CN116090274A

CN116090274A - Material deformation simulation method, device, terminal and medium based on quantum computation

Info

Publication number: CN116090274A
Application number: CN202111274097.1A
Authority: CN
Inventors: 窦猛汉; 李叶; 朱阳
Original assignee: Origin Quantum Computing Technology Co Ltd
Current assignee: Origin Quantum Computing Technology Co Ltd
Priority date: 2021-10-29
Filing date: 2021-10-29
Publication date: 2023-05-09

Abstract

The invention discloses a material deformation simulation method, a device, a terminal and a medium based on quantum computation, wherein the method comprises the following steps: acquiring a control equation for simulating material deformation; discretizing the control equation to obtain a discretization equation; linearizing the discretization equation to obtain a linear equation; and calculating the solution of the linear equation by using a VQLS variable component linear solver to realize material deformation simulation. By utilizing the embodiment of the invention, the advantage of parallel acceleration of quantum computation can be exerted, the application problem of the quantum computation in material deformation is solved, and the blank of the related technology is filled.

Description

Material deformation simulation method, device, terminal and medium based on quantum computation

Technical Field

The invention belongs to the technical field of quantum computing, and particularly relates to a material deformation simulation method, device, terminal and medium based on quantum computing.

Background

The quantum computer is a kind of physical device which performs high-speed mathematical and logical operation, stores and processes quantum information according to the law of quantum mechanics. When a device processes and calculates quantum information and operates on a quantum algorithm, the device is a quantum computer. Quantum computers are a key technology under investigation because of their ability to handle mathematical problems more efficiently than ordinary computers, for example, to accelerate the time to crack RSA keys from hundreds of years to hours.

Material deformation is an important process in modern industrial production, especially in automotive production. In the early stage of engineering application, the research on the deformation characteristics of materials is mainly based on an experimental method. However, due to complex geometries or high experimental costs, experimental methods are highly unsuitable. With the development of computers, it is possible to study material deformation and optimization design by using numerical simulation, which has an irreplaceable role in the current industrial pre-production process.

Currently, with the continuous development of quantum computing, more and more quantum algorithms are generated. However, in solving the problem of material deformation in production, the application of quantum computing in the aspect is lacking to fully exert the advantage of parallel acceleration of quantum computing, which is a problem to be solved.

Disclosure of Invention

The invention aims to provide a material deformation simulation method, device, terminal and medium based on quantum computation, which are used for solving the defects in the prior art, can exert the parallel acceleration advantage of the quantum computation, solve the application problem of the quantum computation in material deformation and fill the blank of the related technology.

One embodiment of the present application provides a material deformation simulation method based on quantum computation, the method comprising:

acquiring a control equation for simulating material deformation;

discretizing the control equation to obtain a discretization equation;

linearizing the discretization equation to obtain a linear equation;

and calculating the solution of the linear equation by using a VQLS variable component linear solver to realize material deformation simulation.

Optionally, the method further comprises:

after the linear equation is obtained, the matrix condition number of the linear equation is reduced.

Optionally, the method further comprises:

after the calculation of the solution of the linear equation, the solution of the linear equation is converted into classical data.

Optionally, the discretizing the control equation to obtain a discretized equation includes:

and discretizing the control equation by using an FEM finite element method to obtain a discretization equation.

Optionally, the linearizing the discretization equation to obtain a linear equation includes:

and carrying out linearization processing on the discretization equation by using an iteration method to obtain a linear equation.

Optionally, the calculating the solution of the linear equation using a VQLS variable component sub-linear solver includes:

constructing a Hamiltonian quantity corresponding to the linear equation;

the ground state of the Ha Midu quantity is solved as a solution to the linear equation.

Optionally, the solving the ground state of the hamiltonian amount as the solution of the linear equation includes:

and solving the ground state of the Hamiltonian amount by using an adiabatic algorithm to obtain a solution of the linear equation.

