Data processing method and electronic device

Abstract

Embodiments of the present disclosure relate to a data processing method, apparatus, electronic device, computer-readable storage medium, and computer program product. The method includes: obtaining an atomic orbital basis set of a unit cell in a supercell of a periodic material; dividing the unit cell into multiple segments based on the atomic orbital basis set of the unit cell; determining multiple bath regions in the supercell respectively corresponding to the multiple segments; and determining the energy of the unit cell based on the multiple segments and the multiple bath regions. In this way, in the embodiments of the present disclosure, the unit cell can be divided into multiple segments based on the orbital basis set, so that the size of the segments is smaller, thereby reducing the calculation scale based on the segments, and enabling the density matrix embedding theory to be applicable to the periodic material system.

Description

Technical Field

[0001] Embodiments of the present disclosure mainly relate to quantum systems, and more particularly, to data processing methods, devices, electronic devices, computer-readable storage media, and computer program products. Background Art

[0002] Precisely solving the ground state energy of molecules or materials is one of the central problems in quantum chemistry. The simulation of quantum chemistry for material systems helps to solve important scientific or industrial problems, such as understanding the mechanism of high-temperature superconductivity, understanding the reaction mechanism of catalytic processes, or rationally designing energy storage materials, etc. Different from the simulation of molecular systems, the simulation of material systems is more difficult. Summary of the Invention

[0003] According to an exemplary embodiment of the present disclosure, a data processing solution is provided, which can more precisely determine the unit cell energy in a periodic material system for a periodic material system.

[0004] In a first aspect of the embodiments of the present disclosure, a data processing method is provided, including: obtaining an atomic orbital basis set of a unit cell in a supercell of a periodic material; dividing the unit cell into multiple segments based on the atomic orbital basis set of the unit cell; determining multiple bath regions in the supercell corresponding to the multiple segments respectively; and determining the energy of the unit cell based on the multiple segments and the multiple bath regions.

[0005] In a second aspect of the embodiments of the present disclosure, an electronic device is provided, including: at least one processing unit; at least one memory, at least one memory being coupled to at least one processing unit and storing instructions for execution by at least one processing unit, the instructions when executed by at least one processing unit causing the electronic device to perform operations, the operations including: obtaining an atomic orbital basis set of a unit cell in a supercell of a periodic material; dividing the unit cell into multiple segments based on the atomic orbital basis set of the unit cell; determining multiple bath regions in the supercell corresponding to the multiple segments respectively; and determining the energy of the unit cell based on the multiple segments and the multiple bath regions.

[0006] In a third aspect of the embodiments of the present disclosure, a data processing device is provided, including: an obtaining module configured to obtain an atomic orbital basis set of a unit cell in a supercell of a periodic material; a dividing module configured to divide the unit cell into multiple segments based on the atomic orbital basis set of the unit cell; a bath region determining module configured to determine multiple bath regions in the supercell corresponding to the multiple segments respectively; and an energy determining module configured to determine the energy of the unit cell based on the multiple segments and the multiple bath regions.

[0007] In a fourth aspect of the embodiments of the present disclosure, there is provided a computer-readable storage medium having machine-executable instructions stored thereon, and the machine-executable instructions, when executed by a device, cause the device to execute the method described in the first aspect of the present disclosure.

[0008] In a fifth aspect of the embodiments of the present disclosure, there is provided a computer program product including computer-executable instructions, where the computer-executable instructions, when executed by a processor, implement the method described in the first aspect of the present disclosure.

[0009] In a sixth aspect of the embodiments of the present disclosure, there is provided an electronic device including: a processing circuit configured to execute the method described in the first aspect of the present disclosure.

[0010] The Summary is provided to introduce a series of concepts in a simplified form, which will be further described in the Detailed Description below. The Summary is not intended to identify the key features or essential features of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In conjunction with the accompanying drawings and with reference to the following detailed description, the above and other features, advantages, and aspects of the embodiments of the present disclosure will become more apparent. In the drawings, the same or similar reference numerals denote the same or similar elements, where:

[0012] Figure 1 A schematic diagram of a periodic material to which the embodiments of the present disclosure can be applied is shown;

[0013] Figure 2 A flowchart of an example process according to some embodiments of the present disclosure is shown;

[0014] Figure 3 A schematic diagram of a processing flow using DMET according to some embodiments of the present disclosure is shown;

[0015] Figure 4 A flowchart of an example process for determining the energy of a unit cell according to some embodiments of the present disclosure is shown;

[0016] Figure 5 A schematic flowchart of a process for obtaining an output through optimization according to some embodiments of the present disclosure is shown;

[0017] Figure 6 A schematic flowchart of a process for determining an embedded Hamiltonian according to some embodiments of the present disclosure is shown;

[0018] Figure 7Shows a schematic diagram of two-dimensional single-layer boron nitride according to some embodiments of the present disclosure;

[0019] Figure 8 Shows a schematic diagram of three-dimensional transition metal oxide nickel oxide according to some embodiments of the present disclosure;

[0020] Figure 9 Shows a block diagram of an example device according to an embodiment of the present disclosure; and

[0021] Figure 10 Shows a block diagram of an example device that can be used to implement embodiments of the present disclosure. Detailed Description of the Invention

[0022] Embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although some embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Instead, these embodiments are provided to more thoroughly and completely understand the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of protection of the present disclosure.

