A material electron density detection method, system, medium and electronic device

Abstract

The present disclosure provides a material electron density detection method, system, medium and electronic equipment, comprising: generating an initial random state of a quantum bit based on a random number, performing time evolution processing on the initial random state to obtain a time evolution operator, and performing Chebyshev polynomial expansion on the time evolution operator; the Hamiltonian of the material to be measured is decomposed into a linear combination of tensor products of Pauli matrices by the Pauli basis decomposition method; according to the tensor product, the time evolution operator is decomposed into the evolution accumulation of multiple time steps, mapped into a quantum circuit, and the probability value of the auxiliary quantum bit in the ground state is measured; according to the probability value processing, the inner product corresponding to each time step is obtained, and the electron density is obtained according to the sum of the product of the inner product and the coefficient. Reduce the number of quantum bits required, realize the filtering of the random state in the evolution process, realize the calculation of the electron density of large-scale multi-electron materials through the mixed calculation of the quantum computer and the classical computer, and reduce the occupied memory.

Description

Technical Field

[0001] This disclosure relates to the field of quantum computing technology, and in particular to a method, system, medium, and electronic device for detecting the electron density of a material. Background Technology

[0002] Electron density is the probability distribution function of electrons at various locations in a material, and it is a physical quantity reflecting the ground state of the material's electrons. Existing methods for calculating electron density include two approaches. One involves using a classical computer to diagonalize the Hamiltonian H of the electrons in the material to obtain the eigenstates. The electron density is then calculated by squared the modulus of the projection amplitudes of these eigenstates at different locations. However, the computation time required for the diagonalization step increases cubically with the number of electrons. Therefore, diagonalizing the Hamiltonian becomes difficult when the number of electrons in the material increases, significantly limiting its application in calculating complex materials with large electron scales. Another approach is the linear random state method. This method filters random states through a Fermi-Dirac distribution to obtain the occupied states. The electron density is then calculated by squared the modulus of the occupied states and averaged over the random states. While this method avoids the time-consuming diagonalization step, the random state matrix used consumes a large amount of memory. Constructing a Hamiltonian and random states containing millions of electrons significantly increases the memory consumption of classical computers. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this disclosure proposes a method, system, medium, and electronic device for detecting the electron density of materials. This method involves expanding the Fermi-Dirac distribution using Chepshev polynomials and mapping it to a quantum circuit. The probability value of the auxiliary qubit in the ground state is measured, filtering random states during the evolution process. In a classical computer, the inner product corresponding to each time step is obtained based on the probability value. The electron density is then calculated by summing the inner product and the coefficients. This hybrid quantum and classical computer computation enables the calculation of the electron density of large-scale multi-electron materials, reducing memory usage.

[0004] To achieve the above objectives, this disclosure provides a method for detecting the electron density of a material, comprising: The initial random state of a qubit is generated based on random numbers, wherein the random numbers are generated by a classical computer based on the number of electrons in the material under test; The initial random state is subjected to time evolution processing to obtain a time evolution operator, and the time evolution operator is subjected to Chepshev polynomial expansion; The Hamiltonian of the material under test is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. Based on the tensor product, the time evolution operator is decomposed into multiple time-step evolution accumulations, mapped onto the quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. The inner product corresponding to each time step is obtained by processing the probability value. The electron density is obtained by summing the products of the inner product and the coefficients, wherein the coefficients are obtained by performing a Chepshov polynomial expansion of the Fermi-Dirac distribution using a classical computer.

[0005] Optionally, the initial random state for generating qubits based on random numbers includes: Generate several random rotation Z-gates and random rotation X-gates based on the random numbers; Each of the qubits is initialized to the ground state; At least one Hadamard gate, the random rotation Z gate, and the random rotation X gate are sequentially applied to each of the qubits to generate the initial random state composed of the qubits.

[0006] Optionally, the step of performing time evolution processing on the initial random state to obtain the time evolution operator includes: The initial random state is subjected to time evolution based on the Fermi-Dirac distribution, and the energy is represented by the Hamiltonian of the material under test to obtain the time evolution operator.

[0007] Optionally, the Chepshov polynomial expanded by the time evolution operator corresponds to the quantum circuit.

