Method, apparatus, device, medium and product for determining density of states of material

Abstract

This application relates to a method, apparatus, device, medium, and product for determining the density of states of a material. The method includes: determining the normalized electron energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points; determining the original summation expression for the density of states of the target material based on the energy spectrum characteristics of the normalized electron energy matrix, and performing a polynomial expansion of the original summation expression to obtain a polynomial weighted combination expression and physical expressions for the weighting coefficients in the polynomial weighted combination expression; using quantum circuits to calculate the physical expressions for weighting coefficients of different orders in parallel to obtain weighting coefficient values ​​of different orders; and substituting the weighting coefficient values ​​of different orders into the polynomial weighted combination expression to determine the density of states of the target material. This method can reduce the complexity of determining the density of states.

Description

Technical Field

[0001] This application relates to the field of materials science and technology, and in particular to a method, apparatus, device, medium, and product for determining the density of states of a material. Background Technology

[0002] In solid-state physics and materials science, the density of states (DOS) reveals the distribution of electronic states that a material can accommodate at different energies, and is one of the most fundamental and important physical quantities describing the electronic structure of a material.

[0003] In related technologies, when calculating the density of states, the kernel polynomial method (KPM) is usually used. The objective function (such as the spectral density) is expressed as a polynomial series expansion. Then, by using a set of kernel functions to harmonic convergence, the spectral function, density of states and other related physical quantities of the system can be quickly estimated without diagonalizing the Hamiltonian.

[0004] However, the computational complexity of the related technologies is high. Summary of the Invention

[0005] Therefore, it is necessary to provide a method, apparatus, device, medium, and product for determining the density of states of a material, which can reduce the complexity of the density of states determination method, in order to address the above-mentioned technical problems.

[0006] In a first aspect, this application provides a method for determining the density of states of a material, the method comprising:

[0007] Based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points, the normalized electronic energy matrix of the target material is determined.

[0008] Based on the energy spectrum characteristics of the normalized electron energy matrix, the original summation expression of the density of states of the target material is determined, and the original summation expression is expanded into a polynomial to obtain the polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression.

[0009] By using quantum circuits to compute the physical expressions of weighting coefficients of different orders in parallel, the weighting coefficient values ​​of different orders are obtained.

[0010] By substituting the weighted coefficients of different orders into the polynomial weighted combination expression, the density of states of the target material is determined.

[0011] In one embodiment, the normalized electronic energy matrix of the target material is determined based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material, including:

[0012] Based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points, the electronic energy matrix of the target material is constructed.

[0013] Based on the energy range of the electron energy matrix and the identity matrix of a preset dimension, a linear mapping is performed on each matrix element in the electron energy matrix to obtain the normalized electron energy matrix; the dimension of the identity matrix matches the dimension of the electron energy matrix.

[0014] In one embodiment, the original summation expression is expanded using a polynomial to obtain a polynomial weighted combination expression and a physical expression for the weighting coefficients in the polynomial weighted combination expression, including:

[0015] According to the orthogonal standard template of the target polynomial, the original summation expression is expanded into an initial polynomial weighted combination expression; the weighting coefficient of each polynomial in the initial polynomial weighted combination expression corresponds to a decay coefficient;

[0016] Based on the preset truncation order, the initial polynomial weighted combination expression is truncated to obtain the polynomial weighted combination expression.

[0017] Substituting the initial polynomial weighted combination expression into the inner product expression corresponding to each weighting coefficient yields the physical expression for each weighting coefficient.

[0018] In one embodiment, a quantum circuit is used to calculate the physical expression of weighting coefficients of different orders, obtaining weighting coefficient values ​​of different orders, including:

[0019] For any order of weighting coefficients, the physical expression for the weighting coefficients is transformed into a combined calculation formula including the cosine trace and the sine trace; and,

[0020] An initial quantum circuit is constructed based on a single auxiliary bit and multiple working bits that match the matrix dimension of the normalized electron energy matrix. The initial quantum circuit is then subjected to quantum state preparation and evolution to obtain the values ​​of the cosine trace and the sine trace.

[0021] Substituting the values ​​of the cosine and sine traces into the combined calculation formula yields the weighted coefficient values.

[0022] In one embodiment, the initial quantum circuit is subjected to quantum state preparation and evolution to obtain the values ​​of the cosine trace and the sine trace, including:

[0023] Phase gates are applied to the auxiliary bits of the initialization quantum circuit, and random circuit gates are applied to each working bit to generate random quantum states;

[0024] The normalized electron energy matrix is ​​quantum operablely decomposed to a specified power to construct the corresponding controlled unitary operation unit. By combining the order-controlled unitary operation unit, the quantum state evolution is completed.

[0025] The quantum measurement probability of the auxiliary bit being in the ground state is obtained by performing multiple sampling measurements on the evolved auxiliary bit;

[0026] Based on the conversion relationship between the trace and the quantum measurement probability, the values ​​of the cosine trace and the sine trace are obtained.

[0027] In one embodiment, the density of states of the target material is determined by substituting weighting coefficients of different orders into a polynomial weighted combination expression, including:

[0028] The energy spectrum of the normalized electron energy matrix is ​​divided into multiple segments that match the order of the weighting coefficients;

[0029] By substituting the weighting coefficients of different orders into the polynomial weighted combination expression, the functional relationship between the density of states and the energy of the normalized electron energy matrix is ​​obtained.

[0030] By performing energy inverse mapping on the energy of the normalized electron energy matrix in the functional relationship, the density of states distribution curve of the target material is obtained, which is used as the density of states of the target material.

[0031] Secondly, this application also provides a device for determining the density of states of a material, comprising:

[0032] The normalization module is used to determine the normalized electronic energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material.

[0033] The expression determination module is used to determine the original summation expression of the density of states of the target material based on the energy spectrum characteristics of the normalized electron energy matrix, and to perform a polynomial expansion on the original summation expression to obtain the polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression.

[0034] The coefficient value calculation module is used to calculate the physical expression of weighting coefficients of different orders in parallel using quantum circuits, and obtain weighting coefficient values ​​of different orders.

[0035] The density of states determination module is used to substitute the weighted coefficient values ​​of different orders into the polynomial weighted combination expression to determine the density of states of the target material.