Yet another embodiment of the present application provides a material deformation simulation apparatus based on quantum computation, the apparatus comprising:

the acquisition module is used for acquiring a control equation for simulating material deformation;

the discretization module is used for discretizing the control equation to obtain a discretization equation;

the linearization module is used for linearizing the discretization equation to obtain a linear equation;

and the calculation module is used for calculating the solution of the linear equation by using a VQLS variable component sub-linear solver so as to realize material deformation simulation.

A further embodiment of the present application provides a storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of the above when run.

Yet another embodiment of the present application provides an electronic device comprising a memory having a computer program stored therein and a processor configured to run the computer program to perform the method of any of the above.

Compared with the prior art, the material deformation simulation method based on quantum computation provided by the invention has the advantages that a control equation for simulating material deformation is obtained; discretizing the control equation to obtain a discretization equation; linearizing the discretization equation to obtain a linear equation; and calculating the solution of the linear equation by using a VQLS variable component linear solver, and realizing material deformation simulation, thereby exerting the parallel acceleration advantage of quantum calculation, solving the application problem of quantum calculation in material deformation and filling the blank of the related technology.

Drawings

Fig. 1 is a hardware structure block diagram of a computer terminal of a material deformation simulation method based on quantum computation according to an embodiment of the present invention;

fig. 2 is a schematic flow chart of a material deformation simulation method based on quantum computation according to an embodiment of the present invention;

fig. 3 is a schematic diagram of a quantum circuit proposed by the efficient hardware according to the embodiment of the present invention;

FIG. 4 shows a measured delta according to an embodiment of the present invention ^j A quantum circuit schematic of the remainder of (2);

fig. 5 is a schematic structural diagram of a material deformation simulator based on quantum computation according to an embodiment of the present invention.

Detailed Description

The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.

The simulation of the material deformation is ultimately attributed to numerically solving the control equation for the material deformation. The main flow thought of classical numerical analysis is to discretize the control equation into algebraic equations, and finally solve the equations numerically and then return to guide production. However, in practical applications, complex geometric regions in 3-dimensional (3D) space are often faced. If the needs of the project are to be met, the number of grids or points is extremely high, whereas classical methods appear to be very time consuming. Although the computational speed can be increased by considering the simplification of the 3D model into a 2D solution, the accuracy of the prediction is lost.

Based on the above, the embodiment of the invention firstly provides a material deformation simulation method based on quantum computation, which can be applied to electronic equipment such as computer terminals, in particular to common computers, quantum computers and the like.

The following describes the operation of the computer terminal in detail by taking it as an example. Fig. 1 is a hardware structure block diagram of a computer terminal of a material deformation simulation method based on quantum computation according to an embodiment of the present invention. As shown in fig. 1, the computer terminal may include one or more (only one is shown in fig. 1) processors 102 (the processor 102 may include, but is not limited to, a microprocessor MCU or a processing device such as a programmable logic device FPGA) and a memory 104 for storing data, and optionally, a transmission device 106 for communication functions and an input-output device 108. It will be appreciated by those skilled in the art that the configuration shown in fig. 1 is merely illustrative and is not intended to limit the configuration of the computer terminal described above. For example, the computer terminal may also include more or fewer components than shown in FIG. 1, or have a different configuration than shown in FIG. 1.

The memory 104 may be used to store software programs and modules of application software, such as program instructions/modules corresponding to the material deformation simulation method based on quantum computation in the embodiment of the present application, and the processor 102 executes the software programs and modules stored in the memory 104, thereby performing various functional applications and data processing, that is, implementing the method described above. Memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory remotely located relative to the processor 102, which may be connected to the computer terminal via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.

The transmission means 106 is arranged to receive or transmit data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider of a computer terminal. In one example, the transmission device 106 includes a network adapter (Network Interface Controller, NIC) that can connect to other network devices through a base station to communicate with the internet. In one example, the transmission device 106 may be a Radio Frequency (RF) module for communicating with the internet wirelessly.