[0008] Optionally, the step of decomposing the time evolution operator into multiple time-step evolution accumulations based on the tensor product and mapping them to the quantum circuit includes: The Chepshov polynomial expanded by the time evolution operator is represented in the quantum circuit by the evolution operator; Based on the tensor product, the evolution operator is decomposed into several evolution accumulations corresponding to the time steps; Several evolutionary accumulations are sequentially mapped onto the quantum circuit to obtain the step-size evolution operator corresponding to each time step.

[0009] Optionally, the probability value of the measurement-assisted qubit in the ground state includes: The auxiliary qubit is prepared in the ground state; Apply a Hadamard gate and / or a phase gate to the auxiliary qubit, evolve and accumulate the initial random state or the random state corresponding to each time step, and apply the Hadamard gate to the auxiliary qubit again to obtain the probability value of the auxiliary qubit being in the ground state.

[0010] Optionally, the step of processing the probability value to obtain the inner product corresponding to each time step, and obtaining the electron density based on the sum of the products of the inner product and the coefficients, includes: Based on the probability value, the real and imaginary parts of the inner product of the random state corresponding to the time step and the initial random state are obtained, and the inner product is determined. Multiply the inner product corresponding to the time step by the coefficient, and sum the products corresponding to each time step to obtain the electron density of the material under test.

[0011] It also includes a system for detecting the electron density of materials, comprising: The random state generation module generates the initial random state of the qubit based on random numbers, wherein the random numbers are generated by a classical computer based on the number of electrons in the material under test; The evolution processing module performs time evolution processing on the initial random state to obtain a time evolution operator, performs Chepshov polynomial expansion on the time evolution operator, and decomposes the Hamiltonian of the material under test into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. The quantum circuit mapping module decomposes the time evolution operator into multiple time-step evolution accumulations based on the tensor product, maps them to the quantum circuit, and measures the probability value of the auxiliary qubit in the ground state. The data processing module processes the probability value to obtain the inner product corresponding to each time step, and obtains the electron density by summing the products of the inner product and the coefficients, wherein the coefficients are obtained by performing a Chepshev polynomial expansion of the Fermi-Dirac distribution using a classical computer.

[0012] It also includes a computer-readable storage medium storing a computer program for running the detection method, wherein the computer program causes a computer to perform the detection method as described in any of the above technical solutions.

[0013] It also includes an electronic device, comprising: A quantum computer generates an initial random state for a qubit based on random numbers, performs time evolution processing on the initial random state to obtain a time evolution operator, and performs a Chepshov polynomial expansion on the time evolution operator. The Hamiltonian of the material under test is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. Based on the tensor products, the time evolution operator is decomposed into evolutionary accumulations of multiple time steps, mapped onto a quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. A classical computer generates the random number based on the number of electrons in the material under test, and receives the probability value sent by the quantum computer. It processes the probability value to obtain the inner product corresponding to each time step, and obtains the electron density by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshov polynomial expansion on the Fermi-Dirac distribution using a classical computer. One or more processors; memory; and One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs being used to perform the detection method as described in any of the above technical solutions.

[0014] The above technical solution has the following beneficial effects: By generating initial random states using a quantum computer, the number of qubits required is reduced. By expanding the Fermi-Dirac distribution into Chepshev polynomials and mapping it to a quantum circuit, the probability value of the auxiliary qubit in the ground state is measured, thus filtering the random states during the evolution process. In a classical computer, the inner product corresponding to each time step is obtained based on the probability value. The electron density is obtained by summing the inner product and the coefficients. By using a hybrid quantum computer and classical computer to calculate the electron density of large-scale multi-electron materials, the memory usage is reduced. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this disclosure 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 this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of the detection method in this disclosure; Figure 2 This is a flowchart illustrating the initial random state for generating qubits in this disclosure; Figure 3 This is a flowchart illustrating the decomposition of the time evolution operator into evolutionary accumulation in this disclosure; Figure 4 This is a flowchart illustrating the process of obtaining electron density in this disclosure; Figure 5 This is a schematic diagram of the detection system in this disclosure; Figure 6 This is a schematic diagram of the quantum circuit for generating the initial random state in this disclosure. Detailed Implementation

[0017] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this disclosure.

