediate-Scale Quantum) devices, too deep a circuit will lead to a decrease in computational accuracy.

[0151] In this embodiment, EfficientSU2 is chosen as Ansatz, which can provide good expressiveness at a relatively shallow circuit depth and is suitable for current quantum hardware.

[0152] (3) Parameter optimization and loss function calculation

[0153] To find the optimal eigenstate, the parameters in the Ansatz need to be continuously optimized so that their expected values converge to the target eigenvalue. This process involves multiple iterative steps, each of which adjusts the parameters and measures the corresponding matrix expectation value. The choice of optimizer is crucial and affects the following three key aspects:

[0154] 1. Computational cost: Different optimization methods require different numbers of measurements, for example, calculating the numerical gradient may require multiple measurements of the expectation value under different parameter configurations.

[0155] 2. Optimization effect: Certain optimization algorithms can alleviate problems such as local minima or gradient vanishing during optimization.

[0156] 3. Convergence speed: The choice of optimizer determines the number of iterations required to solve the eigenvalue.

[0157] The loss function is calculated as follows:

[0158] 1. Generate the quantum state ψ(θ) through the Ansatz, where θ is the adjustable parameter (ψ(θ) corresponds to x in the above).

[0159] 2. Calculate the expectation value of the Hamiltonian under this state: E(θ) = <ψ(θ)|H|ψ(θ)>, where H is the Hamiltonian transformed by the matrix A, and E(θ) corresponds to λ in the above.

[0160] 3. The expectation value E(θ) is used as the loss function, and the optimizer is used to adjust the parameters θ to make them converge.

[0161] For the research needs of the present invention, the SPSA (Simultaneous Perturbation Stochastic Approximation) is chosen as the optimization algorithm. SPSA estimates the gradient by randomly perturbing the parameters, which is suitable for high-dimensional parameter space and performs well under limited computational resources.

[0162] (4) Calculation process and result evaluation

[0163] The entire VQE process consists of multiple iterations, and in each loop:

[0164] 1. Generate the quantum state using the current parameters and measure the corresponding matrix expectation value.

[0165] 2. Calculate the loss function, which is the eigenvalue estimate under the current parameters.

[0166] 3. Adjust the parameters through the optimizer to minimize the loss function and make the eigenvalue converge.

[0167] Finally, the optimization process is visualized by recording the eigenvalue trend in each cycle. At the same time, we compare the eigenvalues obtained by quantum computing with the classical eigenvalue solving method to evaluate the calculation accuracy and the fidelity of the experiment.

[0168] Figure 2 The algorithm is divided into a quantum computing part and a classical computing part, wherein the quantum computing part includes parameter initialization, quantum state preparation, execution of a quantum circuit, measurement of an expected value, quantum expected value estimation, the classical computing part includes total Hamiltonian expected value calculation by a classical adder and variational parameter updating by a classical optimizer to minimize energy. Wherein the classical adder sums all the measured expected values to estimate the total expected value of the Hamiltonian, and judges whether the eigenvalue converges, when the minimum eigenvalue is output, otherwise, the variational parameter is updated by the classical optimizer.

[0169] Figure 3 The figure is a visualization result of an EfficientSU2 quantum circuit, which contains rotation gates R x and R y and a controlled gate CNOT, and quantum bits q0 and q1, and different θ[N] angle parameters.

[0170] Please refer to Figures 4-6 , wherein, Figure 4 is a comparison diagram of the reference value and the quantum-classical hybrid algorithm solving value in the embodiment of the application. Figure 5 is a schematic diagram of the eigenvalue matrix generated by the target matrix [K] in the embodiment of the application. Figure 6 is a schematic diagram of the final target matrix [K] in the embodiment of the application.

[0171] Embodiment two

[0172] Based on the same inventive concept, the embodiment discloses a quantum computing device for structural instability problems, comprising:

[0173] The finite element control equation establishing module is used for establishing a finite element control equation of the instability of the compressed beam.

[0174] The target matrix calculation and conversion module is used for calculating a target matrix of the instability of the compressed beam according to the Euler beam properties and the established finite element control equation, and converting the target matrix of the instability of the compressed beam into a linear combination of Pauli matrix tensor products through data transformation.

[0175] The quantum circuit construction module is used for constructing a parameterized electronic circuit on a classical computer.

[0176] A quantum computing module is configured to run the parameterized quantum circuit by a quantum computer, construct a loss function based on an expected value on a classical computer, and adjust parameters of the loss function by an optimizer so that a corresponding eigenvalue converges.

[0177] Since the device introduced in the embodiment two of the present application is the device used in the quantum computing method for the structural instability problem in the embodiment one of the present application, the specific structure and the deformation of the device can be understood by those skilled in the art based on the method introduced in the embodiment one of the present application, and thus will not be described here again. Any device used in the method in the embodiment one of the present application belongs to the scope of the present application.

[0178] Embodiment three

[0179] Based on the same inventive concept, the present application further provides a computer readable storage medium having a computer program stored thereon, the program being executed by a processor to implement the method of the embodiment one.

[0180] Since the computer readable storage medium introduced in the embodiment three of the present application is the computer readable storage medium used in the quantum computing method for the structural instability problem in the embodiment one of the present application, the specific structure and the deformation of the computer readable storage medium can be understood by those skilled in the art based on the method introduced in the embodiment one of the present application, and thus will not be described here again. Any computer readable storage medium used in the method of the embodiment one of the present application belongs to the scope of the present application.