It should be noted that a real quantum computer is a hybrid structure, which includes two major parts: part of the computers are classical computers and are responsible for performing classical computation and control; the other part is quantum equipment, which is responsible for running quantum programs so as to realize quantum computation. The quantum program is a series of instruction sequences written by a quantum language such as the qlunes language and capable of running on a quantum computer, so that the support of quantum logic gate operation is realized, and finally, quantum computing is realized. Specifically, the quantum program is a series of instruction sequences for operating the quantum logic gate according to a certain time sequence.

In practical applications, quantum computing simulations are often required to verify quantum algorithms, quantum applications, etc., due to the development of quantum device hardware. Quantum computing simulation is a process of realizing simulated operation of a quantum program corresponding to a specific problem by means of a virtual architecture (namely a quantum virtual machine) built by resources of a common computer. In general, it is necessary to construct a quantum program corresponding to a specific problem. The quantum program, namely the program for representing the quantum bit and the evolution thereof written in the classical language, wherein the quantum bit, the quantum logic gate and the like related to quantum computation are all represented by corresponding classical codes.

Quantum circuits, which are one embodiment of quantum programs, also weigh sub-logic circuits, are the most commonly used general quantum computing models, representing circuits that operate on qubits under an abstract concept, the composition of which includes qubits, circuits (timelines), and various quantum logic gates, and finally the results often need to be read out by quantum measurement operations.

Unlike conventional circuits, which are connected by metal lines to carry voltage or current signals, in a quantum circuit, the circuit can be seen as being connected by time, i.e., the state of the qubit naturally evolves over time, as indicated by the hamiltonian operator, during which it is operated until a logic gate is encountered.

One quantum program is corresponding to one total quantum circuit, and the quantum program refers to the total quantum circuit, wherein the total number of quantum bits in the total quantum circuit is the same as the total number of quantum bits of the quantum program. It can be understood that: one quantum program may consist of a quantum circuit, a measurement operation for the quantum bits in the quantum circuit, a register to hold the measurement results, and a control flow node (jump instruction), and one quantum circuit may contain several tens to hundreds or even thousands of quantum logic gate operations. The execution process of the quantum program is a process of executing all quantum logic gates according to a certain time sequence. Note that the timing is the time sequence in which a single quantum logic gate is executed.

It should be noted that in classical computation, the most basic unit is a bit, and the most basic control mode is a logic gate, and the purpose of the control circuit can be achieved by a combination of logic gates. Similarly, the way in which the qubits are handled is a quantum logic gate. Quantum logic gates are used, which are the basis for forming quantum circuits, and include single-bit quantum logic gates, such as Hadamard gates (H gates, ada Ma Men), bery-X gates (X gates), bery-Y gates (Y gates), bery-Z gates (Z gates), RX gates, RY gates, RZ gates, and the like; two or more bit quantum logic gates, such as CNOT gates, CR gates, CZ gates, iSWAP gates, toffoli gates, and the like. Quantum logic gates are typically represented using unitary matrices, which are not only in matrix form, but also an operation and transformation. The effect of a general quantum logic gate on a quantum state is calculated by multiplying the unitary matrix by the matrix corresponding to the right vector of the quantum state.

Referring to fig. 2, fig. 2 is a schematic flow chart of a material deformation simulation method based on quantum computation according to an embodiment of the present invention, which may include the following steps:

s201, acquiring a control equation for simulating material deformation;

in particular, the simulation of material deformation is ultimately attributed to solving the control equation for material deformation. The control equation and the related equations used to solve the equation are described below.

Within a certain calculation domain Ω, the differential control equation (or stress equation) of the stress balance problem is:

wherein sigma represents stress, x represents different directions of material deformation, b represents volume force acting on the object material, and i and j represent dummy marks.

In solving partial differential equations, it is necessary to give boundary conditions that satisfy partial differential equations:

wherein u is _i The displacement is indicated by the fact that,

representing the displacement at boundary 1 Γ ₁ Represents boundary 1, n _i Represents the normal direction of a surface somewhere in the material, +.>

Representing the shear stress at the boundary Γ ₂ Representing boundary 2. The strain tensor is in the form of:

wherein ε _ij Indicating strain.