[0018] Existing methods for calculating electron density obtain the eigenstates of electrons by diagonalizing the Hamiltonian H of the material electrons using classical computers, and then calculate the electron density by squared the modulus of the amplitude projected onto the eigenstates at different positions. However, this approach is significantly limited when calculating complex materials with large-scale, multi-electron structures. Another method filters random states through the Fermi-Dirac distribution to obtain occupied states, then squares the modulus of the occupied states and averages the random states to obtain the electron density. However, the random state matrix consumes a huge amount of memory, requiring the construction of Hamiltonians and random states containing millions of electrons, which greatly consumes the operating memory of classical computers.

[0019] In some embodiments of this disclosure, reference is made to Figure 1 This disclosure provides a method for detecting the electron density of a material, comprising: S1. The initial random state of the qubit is generated based on random numbers, where the random numbers are generated by a classical computer based on the number of electrons in the material under test.

[0020] Specifically, a classical computer generates random numbers corresponding to the number of electrons in the material under test, which the quantum computer then uses to generate the initial random state of the qubits, providing a reference quantum state for subsequent time evolution processing and inner product calculations. For example, for a qubit consisting of 2... N For test materials consisting of 2 electrons, current methods require storing 2 electrons. N In this embodiment, only an initial random state consisting of N qubits needs to be prepared for subsequent time evolution processing.

[0021] S2. Perform time evolution processing on the initial random state to obtain the time evolution operator, and perform Chepshov polynomial expansion on the time evolution operator.

[0022] Specifically, the initial random state is subjected to time evolution processing, using the Fermi-Dirac distribution. By representing energy in terms of the Hamiltonian of the material under test, the time evolution operator is obtained. The time evolution operator is expanded using Chepshev polynomials, decomposed into a polynomial summation form, which simplifies the computational complexity. Each term of the expanded polynomial corresponds to a quantum circuit, enabling fast computation through the quantum circuit.

[0023] S3. The Hamiltonian of the material to be tested is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method.

[0024] Specifically, the Pauliji decomposition method is used to decompose 2 N Hamiltonian of the test material consisting of 1 electron Decomposed into N Pauli matrices { , , , A linear combination of the tensor products of}, i.e. ,in, Let H be the tensor product of N Pauli matrices. Since the Hamiltonian H is a Hermitian matrix and the Pauli matrices can be implemented using quantum gate operations, the specific Pauli decomposition process of the Hamiltonian H can be implemented through the Jordan-Wigner transformation method.

[0025] S4. Based on the tensor product, the time evolution operator is decomposed into multiple time-step evolution accumulations, mapped onto the quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured.

[0026] Specifically, since each term of the polynomial obtained by expanding the time evolution operator into a Chepshov polynomial corresponds to a quantum circuit, and is represented by a step-size evolution operator, the time evolution operator is decomposed into multiple time-step evolution accumulations using a Trotter algorithm. Then, the evolution accumulation of each time step is sequentially mapped to a quantum circuit with N qubits, resulting in a quantum circuit where the evolution accumulation acts on a random state at any time step, reducing the difficulty of quantum circuit implementation. By constructing auxiliary qubits and preparing them to the ground state, performing gate operations, and performing evolution accumulation on the initial random state or the random state corresponding to each time step, the probability value of the auxiliary qubit being in the ground state is measured. Instead of measuring the quantum state of multiple electrons, only the ground state probability of a single auxiliary qubit is measured, reducing measurement complexity.

[0027] S5. The inner product corresponding to each time step is obtained by processing the probability value. The electron density is obtained by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshov polynomial expansion of the Fermi-Dirac distribution using a classical computer.

[0028] Specifically, based on the probability value of the auxiliary qubit in the ground state obtained by measurement, the inner product corresponding to each time step is obtained by classical computer processing. This product is then multiplied by the coefficients of each level of expansion obtained by Chepshev polynomial expansion of the Fermi-Dirac distribution. Finally, the product results of all time steps are summed to obtain the electron density of the material under test. Chepshev polynomial expansion of the Fermi-Dirac distribution is used to reduce the calculation error of the electron density.

[0029] Reference Figure 2 In some embodiments of this disclosure, the initial random state for generating qubits based on random numbers includes: S11. Generate several random rotating Z-gates and random rotating X-gates based on random numbers; S12. Initialize each qubit to the ground state; S13. Apply at least one Hadamard gate, a random rotation Z gate, and a random rotation X gate sequentially to each qubit to generate an initial random state composed of qubits.