[0023] Hereinafter, some basic terms that may be involved in the present disclosure will be described first with reference to Table 1.

[0024] Table 1

[0025]

[0026]

[0027]

[0028] As mentioned above, accurately solving the ground state energy of molecules or materials is the core problem of quantum chemistry. Quantum chemical simulations of material systems are helpful for solving important scientific or industrial problems. Different from the simulations of molecular systems, simulations of material systems are more difficult. Isolated single molecular systems are often small, and relevant properties can be described by simulating only a single molecule. However, for material systems in the aggregated state, a relatively large scale needs to be simulated along the direction of material extension to correctly reflect the properties of the material in the thermodynamic limit.

[0029] On the other hand, in order to solve the ground state energy of molecules or materials, as the scale of the research object becomes larger and larger, the computing resources (such as memory, processors, and time) required to accurately solve the ground state energy of chemical systems on classical computers also increase exponentially, so large systems cannot be processed. Quantum computing has the potential to solve this problem of exponential growth of resources.

[0030] On a classical computer, for each additional electron orbital in the simulated system, there are two possibilities for the orbital to be occupied or unoccupied. Consequently, the number of possible states of the system is multiplied by 2. For a chemical system with n orbitals, the number of possible states is 2 n , and the required memory (classical bits) also exhibits exponential growth.

[0031] On a quantum computer, qubits can store information in quantum superposition states and thus correspond one-to-one with the orbitals of the simulated system. For each additional electron orbital in the simulated system, the number of required classical bits increases by one. Therefore, the growth rate of memory is reduced to linear. In terms of computing time, current theoretical research shows that the time complexity of algorithms such as quantum phase estimation is polynomial complexity. Therefore, quantum computing can solve the problem of the exponentially increasing computing resources required in the above-mentioned two aspects of memory and time processing in classical computing.

[0032] Generally, for a material system, a larger computational supercell can be constructed as a research model. The computational supercell (or simply referred to as the supercell) often consists of many identical and smaller computational unit cells (or simply referred to as unit cells). This means that there are certain translational symmetries in the computational supercell, that is, the entire computational supercell can be constructed by continuously performing translational operations on a certain computational unit cell. To utilize this symmetry to reduce the computational amount, in the actual processing of periodic material systems, the Fourier transform can be performed on the wave function of the unit cell, and k-point sampling is performed in the first Brillouin zone, so that the translational symmetry can be utilized. Performing k×k×k sampling in the first Brillouin zone is equivalent to constructing a k×k×k supercell using the unit cell.

[0033] The quantum embedding method is a class of methods used in quantum chemistry to handle large systems. Its core idea is that for large systems, one often only cares about the properties of a small fragment, or the strong correlations that need to be accurately solved only exist in a part of the system. Therefore, the part that one cares about or where strong correlations exist can be processed using high-precision but expensive methods, while the rest of the system can be processed using low-precision but inexpensive methods. The density matrix embedding theory (DMET) is one such method. It uses Schmidt decomposition to extract the components (also called the bath region) in the large system that are coupled to the fragment, uses high-precision methods to solve the fragment and its coupled bath region, and improves the quality of the solution by fitting the density matrix. However, due to current computational resource limitations, the current density matrix embedding theory is only limited to molecular systems or model systems and is difficult to extend to material systems, such as periodic material systems.

[0034] DMET can extract the components (bath region) coupled with the fragment in a large system by using Schmidt decomposition, solve the fragment and the bath region coupled with it by using high-precision methods, and improve the quality of the solution by fitting the density matrix. If DMET is to be applied to a periodic material system, the current scheme can only consider selecting a unit cell as a fragment, which results in an excessive amount of calculation, for example, far exceeding the capacity of a quantum computer. Therefore, DMET cannot be applied to periodic material systems in related schemes.

[0035] For example, in the current DMET scheme, a unit cell is usually taken as a fragment, and only this one fragment is used throughout the DMET process. In some other implementations of DMET, there are also some multi-fragment partitions. For example, in some layered materials, a layered structure composed of multiple atoms is selected as a fragment, but each fragment is still relatively large. That is to say, whether a unit cell is taken as a fragment or some layered structures are taken as a fragment, the scale of the fragments divided by these partitioning methods is still relatively large. For example, the size of the fragment exceeds the scale that can be processed by a quantum computer at the present stage, resulting in inability to be processed on a quantum computer.

[0036] To at least partially solve the defects in the above technical solutions, embodiments of the present disclosure provide a scheme for a periodic material system, which can partition fragments based on an orbital basis set, so that a unit cell can include multiple fragments, thus reducing the scale of the fragments, and thereby the energy of the periodic material system can be determined based on DMET.