[0036] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method steps of any of the embodiments in the first aspect described above.

[0037] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method steps of any of the embodiments in the first aspect described above.

[0038] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the method steps of any of the embodiments in the first aspect described above.

[0039] The aforementioned methods, apparatus, equipment, media, and products for determining the density of states of the material determine the normalized electron energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points. According to the energy spectrum characteristics of the normalized electron energy matrix, the original summation expression for the density of states of the target material is determined. This original summation expression is then expanded into a polynomial to obtain a polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression. The physical expressions of the weighting coefficients of different orders are calculated in parallel using quantum circuits to obtain the weighting coefficient values ​​of different orders. The weighting coefficient values ​​of different orders are then substituted into the polynomial weighted combination expression to determine the density of states of the target material. This method constructs a normalized electronic energy matrix based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points. This enables precise characterization of the material's intrinsic electronic energy characteristics at the atomic scale, avoiding distortion of microscopic energy laws by macroscopic modeling. By performing a polynomial expansion on the original summation expression of the density of states, the complex statistical problem of the density of states is transformed into a problem of solving for weighting coefficients. At the same time, the physical expression of the weighting coefficients is clarified, which not only simplifies the computational dimension but also ensures the physical correlation between the coefficients and the material's electronic energy spectrum characteristics. By using quantum circuits to compute weighting coefficient values ​​of different orders in parallel, the parallel advantages of quantum computing in handling multidimensional and highly complex matrix operations are fully utilized, improving the computational efficiency and accuracy of high-order weighting coefficients and effectively solving the problem of exponential growth in computational load caused by increasing the order in traditional methods. Finally, the weighting coefficient values ​​are substituted into the polynomial weighted combination expression to obtain the material's density of states, realizing a precise mapping from microscopic electronic parameters to macroscopic density of states, providing an efficient and reliable technical path for material electronic structure analysis and performance prediction. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a diagram illustrating the application environment of a method for determining the density of states of a material in one embodiment.

[0042] Figure 2 This is a flowchart illustrating a method for determining the density of states of a material in one embodiment;

[0043] Figure 3 This is a flowchart illustrating the matrix normalization step in one embodiment;

[0044] Figure 4 This is a flowchart illustrating the expression determination steps in one embodiment;

[0045] Figure 5 This is a flowchart illustrating the steps for determining the weighting coefficient values ​​in one embodiment;

[0046] Figure 6 This is a flowchart illustrating the weighting coefficient value determination step in another embodiment;

[0047] Figure 7 This is a schematic diagram of the internal architecture of a quantum circuit computation step in one embodiment;

[0048] Figure 8 This is a flowchart illustrating a method for determining the density of states of a material in another embodiment;

[0049] Figure 9 This is a flowchart illustrating a method for determining the density of states of a material in another embodiment;

[0050] Figure 10 This is a structural block diagram of a material density of states determination device in one embodiment;

[0051] Figure 11 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] In solid-state physics and materials science, the density of states (DOS) is one of the most fundamental and important physical quantities describing the electronic structure of materials. It not only reveals the distribution of electronic states that a material can accommodate at different energies, but also directly relates to various properties such as conductivity, heat capacity, optical response, and superconductivity. However, with the increasing complexity of research systems, especially in large-scale lattices, strongly correlated materials, defect-doped systems, or aperiodic structures, traditional methods for solving eigenvalues ​​(such as direct diagonalization) face exponential growth in computational resources, becoming increasingly inapplicable. Therefore, developing efficient and scalable energy spectrum estimation methods has become a critical need. To this end, the kernel polynomial method (KPM) has been widely adopted. KPM is a numerical approximation method based on Chebyshev polynomial expansion, capable of rapidly estimating the spectral function, density of states, and other related physical quantities of a system without diagonalizing the Hamiltonian. The core idea is to express the objective function (such as spectral density) as a series expansion of a Chebyshev polynomial, and then harmonize the convergence through a set of kernel functions (such as the Jackson kernel) to avoid the instability caused by Gibbs oscillations.

[0054] In the traditional KPM calculation process, each moment of the Chebyshev polynomial expansion... This is the core numerical value for estimating the spectral function, and its calculation relies on the average sampling of multiple classical random initial states. The main drawbacks of existing methods for calculating the density of states of material systems based on the KPM method are: ① As the system dimension increases, the overhead of classical calculations to generate high-dimensional random states becomes enormous, for example, in large systems such as… Dimensions, randomly generated After generating random states of varying sizes, each random state needs to be normalized. Secondly, in classical computation, high-order Chebyshev polynomial evolution corresponds to multiple matrix-vector multiplications. In each step of the computation, additional memory is required to store the complete matrix and vector. That is, for high-dimensional, large-scale systems (such as material Hamiltonians containing thousands of orbitals or lattice points with degrees of freedom), traditional numerical methods need to generate and propagate random states in an exponentially dimensional Hilbert space and perform high-order matrix-vector multiplications, resulting in extremely high computational complexity and massive memory requirements.

[0055] Based on this, embodiments of this application provide a method for determining the density of states of a material, namely, a KPM momentum estimation method based on the combination of random state preparation of quantum gate circuits and Hadamard Test measurement. This technical solution utilizes the computational advantage of the random parameterization sequence in quantum gate circuits, which can efficiently prepare high-dimensional random states. It transforms the polynomial simulation of Chebyshev's polynomial action and the estimation of the moment of momentum into an ensemble average obtained through Hadamard Test measurement in quantum circuits. This method only requires measuring one auxiliary qubit to obtain the ensemble average of the moment of momentum, avoiding the need for complete sampling measurements in the system space and exponentially reducing measurement costs. Furthermore, the calculations of each order of moment of momentum in quantum circuits are independent, making it highly suitable for distributed quantum parallel computing.

[0056] The method for determining the density of states of materials provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104, or it can be located in the cloud or on other network servers. Terminal 102 can be, but is not limited to, various quantum computers, personal classical computers, or laptops. Server 104 can be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server providing cloud computing services.