[0030] Specifically, for the combination of 2 N The test material consists of 1 electron, and an initial random state consisting of N qubits is prepared. 2N random number generators located between 0 and 2^N qubits are generated using a classical computer's random number generator. A random number between N random numbers Used to generate N random rotating X-gates N random numbers Used to generate N random rotating Z-gates Simultaneously, the N qubits of the quantum computer are initialized to their ground state. Then, N Hadamard gates are applied to the N qubits in the ground state, followed by a random rotation Z-gate applied sequentially to each qubit. and a random rotating X-door Constructing quantum circuits (refer to) Figure 6 To generate a random state consisting of N qubits. As the initial random state, it is ensured that the initial random state has a certain degree of randomness and complexity.

[0031] In some embodiments of this disclosure, the initial random state is subjected to time evolution processing to obtain a time evolution operator, including: The initial random state is processed by time evolution based on the Fermi-Dirac distribution, and the energy is represented by the Hamiltonian of the material under test to obtain the time evolution operator.

[0032] Specifically, based on the Fermi-Dirac distribution, the initial random state is subjected to time evolution processing, and the energy variables in the evolution process are equivalently replaced by the Hamiltonian of the material under test, thus obtaining the time evolution operator. Where β = 1 / (kT), k is the Boltzmann constant, T is the thermodynamic temperature, and μ is the chemical potential, which conforms to the energy level occupancy law of electrons and ensures the accuracy of the measurement.

[0033] In some embodiments of this disclosure, the Chepshov polynomials expanded by the time evolution operator correspond to quantum circuits.

[0034] Specifically, time evolution operators It can be expanded as follows: This yields the random state of each action after expansion. The Chepshev polynomials expanded by the time evolution operator correspond to quantum circuits, allowing the time evolution operator to be... The evolution process is rapidly processed through a quantum circuit that maps to N qubits.

[0035] Reference Figure 3In some embodiments of this disclosure, the time evolution operator is decomposed into multiple time-step evolution accumulations based on the tensor product, and mapped to the quantum circuit as follows: S41. The Chepshov polynomial expanded by the time evolution operator is represented in a quantum circuit by the evolution operator; S42. Based on the tensor product, decompose the evolution operator into evolutionary accumulations corresponding to several time steps; S43. Map several evolution accumulations sequentially into the quantum circuit to obtain the step size evolution operator corresponding to each time step.

[0036] Specifically, after the time evolution operator is expanded using Chepshev polynomial series, the random state of each term in the expansion is obtained. In quantum circuits, it is transformed into an evolution operator. It is indicated by Hamiltonian. It has already been decomposed into a linear combination of Pauli matrix tensor products, therefore the evolution operator can be decomposed using Trotter decomposition. Decomposed into evolutionary accumulation over m time steps m ranges from 0 to K, and the evolution operator corresponds to each time step. for By sequentially mapping m evolutionary cumulative units U onto a quantum circuit of N qubits, the step-size evolution operator corresponding to each time step can be obtained. Used to calculate the random state of the action of the time evolution operator in a quantum circuit. The occupied states of electrons are obtained by filtering quantum random states.

[0037] In some embodiments of this disclosure, measuring the probability value of the auxiliary qubit in the ground state includes: The auxiliary qubit is prepared in the ground state; a Hadamard gate and / or a phase gate are applied to the auxiliary qubit to evolve and accumulate the initial random state or the random state corresponding to each time step, and the Hadamard gate is applied to the auxiliary qubit again to obtain the probability value of the auxiliary qubit being in the ground state.

[0038] Specifically, an auxiliary qubit is set up and initialized to the ground state. This is used to determine the initial reference for measurement. By obtaining the real part of the inner product corresponding to the random states with even time steps m = 0, 2, 4…2n and the initial random state, the inner product required to calculate the electron density is obtained when k is even. By obtaining the imaginary part of the inner product between the random state and the initial random state corresponding to odd time steps m = 1, 3, 5, 7…2n+1, the inner product required to calculate the electron density is obtained when k is odd. .

[0039] Furthermore, when obtaining even-numbered time steps, an auxiliary qubit is prepared in the initial state, and then a Hadamard gate is applied to the auxiliary qubit. Then, the random state corresponding to each time step is accumulated and evolved by mapping the initial random state through a quantum circuit. Then, the Hadamard gate operation is performed again on the auxiliary qubit, and finally the probability value P(0) of the auxiliary qubit being in the ground state is measured.