[0181] Embodiment four

[0182] The present application further provides an electronic device, comprising: at least one processor; and a memory connected with the at least one processor in communication; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the quantum computing method for the structural instability problem of the embodiment one.

[0183] Since the electronic device introduced in the embodiment four of the present application is the electronic device used in the quantum computing method for the structural instability problem in the embodiment one of the present application, the specific structure and the deformation of the electronic device can be understood by those skilled in the art based on the method introduced in the embodiment one of the present application, and thus will not be described here again. Any electronic device used in the method of the embodiment one of the present application belongs to the scope of the present application.

[0184] Those skilled in the art will appreciate that embodiments of the present application can be devised for a variety of other systems which are currently developed or later developed. Those skilled in the art will appreciate that the embodiments of the present application can provide for a method, a system, or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, and the like) embodying computer-readable program code.

[0185] The present application is described in reference to the flowchart illustrations and / or block diagrams of the methods, apparatus (systems) and computer program products according to embodiments of the application. 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, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in one or more of the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in one or more of the flowchart illustrations and / or block diagrams.

[0186] While the preferred embodiments of the application have been described, additional variations and modifications can be made to the embodiments described and shown herein. It is therefore intended that the appended claims cover all such variations and modifications that come within the scope of the application. It should be apparent that apparent that those skilled in the art can make modifications and variations to the embodiments of the application without departing from the spirit and scope of the application. Accordingly, it is intended that the application be construed as including all such modifications and variations as fall within the scope of the claims.

Claims

1. A quantum computing method for structural instability problems, characterized in that, include: Establish the finite element governing equations for the instability of the compressed beam; Based on the properties of Euler beams and the established finite element control equations, the target matrix of the compressive beam instability is calculated, and the target matrix of the compressive beam instability is transformed into a linear combination of Pauli matrix tensor products through data transformation. Constructing parameterized quantum circuits on classical computers; Running the parameterized quantum circuit on a quantum computer, constructing a loss function based on the expected value on a classical computer, and adjusting the parameters of the loss function through an optimizer to make the corresponding eigenvalues ​​converge, includes: running the parameterized quantum circuit on a quantum computer, generating quantum states through the quantum part using the parameterized quantum circuit, and calculating the expected value of Hamiltonian under different quantum states; On a classical computer, a loss function is constructed based on the expected value. The total expected value of the Hamiltonian is estimated by classical computation based on the expected values ​​of each Hamiltonian term, and the variational parameters are adjusted to minimize the energy.

2. The quantum computing method for structural instability problems as described in claim 1, characterized in that, Establish the finite element governing equations for the instability of the compressed beam, including: For the problem of a centrally compressed column, the classic incremental equilibrium equation is obtained: The classical incremental equilibrium equation is transformed into: Where [Ke] is the elastic stiffness matrix, Let the initial stress matrix be given under a certain stress condition. For coefficients, Represents the displacement matrix. Indicates the increment.

3. The quantum computing method for structural instability problems as described in claim 1, characterized in that, Quantum states are generated using parameterized quantization circuits in the quantum part, and the expected value of Hamiltonian in different quantum states is calculated, including: Initialization and preparation of variable quantum states; Execute multiple different quantum circuits to measure different Hamiltonians; Calculate the expected value of each Hamiltonian term.

4. The quantum computing method for structural instability problems as described in claim 1, characterized in that, The overall expectation of the Hamiltonian is estimated based on the expectation of each Hamiltonian term using classical computation, and the variational parameters are adjusted to minimize the energy, including: The expected values ​​of all measurements are summed to estimate the total expected value of the Hamiltonian; Based on the optimization algorithm, the variational parameters are adjusted to minimize the energy.

5. The quantum computing method for structural instability problems as described in claim 1, characterized in that, The parameterized quantum circuit used is EfficientSU2.

6. The quantum computing method for structural instability problems according to claim 5, characterized in that, The optimization algorithm used is the synchronous perturbation stochastic approximation algorithm. SPSA .

7. A quantum computing device for solving structural instability problems, characterized in that, include: The finite element governing equation establishment module is used to establish the finite element governing equations for the instability of a compressed beam. The target matrix calculation and conversion module is used to calculate the target matrix of the compressive beam instability based on the properties of the Euler beam and the established finite element control equations, and to convert the target matrix of the compressive beam instability into a linear combination of Pauli matrix tensor products through data transformation. A quantum circuit building block for constructing parameterized quantum circuits on classical computers; The quantum computing module is used to run the parameterized quantum circuit through a quantum computer, construct a loss function based on the expected value on a classical computer, and adjust the parameters of the loss function through an optimizer to make the corresponding eigenvalues ​​converge. The module includes: running the parameterized quantum circuit through a quantum computer, generating quantum states through the quantum part using the parameterized quantum circuit, and calculating the expected value of Hamiltonian under different quantum states. On a classical computer, a loss function is constructed based on the expected value. The total expected value of the Hamiltonian is estimated by classical computation based on the expected values ​​of each Hamiltonian term, and the variational parameters are adjusted to minimize the energy.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the quantum computing method for structural instability problems as described in any one of claims 1 to 6.

9. An electronic device, comprising: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the quantum computing method for structural instability problems as described in any one of claims 1 to 6.

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