[0057] In one exemplary embodiment, such as Figure 2 As shown, a method for determining the density of states of a material is provided. Taking the application of this method to a terminal processor as an example, the method includes the following steps:

[0058] S201, based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points, determines the normalized electronic energy matrix of the target material.

[0059] In this table, the electron transition term corresponds to the values ​​between different cells / orbitals, describing the energy required for an electron to jump from one position to another; the potential energy corresponds to the value of each cell / orbital itself, describing the basic energy of an electron remaining stationary. The normalized electron energy matrix is ​​a matrix used to describe the electron energy patterns of materials.

[0060] We can first construct an electronic energy matrix based on the electronic transition terms and in-situ potential energy of each atomic lattice point of the target material, and then normalize the electronic energy matrix to obtain a normalized electronic energy matrix.

[0061] Optionally, when constructing the electron energy matrix, for new materials or strongly correlated systems with high precision requirements, the matrix can be directly calculated from the atomic structure of the target material using first-principles methods such as density functional theory. For disordered materials such as amorphous and nanostructured materials, the electron energy matrix can be constructed by discretizing the real space grid.

[0062] Optionally, when performing energy normalization, nonlinear mapping methods, such as sigmoid function mapping, can be used for materials with uneven energy spectrum distribution to improve the resolution of dense regions. For the need for fast calculation of large-scale matrices, the normalization can be performed based on the statistical characteristics of the energy spectrum mean and standard deviation, and then scaled to the target interval to construct the normalized electron energy matrix of the target material.

[0063] S202. Based on the energy spectrum characteristics of the normalized electron energy matrix, the original summation expression of the density of states of the target material is determined, and the original summation expression is expanded into a polynomial to obtain the polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression.

[0064] The energy spectrum characteristics of the normalized electron energy matrix refer to the data describing the matrix's eigenvalues, including the characteristic sequence constructed from the various eigenvalues ​​of the normalized electron energy matrix and the statistical distribution characteristics of the eigenvalues. The characteristic sequence characterizes the energy values ​​of electrons within the standard energy range.

[0065] Density of states refers to the number of electronic states per unit energy range, which can be determined by statistically analyzing the electronic states corresponding to each intrinsic energy.

[0066] Based on this, we can statistically analyze the discrete eigenvalues ​​in the energy spectrum characteristics, that is, traverse all normalized intrinsic energies, mark the number of electronic states at each energy position, and then summarize them into a correspondence between energy and the number of states to obtain the original summation expression of the density of states.

[0067] Furthermore, since the original summation expression is a discrete statistical form, it is not convenient for subsequent continuous calculations in quantum circuits. Therefore, it needs to be transformed into a continuous analytical form using mathematical methods. In the embodiments of this application, the original summation expression of the discrete density of states is decomposed into a weighted superposition form of several Chebyshev polynomials (polynomial weighted combination expression). Utilizing the orthogonality of Chebyshev polynomials, the weighting coefficients are transformed into matrix trace operations related to the normalized electron energy matrix (the physical expression of the weighting coefficients). These trace operations directly correspond to the statistical average characteristics of electrons in different energy states, serving as a key basis for subsequent calculations of coefficients using quantum circuits.

[0068] S203 utilizes quantum circuits to calculate the physical expressions of weighting coefficients of different orders in parallel, thereby obtaining weighting coefficient values ​​of different orders.

[0069] In this context, quantum circuits refer to the core hardware carriers of quantum computing, consisting of a series of quantum gates (such as phase gates and Hadamard gates) and qubits (information storage and processing units) connected according to specific logic, enabling the preparation, evolution, and measurement of quantum states. In this embodiment, a customized quantum circuit based on the Hadamard Test architecture is employed, specifically adapted to the measurement requirements of trace computation.

[0070] Taylor expansion is performed on the weighting coefficients of different orders, decomposing the physical expression of each weighting coefficient into several fundamental quantities, supporting direct measurement by quantum circuits. Next, the fundamental quantities of the weighting coefficients of different orders are calculated using quantum circuits to determine the values ​​of the weighting coefficients for each order. Using qubits (auxiliary qubits + working qubits) as information carriers, the quantum state is manipulated through logical combinations of quantum gates (such as phase gates and Hadamard gates), realizing the complete process from initial state preparation and directed evolution to measurement, ultimately converting quantum state information into classically readable data.

[0071] S204, by substituting the weighting coefficients of different orders into the polynomial weighted combination expression, determines the density of states of the target material.

[0072] The polynomial weighted combination expression characterizes the functional relationship between the density of states and the energy of the normalized electron energy matrix. After determining the weighting coefficients of different orders, they are substituted into the polynomial weighted combination expression to obtain a functional relationship with the normalized electron energy as the independent variable and the density of states as the dependent variable. Then, the normalized electron energy is inversely mapped to obtain a functional relationship with the original electron energy as the independent variable and the density of states as the dependent variable, which is used as the density of states of the target material.

[0073] In this embodiment, the normalized electronic energy matrix of the target material is determined based on the electronic transition terms and in-situ potential energy of the atomic lattice points. According to the energy spectrum characteristics of the normalized electronic energy matrix, the original summation expression of the density of states of the target material is determined. This original summation expression is then expanded using a polynomial to obtain a polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression. The physical expressions of the weighting coefficients of different orders are calculated in parallel using quantum circuits to obtain the weighting coefficient values ​​of different orders. These weighting coefficient values ​​of different orders are then substituted into the polynomial weighted combination expression to determine the density of states of the target material. This method constructs a normalized electronic energy matrix based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points. This enables precise characterization of the material's intrinsic electronic energy characteristics at the atomic scale, avoiding distortion of microscopic energy laws by macroscopic modeling. By performing a polynomial expansion on the original summation expression of the density of states, the complex statistical problem of the density of states is transformed into a problem of solving for weighting coefficients. At the same time, the physical expression of the weighting coefficients is clarified, which not only simplifies the computational dimension but also ensures the physical correlation between the coefficients and the material's electronic energy spectrum characteristics. By using quantum circuits to compute weighting coefficient values ​​of different orders in parallel, the parallel advantages of quantum computing in handling multidimensional and highly complex matrix operations are fully utilized, improving the computational efficiency and accuracy of high-order weighting coefficients and effectively solving the problem of exponential growth in computational load caused by increasing the order in traditional methods. Finally, the weighting coefficient values ​​are substituted into the polynomial weighted combination expression to obtain the material's density of states, realizing a precise mapping from microscopic electronic parameters to macroscopic density of states, providing an efficient and reliable technical path for material electronic structure analysis and performance prediction.