[0040] Furthermore, when obtaining odd-numbered time steps, an auxiliary qubit is prepared in the initial state, a Hadamard gate is applied to the auxiliary qubit, and a phase gate is applied to the auxiliary qubit. Then, for the random state corresponding to each time step and the initial random state, evolution accumulation is performed through a mapping quantum circuit. Then, the Hadamard gate operation is performed again on the auxiliary qubit, and finally the probability value P(0) of the auxiliary qubit being in the ground state is measured.

[0041] By using measurement-assisted qubits to replace the overall measurement of the quantum circuit, the inner product solution is transformed into the probability calculation of the ground state of a single qubit, reducing the difficulty of quantum measurement. The quantum circuit at each time step can be measured by the auxiliary qubits, which is suitable for subsequent calculation of electron density.

[0042] Reference Figure 4 In some embodiments of this disclosure, the inner product corresponding to each time step is obtained based on the probability value, and the electron density is obtained by summing the products of the inner product and the coefficients, including: S51. Based on the probability value, obtain the real and imaginary parts of the inner product between the random state corresponding to the time step and the initial random state, and determine the inner product; S52. Multiply the inner product corresponding to the time step by the coefficient, and sum the products corresponding to each time step to obtain the electron density of the material under test.

[0043] Specifically, the probability value P(0) obtained from the quantum computer is acquired using a classical computer. Then, 2P(0)⁻¹ is calculated to obtain the real part Re(Un) of the inner product of the random state and the initial random state when the time step is even, and the imaginary part Im(Un) of the inner product when the time step is odd. This yields the real and imaginary parts of the inner product of the random state and the initial random state over m time steps, thus determining the inner product as... =Re(Un)+Im(Un).

[0044] Obtaining the Fermi-Dirac distribution on a classical computer The coefficients after Chepshev polynomial expansion: ; in, For Chepshev polynomials The energy E is obtained by integrating over the interval [-1, 1].

[0045] Multiply the inner product corresponding to the time step by the coefficient, i.e. And sum the products corresponding to each time step: ρ= ; The electron density ρ of the material under test is obtained by processing, and a reliable electron density can be obtained with a small time step by weighted summation of the coefficients after Chepshev polynomial expansion.

[0046] Reference Figure 5 In some embodiments of this disclosure, the disclosure also includes a system for detecting the electron density of a material, comprising: Random state generation module 1 generates the initial random state of the qubit based on random numbers, wherein the random numbers are generated by a classical computer based on the number of electrons in the material under test; Evolution processing module 2 performs time evolution processing on the initial random state to obtain a time evolution operator, and performs Chepshov polynomial expansion on the time evolution operator; the Hamiltonian of the material under test is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method; Quantum circuit mapping module 3 decomposes the time evolution operator into multiple time step evolution accumulations based on the tensor product, maps them to the quantum circuit, and measures the probability value of the auxiliary qubit in the ground state. Data processing module 4 processes the probability values ​​to obtain the inner product corresponding to each time step, and obtains the electron density by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshev polynomial expansion of the Fermi-Dirac distribution using a classical computer.

[0047] Specifically, the random state generation module 1 generates several random rotation Z-gates and random rotation X-gates based on random numbers generated by a classical computer according to the number of electrons in the material under test. Each qubit is initialized to its ground state, and at least one Hadamard gate, the random rotation Z-gate, and the random rotation X-gate are applied sequentially to generate an initial random state. The evolution processing module 2 receives the initial random state from the random state generation module 1, performs time evolution processing based on the Fermi-Dirac distribution, obtains the time evolution operator, and performs a Chepshov polynomial expansion. The Hamiltonian of the material under test is then decomposed into a linear combination of tensor products of several Pauli matrices using the Pauli decomposition method. The quantum circuit mapping module 3, based on the tensor product obtained by the evolution processing module 2, represents the Chepshov polynomial expanded by the time evolution operator in the quantum circuit through the evolution operator. According to the tensor product, the evolution operator is decomposed into several evolution accumulations corresponding to several time steps, and these evolution accumulations are sequentially mapped to the quantum circuit to obtain the step-size evolution operator corresponding to each time step. The probability value of the auxiliary qubit in the ground state is measured. The data processing module 4 receives the probability value sent by the quantum circuit mapping module 3, processes it to obtain the real and imaginary parts of the inner product of the random state corresponding to the time step and the initial random state, determines the inner product, multiplies the inner product corresponding to the time step with the coefficient, and sums the products corresponding to each time step to obtain the electron density of the material under test.