Constitutive equations are determined by the physical properties of a material, and the stress and strain rates, or the functional relationship between the stress tensor and the strain tensor, are generally referred to as constitutive equations. The constitutive equation for the secondary elasticity is:

wherein S represents a nominal shear force, delta represents a Cronecker symbol, epsilon _e Indicating effective deflection strain, v indicatingPoisson's ratio, k represents the principal stress direction index, offset strain

And:

wherein e=nσ ₀ /ε ₀ Stress-strain curve for uniaxial at ε _e Slope at =0, σ _e Is the elastic limit. The relationship of the power exponent is satisfied between the shear strain and the shear stress, wherein the power exponent is represented by n. Wherein sigma ₀ ,ε ₀ Respectively represent the stress and strain of the material under pure shear stress, not 0 terms.

The set of equations constructed above can be used to solve the stress balance problem of any sub-elastic material in the field of material deformation.

S202, discretizing the control equation to obtain a discretization equation;

specifically, the control equation may be discretized by using a FEM (Finite Element Method) finite element method to obtain a discretized equation.

Illustratively, the control equation is converted to a weak form using the test function Φ:

wherein sigma _ij (u _k ) Representing the stress to which the object is subjected, the function Φ is a test function. For numerical solution, all variables within the computation domain Ω need to be discretized and the intra-object determination by interpolation between nodesA displacement field at any point. The displacement and test functions in the weak form of the control equation can be represented by a shape function N (x) by discretizing the computational domain into a finite number of cells:

wherein the function N is a shape function, and the test function can be given by using a Bubnov-Galerkin (Bubanov-Galerkin) method, and the strain displacement is expressed in the following discrete form by the shape function:

the simultaneous discretized stress and strain equations by which the stress can be expressed as a function of strain:

where a denotes a discrete point, k, l denotes meaning consistent with i, j, only for distinguishing i, j.

The final discretized equation set is:

s203, linearizing the discretization equation to obtain a linear equation;

specifically, the discretization equation may be linearized by using an iterative method to obtain a linear equation.

Illustratively, the discretized equation is a nonlinear algebraic equation set, which cannot be directly solved. Can be utilizedThe Newton-Raphson method solves this equation with the basic idea: for the solution of the equation, first a solution is given

Is +.>

To correct this predicted value, a correction value is introduced +.>

Namely: />

When (when)

Small enough, the nonlinear equation set is solved by iteration, and each iteration equation set can be converted into a linear equation set:

wherein:

s204, calculating a solution of the linear equation by using a VQLS variable component sub-linear solver, and realizing material deformation simulation.

Specifically, the hamiltonian amount corresponding to the linear equation may be constructed; the ground state of the Ha Midu quantity is solved as a solution to the linear equation.

For a linear system

Wherein A is an N x N dimensional hermitian,/a matrix>

Is an N-dimensional vector. In this section, a variable component sub-linear solver (Variational Quantum Linear Solver, VQLS) may be employed to solve the system of linear equations. />

The linear equation is rewritten as

In which A= [ K ] _aibk ],/>

In the VQLS solving process, information of the linear equation may be input to the solver. One is a linear combination of S unitary matrices (unitary) decomposed from matrix a to facilitate encoding matrix a into quantum wires. Here, a may be expressed as:

wherein lambda is _s Coefficients, ω, being linear combinations _s Is a unitary matrix (unitary operator). The other input information of VQLS is represented by vector +.>

Encoding the resulting unitary matrix U, the unitary matrix U being used for preparing an AND vector +.>

Proportional quantum state |b>The method comprises the following steps: vector +.>

Normalized and encoded into a quantum wire in the form of |b>＝U|0>. Solution of linear system>

Represented by a variable-factorized quantum state heuristic wave function>

May be constructed using variable interconnect lines such as HEA (Hardware Efficient Ansatz, high efficiency hardware interconnect), as shown in fig. 3. Wherein, the quantum logic gate combination comprising d layers of RY gates and CNOT gates, the variable parameter is expressed as rotation angle +.>

Is a vector of (a). Solution |x>Is Hamiltonian quantity H _G Is the ground state of (2):

defining a Global loss function C _G The method comprises the following steps:

wherein, the liquid crystal display device comprises a liquid crystal display device,

representing a series of U-gates.