[0074] In one exemplary embodiment, such as Figure 3 As shown, based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points, the normalized electronic energy matrix of the target material is determined, including:

[0075] S301, based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points, constructs the electronic energy matrix of the target material.

[0076] An electronic energy matrix is ​​constructed by taking the electronic transition terms of each atomic lattice point of the target material as off-diagonal elements and the in-situ potential energy of each atomic lattice point of the target material as diagonal elements.

[0077] Using the electron energy matrix as the tight-bound Hamiltonian For example, the matrix representation of a matrix in orbital space is as follows:

[0078]

[0079] in, Let be the transition term between different orbits (orbit i and orbit j) with varying degrees of freedom. For in-situ potential energy, The electron production operator characterizing orbital i, The electron annihilation operator characterizing orbital j.

[0080] S302, based on the energy range of the electron energy matrix and the unit matrix of the preset dimension, performs linear mapping on each matrix element in the electron energy matrix to obtain the normalized electron energy matrix.

[0081] The dimensions of the identity matrix match the dimensions of the electron energy matrix.

[0082] The energy range of the electron energy matrix includes the minimum energy value and the maximum energy value. Based on the minimum energy value, the maximum energy value, and the identity matrix that matches the dimension of the electron energy matrix, each matrix element in the electron energy matrix is ​​linearly mapped to a preset interval, such as the interval [-1, 1], to obtain the normalized electron energy matrix.

[0083] Optionally, the first matrix is ​​obtained by multiplying each element of the electron energy matrix by 2; the minimum and maximum energy values ​​are summed, and the summation result is multiplied by each element of the identity matrix to obtain the second matrix; the energy difference between the maximum and minimum energy values ​​is calculated; then, the first and second matrices are subtracted element by element, and the ratio of the subtraction result to the calculated energy difference between the maximum and minimum energy values ​​is determined as the normalized electron energy matrix.

[0084] Continuing with the electron energy matrix as the tight-binding Hamiltonian For example, using the Lanczos method to extract... Energy range, i.e., minimum energy value Maximum energy value .Will linear mapping of energy range to The linear mapping expression within the interval is as follows:

[0085]

[0086] in, Is with Identity matrices of the same dimension It is a very small value to prevent the denominator from having singular values.

[0087] In this embodiment, an electronic energy matrix of the target material is constructed based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material. Then, according to the energy range of the electronic energy matrix and the identity matrix of the preset dimension, each matrix element in the electronic energy matrix is ​​linearly mapped to obtain a normalized electronic energy matrix. This eliminates the computational incompatibility problem caused by the difference in energy scale between different materials. At the same time, the introduction of the identity matrix ensures the consistency of the matrix operation format, and the introduction of minimal values ​​effectively avoids the risk of computational failure caused by singular values ​​of the denominator during the calculation process. This lays a unified and stable numerical calculation premise for subsequent polynomial expansion, quantum circuit calculation and other links.

[0088] In one exemplary embodiment, such as Figure 4 As shown, the original summation expression is expanded into a polynomial to obtain the polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression, including:

[0089] S401, according to the orthogonal standard template of the target polynomial, expand the original summation expression into the weighted combination expression of the initial polynomial.

[0090] In the initial polynomial weighted combination expression, each polynomial weighting coefficient corresponds to a decay coefficient.

[0091] The objective polynomial can be a Chebyshev polynomial, and its working principle is: to transform the objective function... Through Chebyshev polynomials, such as polynomials of the first kind Expand: ,in To improve spectral convergence, a kernel function is introduced before each coefficient term. After applying the corresponding weights, the expanded expression of the orthogonal standard template is:

[0092]

[0093] in, Characterizes Gibbs parameters; Characterizing the moment momentum obtained through quantum computing; These respectively represent Chebyshev polynomials.

[0094] The core parameters in the original summation expression are extracted and substituted into the standard expansion formula of the target orthogonal polynomial. Through the linear superposition operation of orthogonal polynomials, the discrete original summation expression is transformed into a continuous weighted combination expression of the initial polynomials. The form of the weighted combination expression of the initial polynomials is the sum of the products of each orthogonal polynomial term and its corresponding weighting coefficient.

[0095] Furthermore, in the initial polynomial weighted combination expression, a corresponding attenuation coefficient is assigned to the weighting coefficient of each polynomial term to suppress the Gibbs oscillation effect caused by higher-order polynomial terms. Optionally, the attenuation coefficient is calculated using the Jackson kernel function, and the higher-order weighting coefficients are smoothed using the attenuation coefficient to ensure the numerical stability of the expression.

[0096] S402, based on the preset truncation order, truncate the initial polynomial weighted combination expression to obtain the polynomial weighted combination expression.

[0097] The order of each polynomial in the initial polynomial weighted combination expression is compared with the preset truncation order. Orthogonal polynomial terms with orders less than or equal to the preset truncation order and their corresponding weighting coefficients (including attenuation coefficients) are retained, while polynomial terms with orders greater than the preset truncation order are removed, thus obtaining the polynomial weighted combination expression.

[0098] S403, substitute the initial polynomial weighted combination expression into the inner product expression corresponding to each weighting coefficient to obtain the physical expression of each weighting coefficient.

[0099] The inner product expression corresponding to each weighting coefficient is the standard coefficient solution formula under the orthogonal polynomial system, which is derived by utilizing the characteristic of orthogonal polynomials that "the inner product of terms of different orders is 0 and the inner product of terms of the same order is a fixed constant".

[0100] Substituting the initial polynomial weighted combination expression into the inner product expression corresponding to each weighting coefficient, and simplifying through integration and orthogonality, the polynomial terms in the inner product expression are eliminated to obtain the physical expression corresponding to each weighting coefficient. This physical expression takes the trace operation of the normalized electron energy matrix as its core form. Specifically, the weighting coefficient is linearly correlated with the trace of a specific power of the normalized electron energy matrix, which is directly related to the electronic energy spectrum characteristics of the target material and can serve as the core basis for subsequent quantum circuit calculation of weighting coefficients.