[0048] In some embodiments of this disclosure, the disclosure also includes a computer-readable storage medium storing a computer program for running a detection method, wherein the computer program causes a computer to perform the following steps: S1. The initial random state of the qubit is generated based on random numbers, where the random numbers are generated by a classical computer based on the number of electrons in the material under test; S2. Perform time evolution processing on the initial random state to obtain the time evolution operator, and perform Chepshov polynomial expansion on the time evolution operator; S3. The Hamiltonian of the material to be tested is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. S4. Based on the tensor product, the time evolution operator is decomposed into the evolution accumulation of multiple time steps, mapped onto the quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. S5. The inner product corresponding to each time step is obtained by processing the probability value. The electron density is obtained by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshov polynomial expansion of the Fermi-Dirac distribution using a classical computer.

[0049] The computer-readable storage medium can be a computer storage medium or a communication medium. A communication medium includes any medium that facilitates the transfer of a computer program from one location to another. A computer storage medium can be any available medium accessible to a general-purpose or special-purpose computer. For example, a computer-readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the computer-readable storage medium. Of course, the computer-readable storage medium can also be a component of the processor. The processor and the computer-readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the ASIC can reside in a user equipment. Of course, the processor and the computer-readable storage medium can also exist as discrete components in a communication device.

[0050] Specifically, the computer-readable storage medium can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as Static Random-Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium accessible to general-purpose or special-purpose computers.

[0051] In some embodiments of this disclosure, the disclosure also includes an electronic device comprising: A quantum computer generates an initial random state for a qubit based on random numbers, performs time evolution processing on the initial random state to obtain a time evolution operator, and performs a Chepshov polynomial expansion on the time evolution operator. The Hamiltonian of the material under test is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. Based on the tensor products, the time evolution operator is decomposed into evolutionary accumulations of multiple time steps, mapped onto a quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. A classical computer generates the random number based on the number of electrons in the material under test, and receives the probability value sent by the quantum computer. It processes the probability value to obtain the inner product corresponding to each time step, and obtains the electron density by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshov polynomial expansion on the Fermi-Dirac distribution using a classical computer. One or more processors; memory; and One or more programs, wherein the programs are stored in memory and configured to be executed by one or more processors, the programs being used to perform the following steps: S1. The initial random state of the qubit is generated based on random numbers, where the random numbers are generated by a classical computer based on the number of electrons in the material under test; S2. Perform time evolution processing on the initial random state to obtain the time evolution operator, and perform Chepshov polynomial expansion on the time evolution operator; S3. The Hamiltonian of the material to be tested is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. S4. Based on the tensor product, the time evolution operator is decomposed into the evolution accumulation of multiple time steps, mapped onto the quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. S5. The inner product corresponding to each time step is obtained by processing the probability value. The electron density is obtained by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshov polynomial expansion of the Fermi-Dirac distribution using a classical computer.

[0052] Memory is used to store computer programs. This memory may include high-speed random access memory (RAM) and may also include non-volatile memory (Non-volatile memory). Volatile Memory (NVM), such as at least one disk storage device, can also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0053] A processor is used to execute computer programs stored in memory. The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0054] Optionally, the memory can be either standalone or integrated with the processor.

[0055] When memory is a device independent of the processor, electronic devices may also include a bus. This bus is used to connect the memory and the processor. This bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc.

[0056] It should be noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to perform the methods described in various embodiments or some parts of the embodiments. In this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0057] Finally, it should be noted that the above description is only a preferred embodiment of this disclosure and is not intended to limit this disclosure. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the protection scope of this disclosure.

Claims

1. A method for detecting the electron density of a material, characterized in that, include: The initial random state of a qubit is generated based on random numbers, wherein the random numbers are generated by a classical computer based on the number of electrons in the material under test; The initial random state is subjected to time evolution processing to obtain a time evolution operator, and the time evolution operator is subjected to Chepshev polynomial expansion; The Hamiltonian of the material under test is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. Based on the tensor product, the time evolution operator is decomposed into multiple time-step evolution accumulations, mapped onto the quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. The inner product corresponding to each time step is obtained by processing the probability value. The electron density is obtained by summing the products of the inner product and the coefficients, wherein the coefficients are obtained by performing a Chepshov polynomial expansion of the Fermi-Dirac distribution using a classical computer.