Whereas for a large number of qubit cases, the global loss function has a large part of regional gradients equal to zero, like a Barren Plateau (BP). To improve the situation in a large number of qubitsWith the trainability, a local loss function can be introduced. First, a local Hamiltonian H is defined _L The method comprises the following steps:

wherein 0 _j >In the zero state of the qubit j,

is an identity matrix other than qubit j. The corresponding local loss function is defined as:

in a specific implementation, an adiabatic algorithm may be utilized to solve for the ground state of the hamiltonian.

Illustratively, a random one is initialized

Start and use->

Updating parameters, wherein β is the time step, +.>

About->

And C _G Corresponding quantum wire measurements may be constructed. For C _L The measurement is required:

/>

due to |0 _j ><0 _j |＝(I _j +Z _j )/2，Z _j Quantum logic gate Z gate represented on jth qubit. The above formula can be expressed as:

already at C _G Measurement of (1), except->

Outer delta ^j The remainder of (a) can be measured by the quantum wire shown in FIG. 4, and when the wire does not include (includes) the S gate,/can be calculated>

Real (imaginary) part of (a) a (b). When->

At this time, the local and global loss functions decrease with increasing virtual time (virtual time) until C _L (C _G ) When the value of the sum is =0,

i.e. the final solution of the linear system.

In order to improve the efficiency of finding the Hamiltonian amount, a Hamiltonian amount evolution method is proposed.

Illustratively, the hamiltonian as a function of time t is constructed using Hamiltonian Morphing (hamiltonian evolution):

wherein (1)>

t∈[0,1]X represents a quantum logic gate X gate.

In order to find the ground state of the hamiltonian at each moment, an adiabatic algorithm is used to construct the energy expectations of the hamiltonian:

in this process, the gradient descent method can be used to update parameters

Beta is the time step, < >>

By quantum circuit measurement, parameter->

Classical computer updates may be employed. The parameters when the hamiltonian ground state is found at each moment are +.>

As initial parameters at the next time, namely: for arbitrary matrix A (t _i ) Coefficient t _i Gradually increasing from 0 to 1, at each t _i Find H (t) _i ) Is the ground state of (2); parameter of the above moment->

For the initial position, find H (t _i+1 ) Is a ground state of (c). And when t=1, the obtained hamiltonian ground state is the solution of the linear equation set.

In practical applications, after the linear equation is obtained, the number of matrix conditions of the linear equation can be reduced. Specifically, the time complexity of the variable component linear solver is related to the condition number of the matrix, and in order to increase the computation speed of VQLS, the condition number of the matrix a may be reduced by using a SPAI (Sparse Approximate Inverse, sparse approximation inverse) preprocessing method.

In practical application, the solution of the linear equation is calculatedThe solution of the linear equation is then converted into classical data. Specifically, in order to realize the conversion from quantum data to classical data, a tomograph algorithm may be used to extract the |x > of the quantum state into classical vector data

?>

Wherein the coefficient eta may be determined by

And (5) obtaining.

QRAM in tomography algorithms is a quantum storage device for quantum computers. QRAM can perform the conversion as follows:

∑α _i |i>|0>→∑α _i |i>|d _i >

wherein i>＝|i _n-1 ,i _n-2 ,…,i ₂ ,i ₁ ,i ₀ >Representing an n-bit address register, data register |d _i >Representing a classical data entry stored at address i, a _i Is a complex amplitude. QRAM is compatible with classical computers, which read the data in QRAM without additional consumption. Quantum data can be conveniently post-processed to classical data using QRAM.