[0101] For example, the expression for the original summation polynomial is as follows:

[0102]

[0103] in, Represents the effective Hamiltonian after renormalization The energy spectral density function; for The Each intrinsic energy level; It is the Dirac delta function; This represents the number of effective bits (or degrees of freedom) in the system, corresponding to the dimension of the Hilbert space. Prefactor Used to normalize the energy spectral density.

[0104] The initial polynomial weighted combination expression is as follows:

[0105]

[0106] in, This represents the Jackson kernel function, used to reduce the oscillation effect of Gibbs ensemble summation. Let the order of the spectral expansion be , For the first Spectral moments, This represents the order of the truncation approximation in moment calculation. For Chebyshev polynomials and This represents the normalized weighting factor.

[0107] In this embodiment, the discrete original summation expression is transformed into a continuous initial polynomial weighted combination expression using an orthogonal standard template. The expression is simplified and optimized by pre-setting the truncation order, and the Gibbs oscillation is effectively suppressed by the attenuation coefficient to ensure numerical stability. The physical expression of the weighting coefficients derived based on the orthogonality principle establishes a direct correlation between the coefficients and the electronic energy spectrum characteristics of the material, providing a core basis for the efficient and accurate calculation of the weighting coefficients in subsequent quantum circuits. Ultimately, the transformation of density of states calculation from discrete statistics to continuous quantifiable calculation is realized, taking into account the calculation accuracy, stability and computational efficiency, and laying a key foundation for the accurate solution of the density of states of the target material.

[0108] In one exemplary embodiment, such as Figure 5 As shown, the physical expressions for calculating weighting coefficients of different orders are obtained using quantum circuits, resulting in weighting coefficient values ​​for different orders, including:

[0109] S501, for any order of weighting coefficients, transforms the physical expression of the weighting coefficients into a combined calculation formula including the cosine trace and the sine trace.

[0110] For any order of weighting coefficients, the trace operation of a specific power of the normalized electron energy matrix is ​​extracted; based on the Taylor expansion approximation principle, the trace operation is decomposed into a linear combination of cosine trace and sine trace, and a combined calculation formula is constructed.

[0111] S502, based on a single auxiliary bit and multiple working bits that match the matrix dimension of the normalized electron energy matrix, constructs an initial quantum circuit, and performs quantum state preparation and evolution on the initial quantum circuit to obtain the values ​​of the cosine trace and the sine trace.

[0112] The number of working bits is determined based on the matrix dimension of the normalized electron energy matrix, and the corresponding expression is as follows: ,in, Let N be the matrix dimension and N be the number of working bits.

[0113] A Hadamard Test architecture with a single auxiliary bit and N working bits is adopted, integrating phase gates, random circuit gates, and a controlled unitary operation module as the initialization quantum circuit. Next, the auxiliary bit and working bits are initialized to all-zero states. Then, Hadamard gates and phase gates are applied to the auxiliary bit to complete the measurement mode configuration, and random circuit gates are applied to the working bits to prepare the initial quantum state. The controlled unitary operation module is then driven to run a preset number of times to achieve the directed evolution of the quantum state, ensuring a unique correspondence between the evolved quantum state and the cosine and sine traces. Finally, the auxiliary bit in the evolved quantum state is sampled multiple times, and its probability value in the ground state is recorded. Based on the probabilistic statistical principle of quantum measurement, the measured probability values ​​are converted using a preset conversion formula (2 × ground state probability value - 1) to obtain the values ​​of the cosine and sine traces, respectively.

[0114] S503, substitute the values ​​of the cosine trace and the sine trace into the combined calculation formula to obtain the weighted coefficient value of the weighted coefficient.

[0115] Substitute the values ​​of the cosine and sine traces into the combined calculation formula, and complete the numerical solution through linear operations to obtain the weighted coefficient values ​​of the weighted coefficients.

[0116] In this embodiment, for any order of weighting coefficients, the physical expression of the weighting coefficients is transformed into a combined calculation formula including cosine and sine traces. Furthermore, based on a single auxiliary bit and multiple working bits matching the matrix dimension of the normalized electron energy matrix, an initialization quantum circuit is constructed. The initialization quantum circuit is then used for quantum state preparation and evolution to obtain the values ​​of the cosine and sine traces. These values ​​are then substituted into the combined calculation formula to obtain the weighting coefficient values. Thus, by utilizing a customized quantum circuit architecture with a single auxiliary bit and working bits of adapted dimensions, the stability of quantum state preparation and evolution is ensured while achieving time-division precise measurement of the cosine and sine traces. This eliminates the need for repeated circuit construction, significantly improving measurement efficiency. Finally, the combined calculation formula completes the conversion of trace values ​​to weighting coefficient values, fully leveraging the parallel advantages and high-precision characteristics of quantum computing in high-dimensional, high-complexity operations.

[0117] In one exemplary embodiment, such as Figure 6 As shown, quantum state preparation and evolution are performed on the initialized quantum circuit to obtain the values ​​of the cosine trace and the sine trace, including:

[0118] S601 applies a phase gate to the auxiliary bits of the initialization quantum circuit and applies a random circuit gate to each working bit to generate a random quantum state.

[0119] First, the auxiliary bit and the working bit are initialized with all-zero states. Then, the phase gate and random circuit gate are manipulated respectively to complete the quantum state preparation: different phase gate parameters are applied to the auxiliary bit to distinguish between cosine trace measurement and sine trace measurement scenarios. Random circuit gates are applied to the working bit to generate random quantum states. The uniform distribution characteristics of random quantum states are used to ensure that the measurement results can reflect the overall characteristics of the normalized electron energy matrix and avoid measurement deviations caused by a single initial state.

[0120] For example, a phase gate is applied to the auxiliary bit. ,at this time Simultaneously, random circuit gate operations are applied to the working bits to generate random quantum states, such as... Figure 7 The rectangular block RCS is shown in the figure.

[0121] S602 performs quantum-operable decomposition of a specified power of the normalized electron energy matrix to construct the corresponding controlled unitary operation unit. By combining the controlled unitary operation unit with order control, the quantum state evolution is completed.