2. The detection method according to claim 1, characterized in that: The initial random state of the qubit generated based on random numbers includes: Generate several random rotation Z-gates and random rotation X-gates based on the random numbers; Each of the qubits is initialized to the ground state; At least one Hadamard gate, the random rotation Z gate, and the random rotation X gate are sequentially applied to each of the qubits to generate the initial random state composed of the qubits.

3. The detection method according to claim 1, characterized in that: The step of performing time evolution processing on the initial random state to obtain the time evolution operator includes: The initial random state is subjected to time evolution based on the Fermi-Dirac distribution, and the energy is represented by the Hamiltonian of the material under test to obtain the time evolution operator.

4. The detection method according to claim 1, characterized in that: The Chepshov polynomial expanded by the time evolution operator corresponds to the quantum circuit.

5. The detection method according to claim 1, characterized in that: The step of decomposing the time evolution operator into multiple time-step evolution accumulations based on the tensor product and mapping them to the quantum circuit includes: The Chepshov polynomial expanded by the time evolution operator is represented in the quantum circuit by the evolution operator; Based on the tensor product, the evolution operator is decomposed into several evolution accumulations corresponding to the time steps; Several evolutionary accumulations are sequentially mapped onto the quantum circuit to obtain the step-size evolution operator corresponding to each time step.

6. The detection method according to claim 1, characterized in that: The probability values ​​of the measurement-aided qubit in the ground state include: The auxiliary qubit is prepared in the ground state; Apply a Hadamard gate and / or a phase gate to the auxiliary qubit, evolve and accumulate the initial random state or the random state corresponding to each time step, and apply the Hadamard gate to the auxiliary qubit again to obtain the probability value of the auxiliary qubit being in the ground state.

7. The detection method according to claim 1, characterized in that: The process of obtaining the inner product corresponding to each time step based on the probability value, and then obtaining the electron density by summing the products of the inner product and the coefficients, includes: Based on the probability value, the real and imaginary parts of the inner product of the random state corresponding to the time step and the initial random state are obtained, and the inner product is determined. Multiply the inner product corresponding to the time step by the coefficient, and sum the products corresponding to each time step to obtain the electron density of the material under test.

8. A system for detecting the electron density of a material, characterized in that, include: The random state generation module generates the initial random state of the qubit based on random numbers, wherein the random numbers are generated by a classical computer based on the number of electrons in the material under test; The evolution processing module performs time evolution processing on the initial random state to obtain a time evolution operator, performs Chepshov polynomial expansion on the time evolution operator, and decomposes the Hamiltonian of the material under test into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. The quantum circuit mapping module decomposes the time evolution operator into multiple time-step evolution accumulations based on the tensor product, maps them to the quantum circuit, and measures the probability value of the auxiliary qubit in the ground state. The data processing module processes the probability value to obtain the inner product corresponding to each time step, and obtains the electron density by summing the products of the inner product and the coefficients, wherein the coefficients are obtained by performing a Chepshev polynomial expansion of the Fermi-Dirac distribution using a classical computer.

9. A computer-readable storage medium, characterized in that, It stores a computer program for running a detection method, wherein the computer program causes a computer to perform the detection method as described in any one of claims 1-7.

10. An electronic device, characterized in that, include: A quantum computer generates an initial random state for a qubit based on random numbers, performs time evolution processing on the initial random state to obtain a time evolution operator, and performs a Chepshov polynomial expansion on the time evolution operator. The Hamiltonian of the material under test is decomposed into a linear combination of tensor products of Pauli matrices using the Pauli decomposition method. Based on the tensor products, the time evolution operator is decomposed into evolutionary accumulations of multiple time steps, mapped onto a quantum circuit, and the probability value of the auxiliary qubit in the ground state is measured. A classical computer generates the random number based on the number of electrons in the material under test, and receives the probability value sent by the quantum computer. It processes the probability value to obtain the inner product corresponding to each time step, and obtains the electron density by summing the inner product and the product of the coefficients. The coefficients are obtained by performing a Chepshov polynomial expansion on the Fermi-Dirac distribution using a classical computer. One or more processors; memory; and One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs being used to perform the detection method as described in any one of claims 1-7.

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