It can be seen that by obtaining a control equation for modeling material deformation; discretizing the control equation to obtain a discretization equation; linearizing the discretization equation to obtain a linear equation; and calculating the solution of the linear equation by using a VQLS variable component linear solver, and realizing material deformation simulation, thereby exerting the parallel acceleration advantage of quantum calculation, solving the application problem of quantum calculation in material deformation and filling the blank of the related technology.

Referring to fig. 5, fig. 5 is a schematic structural diagram of a quantum circuit-based data size comparison device according to an embodiment of the present invention, corresponding to the flow shown in fig. 2, the device includes:

an acquisition module 501 for acquiring a control equation for modeling material deformation;

the discretization module 502 is configured to discretize the control equation to obtain a discretization equation;

a linearization module 503, configured to perform linearization processing on the discretization equation to obtain a linear equation;

and the calculating module 504 is used for calculating the solution of the linear equation by using the VQLS variable component sub-linear solver to realize material deformation simulation.

Specifically, the device further comprises:

and the reducing module is used for reducing the number of matrix conditions of the linear equation after the linear equation is obtained.

Specifically, the device further comprises:

and the conversion module is used for converting the solution of the linear equation into classical data after the solution of the linear equation is calculated.

Specifically, the discretization module is specifically configured to:

Specifically, the linearization module is specifically configured to:

Specifically, the computing module includes:

the construction unit is used for constructing the Hamiltonian quantity corresponding to the linear equation;

and the solving unit is used for solving the ground state of the Ha Midu quantity as a solution of the linear equation.

Specifically, the solving unit is specifically configured to:

The embodiment of the invention also provides a storage medium, in which a computer program is stored, wherein the computer program is configured to perform the steps of any of the method embodiments described above when run.

Specifically, in the present embodiment, the above-described storage medium may be configured to store a computer program for executing the steps of:

s1, acquiring a control equation for simulating material deformation;

s2, discretizing the control equation to obtain a discretization equation;

s3, linearizing the discretization equation to obtain a linear equation;

s4, calculating a solution of the linear equation by using a VQLS variable component sub-linear solver, and realizing material deformation simulation.

Specifically, in the present embodiment, the storage medium may include, but is not limited to: a usb disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a removable hard disk, a magnetic disk, or an optical disk, or other various media capable of storing a computer program.

The present invention also provides an electronic device comprising a memory having a computer program stored therein and a processor arranged to run the computer program to perform the steps of any of the method embodiments described above.

Specifically, the electronic apparatus may further include a transmission device and an input/output device, where the transmission device is connected to the processor, and the input/output device is connected to the processor.

Specifically, in the present embodiment, the above-described processor may be configured to execute the following steps by a computer program:

s1, acquiring a control equation for simulating material deformation;

s2, discretizing the control equation to obtain a discretization equation;

s3, linearizing the discretization equation to obtain a linear equation;

While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims

1. A method for modeling deformation of a material based on quantum computation, the method comprising:

acquiring a control equation for simulating material deformation;

discretizing the control equation to obtain a discretization equation;

linearizing the discretization equation to obtain a linear equation;

2. The method according to claim 1, wherein the method further comprises:

3. The method according to claim 1, wherein the method further comprises:

4. The method of claim 1, wherein discretizing the control equation results in a discretized equation comprising:

5. The method of claim 1, wherein linearizing the discretized equation to obtain a linear equation comprises:

6. The method of claim 1, wherein calculating the solution of the linear equation using a VQLS variable component sub-linear solver comprises:

constructing a Hamiltonian quantity corresponding to the linear equation;

7. The method of claim 6, wherein said solving the ground state of the hamiltonian amount as a solution of the linear equation comprises:

8. A material deformation simulation device based on quantum computing, the device comprising:

9. A computer terminal comprising a machine-readable storage medium having stored therein a computer program and a processor arranged to run the computer program to perform the method of any of claims 1-7.

10. A computer readable storage medium, characterized in that the computer readable storage medium has stored therein a computer program which, when executed by a computer, implements the method of any of claims 1-7.