[0122] The specified power of the normalized electron energy matrix is ​​decomposed into a linear combination of tensor products composed of a series of Pauli matrices. Based on the decomposition results, a controlled unitary operation unit is constructed, making the operation logic of the controlled unitary operation unit equivalent to the operation logic of the specified power of the matrix. Subsequently, according to the order of the weighting coefficients to be calculated, the number of runs of the controlled unitary operation unit is adjusted (the order directly corresponds to the matrix power). The number of runs of the controlled unitary operation unit matches the matrix power requirement, driving the prepared quantum state to undergo directional evolution, and finally making the evolved quantum state uniquely correspond to the target cosine trace and sine trace.

[0123] For example, continue with Figure 7 This illustrates how the normalized electron energy matrix is ​​decomposed into a linear combination of tensor products of a series of Pauli matrices. Number of repetitions of a unit , representing the results obtained at different orders and The ensemble average.

[0124] S603 performs multiple sampling measurements on the evolved auxiliary bit to obtain the quantum measurement probability that the auxiliary bit is in the ground state.

[0125] By sampling and measuring the auxiliary bit multiple times, and using a measurement device to identify and statistically analyze the percentage of times it is in the ground state (the fundamental state in quantum computing), the quantum measurement probability is obtained.

[0126] S604, based on the conversion relationship between the trace and the quantum measurement probability, obtain the values ​​of the cosine trace and the sine trace.

[0127] The conversion relationship between trace and quantum measurement probability is expressed as follows: Trace = 2 × ground state probability value - 1. Based on this, substituting the quantum measurement probability into the conversion relationship between trace and quantum measurement probability yields the classical values ​​of cosine trace or sine trace.

[0128] By switching the phase gate configuration of the auxiliary bits, time-division measurement of cosine and sine traces can be performed under the same quantum circuit architecture, eliminating the need to build circuits repeatedly and improving computational efficiency.

[0129] In this embodiment, through the synergy of architectural adaptability design, precise configuration of measurement modes, and directed evolution of quantum states, the stability of quantum measurement and data reliability are ensured, and the complete transformation of classical matrix operations into quantum operability is realized, which can adapt to the calculation requirements of weighting coefficients of different orders. At the same time, relying on the design of measuring two traces in time division by the same circuit, the quantum computing process is simplified and the computing efficiency is improved.

[0130] In one exemplary embodiment, such as Figure 8 As shown, by substituting the weighting coefficients of different orders into the polynomial weighted combination expression, the density of states of the target material is determined, including:

[0131] S801 divides the energy spectrum of the normalized electron energy matrix into multiple intervals that match the order of the weighting coefficients.

[0132] The order of the weighting coefficients is the cutoff order of the weighting coefficients. Following the principle that the number of intervals matches the order of the weighting coefficients (e.g., the number of intervals is greater than or equal to the order of the weighting coefficients), the energy spectrum of the normalized electron energy matrix is ​​divided into multiple intervals, ensuring that the energy variation range within each interval can be accurately fitted by polynomial terms of the corresponding order.

[0133] S802, by substituting the weighting coefficients of different orders into the polynomial weighted combination expression, obtains the functional relationship between the density of states and the energy of the normalized electron energy matrix.

[0134] By substituting the weighted coefficients of different orders into the polynomial weighted combination expression and eliminating the coefficient variables in the polynomial terms, a functional relationship with normalized electron energy as the independent variable and density of states as the dependent variable is finally obtained.

[0135] S803 performs energy inverse mapping on the energy of the normalized electron energy matrix in the functional relationship to obtain the density of states distribution curve of the target material, which is used as the density of states of the target material.

[0136] The normalized electron energy in the functional relationship obtained by S802 is reverse mapped to restore the normalized electron energy in the interval [-1,1] to the true energy value of the electrons in the target material. At the same time, the corresponding density of states value is matched with the true energy value to obtain the corresponding data of "true energy-density of states". Based on this data, the density of states distribution curve is plotted to characterize the density of states of the target material.

[0137] In this embodiment, energy inverse mapping is used to achieve accurate regression of the calculation results from the normalized virtual interval to the real physical scene of the material, ensuring the physical validity of the density of states results; and the curve of real energy versus density of states is plotted to more intuitively display the electronic properties of the target material, which facilitates the subsequent analysis and application of the material's electronic properties.

[0138] In one exemplary embodiment, a method for determining the density of states of a material is provided, such as... Figure 9 As shown, it includes the following steps:

[0139] S901, begin.

[0140] S902, establish the Hamiltonian model and perform spectral function renormalization.

[0141] Constructing the tight-binding Hamiltonian of the target material system The second-order quantization expression of , its matrix expression in orbital space is as follows:

[0142]

[0143] in, For the transition terms between different orbital degrees of freedom, This represents the in-situ potential energy.

[0144] Extracting using the Lanczos method Energy range, i.e.: The original linear mapping of energy range to Within the interval, ,in Is with identity matrices of the same dimension and It is a numerical processing technique to prevent singular values ​​from appearing in the denominator.

[0145] S903 determines the approximate order K of the Hamiltonian and the truncation order M of the moment momentum, runs the quantum circuit, and obtains the sine and cosine traces based on the measurement results of the auxiliary bits in the quantum circuit, and then calculates the moment momentum of different orders.

[0146] Based on the renormalization, the expression for the lattice state Millton is:

[0147]

[0148] at this time After renormalization The corresponding energy spectrum. Expanded using Chebyshev polynomials, it is:

[0149]

[0150] in This represents the Jackson kernel function, which reduces the oscillation effect of Gibbs ensemble summation. To control the calculated moment momentum The order of the approximate truncation used is determined by the polynomial expansion. The core step in the above polynomial expansion lies in using quantum circuits to calculate... The expressions for different orders of moment momentum based on the general case are as follows:

[0151]

[0152] in, Indicates the first Chebyshev spectral moments of order; Let be the energy spectral density function of the system; For the first Chebyshev polynomial of order 1; This is the effective Hamiltonian after linear scaling; This represents the trace over a Hilbert space, where the space dimension is . ,in The effective degrees of freedom (or number of bits) of the system; To achieve a complete orthogonal ground state.

[0153] S904 sets the discrete parameters of the renormalization energy, which is used to calculate the density of states at each energy point using polynomial expansion.

[0154] Calculation of different orders of moment momentum using the Hadamard Test quantum circuit .because

[0155]

[0156] Will Perform a Taylor expansion near the center 0 of the energy spectrum:

[0157]

[0158] in, This represents the original Hamiltonian after linear scaling and spectral range normalization to ([-1,1]); Let be the inverse trigonometric function defined in the sense of an operator; k is the summation index of the series expansion; represents the coefficients of the power series expansion; K is the polynomial truncation order, used to control the approximation accuracy; Pi is the mathematical constant of a circle.

[0159] In the above formula and Can be accessed separately Figure 7 The quantum circuit shown is implemented using the following steps:

[0160] The entire quantum circuit uses an auxiliary bit and ,in For matrix The dimension. First, a phase gate is applied to the auxiliary bits. ,at this time Simultaneously, random circuit gate operations are applied to the working bits to generate random quantum states, such as... Figure 7 The rectangular block RCS is shown in the figure.

[0161] Take an appropriate order for the Hamiltonian in the above formula. Approximation, i.e. Figure 7 Each rectangular block Representative under control This step requires converting the matrix It can be decomposed into a linear combination of tensor products consisting of a series of Pauli matrices. At this point... Number of repetitions of a unit , representing the results obtained at different orders and The ensemble average.

[0162] right Figure 7 If the single auxiliary bit shown is sampled multiple times, then... , The difference is that the P gate is before measurement. When (SH), the corresponding measurement results are respectively ( ).

[0163] Finally, the result obtained in step c and Substituting moment of momentum The approximate formula can be used to obtain the moment momentum of different orders. .

[0164] S905 converts the calculation results back to the original energy and outputs the relationship between the original Hamiltonian density of states and energy.

[0165] The renormalized energy spectrum region Divide into several equally spaced parts, and set the order of the cutoff moment momentum. Different orders of moment momentum are obtained by measuring the quantum circuit in step S904. Substituting this into the formula in step S903, we obtain the numerical value of the density of states. and The one-to-one correspondence, and then Using the linear mapping in step b of step S902, the energy is inversely transformed to the unrenormalized energy. The original density of states can then be obtained. and The functional relationship.

[0166] S906, End.

[0167] In this embodiment, firstly, a quantum circuit composed of a randomly parameterized quantum gate sequence is used to generate a random initial state instead of the traditional classical method. Applying rotation gates and CNOT gates with random parameters to each qubit constructs a quantum random state approximating a Haar distribution, enabling efficient sampling in an exponentially dimensional Hilbert space. Secondly, the recursive evolution process of Chebyshev polynomials acting on Hamiltonians is transformed into an iterative simulation of unitary evolution in quantum circuits, constructing programmable quantum gate sequences to achieve... The recursive generation process. Finally, by constructing the HadamardTest quantum circuit, the moment momentum of different orders is generated. The expectation estimation is transformed into the measurement of auxiliary individual bits, thereby achieving ensemble averaging and avoiding the complete reading and sampling of high-dimensional wavefunctions in traditional methods. This technical solution fully leverages the advantages of quantum computing in the preparation of high-dimensional random states, unitary evolution simulation, and low-overhead expectation measurement. It not only significantly reduces computational resource consumption but also possesses good parallelism and scalability, making it suitable for efficient estimation of Chebyshev angular momentum in large-scale material systems.

[0168] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0169] Based on the same inventive concept, this application also provides a material density-state determination apparatus for implementing the above-described method for determining the density of states of materials. The solution provided by this apparatus is similar to the implementation described in the above-described method; therefore, the specific limitations in one or more material density-state determination apparatus embodiments provided below can be found in the limitations of the material density-state determination method described above, and will not be repeated here.

[0170] In one exemplary embodiment, such as Figure 10 As shown, a device for determining the density of states of a material is provided, comprising: a normalization module 1001, an expression determination module 1002, a coefficient value calculation module 1003, and a density of states determination module 1004, wherein:

[0171] Normalization module 1001 is used to determine the normalized electronic energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material.

[0172] The expression determination module 1002 is used to determine the original summation expression of the density of states of the target material based on the energy spectrum characteristics of the normalized electron energy matrix, and to perform a polynomial expansion on the original summation expression to obtain the polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression.

[0173] The coefficient value calculation module 1003 is used to calculate the physical expression of weighting coefficients of different orders in parallel using quantum circuits, and obtain weighting coefficient values ​​of different orders.

[0174] The density of states determination module 1004 is used to substitute the weighted coefficient values ​​of different orders into the polynomial weighted combination expression to determine the density of states of the target material.

[0175] In an exemplary embodiment, the normalization module 1001 is further configured to construct an electronic energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material; and to perform linear mapping on each matrix element in the electronic energy matrix according to the energy range of the electronic energy matrix and the identity matrix of a preset dimension to obtain a normalized electronic energy matrix; the dimension of the identity matrix matches the dimension of the electronic energy matrix.

[0176] In an exemplary embodiment, the expression determination module 1002 is further configured to: expand the original summation expression into an initial polynomial weighted combination expression according to the orthogonal standard template of the target polynomial; each polynomial weighting coefficient in the initial polynomial weighted combination expression corresponds to a decay coefficient; truncate the initial polynomial weighted combination expression based on a preset truncation order to obtain a polynomial weighted combination expression; and substitute the initial polynomial weighted combination expression into the inner product expression corresponding to each weighting coefficient to obtain the physical expression of each weighting coefficient.

[0177] In an exemplary embodiment, the coefficient value calculation module 1003 is further configured to, for any order of weighted coefficients, transform the physical expression of the weighted coefficients into a combined calculation formula including cosine traces and sine traces; and, based on a single auxiliary bit and multiple working bits matching the matrix dimension of the normalized electron energy matrix, construct an initialization quantum circuit, and perform quantum state preparation and evolution on the initialization quantum circuit to obtain the values ​​of the cosine trace and the sine trace; and substitute the values ​​of the cosine trace and the sine trace into the combined calculation formula to obtain the weighted coefficient values ​​of the weighted coefficients.

[0178] In an exemplary embodiment, the coefficient value calculation module 1003 is further configured to apply a phase gate to the auxiliary bits of the initialized quantum circuit, and apply random circuit gates to each working bit to generate random quantum states; perform quantum operable decomposition of the specified power of the normalized electron energy matrix to construct the corresponding controlled unitary operation unit, and combine the order-controlled unitary operation unit to complete the quantum state evolution; perform multiple sampling measurements on the evolved auxiliary bits to obtain the quantum measurement probability of the auxiliary bits being in the ground state; and obtain the values ​​of the cosine trace and the sine trace according to the conversion relationship between the trace and the quantum measurement probability.

[0179] In an exemplary embodiment, the density of states determination module 1004 is further configured to divide the energy spectrum interval of the normalized electron energy matrix into multiple interval segments matching the order of the weighting coefficients; substitute the weighting coefficient values ​​of different orders into the polynomial weighted combination expression to obtain the functional relationship between the density of states and the energy of the normalized electron energy matrix; perform energy inverse mapping on the energy of the normalized electron energy matrix in the functional relationship to obtain the density of states distribution curve of the target material, which is used as the density of states of the target material.

[0180] Each module in the aforementioned density of states determination device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0181] In one exemplary embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 11 As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, Near Field Communication (NFC), or other technologies. When the computer program is executed by the processor, it implements a method for determining the density of states of a material. The display unit is used to form a visually visible image and can be a display screen, projection device, or virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0182] Those skilled in the art will understand that Figure 11 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0183] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0184] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0185] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0186] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0187] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0188] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0189] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for determining the density of states of a material, characterized in that, The method includes: Based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material, the normalized electronic energy matrix of the target material is determined. Based on the energy spectrum characteristics of the normalized electron energy matrix, the original summation expression of the density of states of the target material is determined, and the original summation expression is expanded into a polynomial to obtain a polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression. By using quantum circuits to compute the physical expressions of weighting coefficients of different orders in parallel, the weighting coefficient values ​​of different orders are obtained. By substituting the weighted coefficients of different orders into the polynomial weighted combination expression, the density of states of the target material is determined.

2. The method according to claim 1, characterized in that, The determination of the normalized electronic energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material includes: Based on the electronic transition terms and in-situ potential energy of the target material's atomic lattice points, the electronic energy matrix of the target material is constructed. Based on the energy range of the electron energy matrix and a preset dimension identity matrix, each matrix element in the electron energy matrix is ​​linearly mapped to obtain a normalized electron energy matrix; the dimension of the identity matrix matches the dimension of the electron energy matrix.

3. The method according to claim 1 or 2, characterized in that, The step of performing a polynomial expansion on the original summation expression to obtain a polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression includes: According to the orthogonal standard template of the target polynomial, the original summation expression is expanded into an initial polynomial weighted combination expression; in the initial polynomial weighted combination expression, each polynomial weighting coefficient corresponds to a decay coefficient; Based on a preset truncation order, the initial polynomial weighted combination expression is truncated to obtain the polynomial weighted combination expression. Substituting the initial polynomial weighted combination expression into the inner product expression corresponding to each weighting coefficient yields the physical expression for each weighting coefficient.

4. The method according to claim 1 or 2, characterized in that, The physical expression for calculating weighting coefficients of different orders using quantum circuits, and obtaining weighting coefficient values ​​of different orders, includes: For any order of weighting coefficients, the physical expression for the weighting coefficients is transformed into a combined calculation formula including the cosine trace and the sine trace; and, An initial quantum circuit is constructed based on a single auxiliary bit and multiple working bits that match the matrix dimension of the normalized electron energy matrix. The initial quantum circuit is then subjected to quantum state preparation and evolution to obtain the values ​​of the cosine trace and the sine trace. Substituting the values ​​of the cosine trace and the sine trace into the combined calculation formula, the weighted coefficient values ​​of the weighting coefficients are obtained.

5. The method according to claim 4, characterized in that, The process of preparing and evolving quantum states in the initialized quantum circuit to obtain the values ​​of the cosine trace and the sine trace includes: A phase gate is applied to the auxiliary bits of the initialization quantum circuit, and a random circuit gate is applied to each of the working bits to generate a random quantum state; The normalized electron energy matrix is ​​quantum operablely decomposed to a specified power to construct a corresponding controlled unitary operation unit. The controlled unitary operation unit is then controlled by the order to complete the quantum state evolution. The evolved auxiliary bit is sampled and measured multiple times to obtain the quantum measurement probability that the auxiliary bit is in the ground state; Based on the conversion relationship between the trace and the quantum measurement probability, the values ​​of the cosine trace and the sine trace are obtained.

6. The method according to claim 1 or 2, characterized in that, The step of substituting weighted coefficients of different orders into the polynomial weighted combination expression to determine the density of states of the target material includes: The energy spectrum of the normalized electron energy matrix is ​​divided into multiple segments that match the order of the weighting coefficients; By substituting the weighting coefficients of different orders into the polynomial weighted combination expression, the functional relationship between the density of states and the energy of the normalized electron energy matrix is ​​obtained; Energy inverse mapping is performed on the energy of the normalized electron energy matrix in the functional relationship to obtain the density of states distribution curve of the target material, which is used as the density of states of the target material.

7. A device for determining the density of states of a material, characterized in that, The device includes: The normalization module is used to determine the normalized electronic energy matrix of the target material based on the electronic transition terms and in-situ potential energy of the atomic lattice points of the target material. The expression determination module is used to determine the original summation expression of the density of states of the target material based on the energy spectrum characteristics of the normalized electron energy matrix, and to perform a polynomial expansion on the original summation expression to obtain a polynomial weighted combination expression and the physical expression of the weighting coefficients in the polynomial weighted combination expression. The coefficient value calculation module is used to calculate the physical expression of weighting coefficients of different orders in parallel using quantum circuits, and obtain weighting coefficient values ​​of different orders. The density of states determination module is used to substitute the weighted coefficient values ​​of different orders into the polynomial weighted combination expression to determine the density of states of the target material.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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