[0037] In the present disclosure, terms such as "material system", "periodic material system", "periodic material", "periodic system", etc. can be used interchangeably.

[0038] Figure 1 The schematic diagrams of periodic materials to which embodiments of the present disclosure can be applied are shown. Exemplarily, (1-1) shows a one-dimensional hydrogen (1D-H) structure, where the frame 101 is its unit cell. Exemplarily, (1-2) shows two-dimensional single-layer boron nitride (2D-BN), where the frame 111 is its unit cell. Exemplarily, (1-3) shows three-dimensional transition metal oxide nickel oxide (3D-NiO), where 121 is its unit cell. Since NiO has a type II antiferromagnetic (AFII) ground state, a rhombohedral structure 121 with two molecular units can be taken as the unit cell.

[0039] It should be noted that Figure 1 The periodic materials shown are only examples, and embodiments of the present disclosure can also be applied to other periodic materials, which will not be listed one by one here.

[0040] Figure 2 FIG. 200 shows a flowchart of an exemplary process according to some embodiments of the present disclosure. At block 210, an atomic orbital basis set of unit cells in a supercell of a periodic material is obtained. At block 220, based on the atomic orbital basis set of the unit cell, the unit cell is divided into multiple segments. At block 230, multiple bath regions corresponding to the multiple segments in the supercell are determined. At block 240, the energy of the unit cell is determined based on the multiple segments and the multiple bath regions.

[0041] In this way, in the embodiments of the present disclosure, the unit cell can be divided into multiple segments based on the orbital basis set, so that the size of the segments is smaller, thereby reducing the calculation scale based on the segments, and enabling the density matrix embedding theory to be applicable to the periodic material system.

[0042] In some embodiments, the periodic material may include, for example, a one-dimensional hydrogen structure, a two-dimensional single-layer boron nitride, or a three-dimensional transition metal oxide nickel oxide, as Figure 1 shown. Exemplarily, the periodic material may have a crystal structure.

[0043] In some embodiments, the supercell can be determined by sampling in k-space. For example, k x ×k y ×k z sampling can be performed to construct a supercell of size k x ×k y ×k z For example, 5×5×1 sampling can be performed on two-dimensional single-layer boron nitride to construct a supercell of size 5×5.

[0044] In some embodiments of the present disclosure, the operation at block 220 may include: determining a localized orbital basis set that is orthogonal to each other based on the atomic orbital basis set of the unit cell; dividing the localized orbital basis set that is orthogonal to each other into multiple orbital subgroups; and determining multiple segments based on the multiple orbital subgroups. Exemplarily, the localized orbital basis set that is orthogonal to each other may also be referred to as localized orthogonal basis functions. Exemplarily, multiple segments can be obtained by merging related orbits. It can be seen that in the embodiments of the present disclosure, the segments are determined based on the orbital basis set, so it can be referred to as a multi-segment orbital partitioning mechanism, or an orbital-based multi-segment partitioning mechanism. The present disclosure is not limited thereto.

[0045] In some embodiments of the present disclosure, the operation at block 230 may include: performing a space transformation operation to transform from k-space to R-space; and determining multiple bath regions corresponding to the multiple segments in R-space. Exemplarily, the space transformation operation may also be referred to as an integral transformation or a space conversion, etc. The present disclosure is not limited thereto.

[0046] Exemplarily, the remaining part of the supercell except the first fragment can be determined as the environment of the first fragment in the R-space; and the singular value decomposition is performed on the non-diagonal block of the first-order reduced density matrix of the first fragment and the environment to determine the first bath region corresponding to the first fragment. It can be understood that initially, based on the wave function under the mean-field approximation, the bath region can be determined by Schmidt decomposition.

[0047] In some embodiments of the present disclosure, the operation at block 240 may include: constructing a plurality of embeddings based on a plurality of fragments and a plurality of bath regions; determining the Hamiltonian of each embedding among the plurality of embeddings; determining the energy of each fragment among the plurality of fragments based on the Hamiltonian of each embedding among the plurality of embeddings; and determining the sum of the energies of the plurality of fragments as the energy of the unit cell.

[0048] Exemplarily, the orbital coefficients embedded in the R-space can be determined; based on the orbital coefficients embedded in the R-space, the coefficient matrix for converting from atomic orbitals to embedded orbitals in the k-space can be determined; and the Hamiltonian of the embedding can be constructed based on the coefficient matrix. In this way, in the k-space, the Hamiltonian based on atomic orbitals can be projected onto the Hamiltonian based on embedded orbitals based on the coefficient matrix.

[0049] Optionally, the Hamiltonian of the embedding can be determined on a classical computer. Optionally, on a numerical quantum simulator or a quantum computer, the Hamiltonian of each embedding among the plurality of embeddings can be obtained by solving using a variational quantum eigensolver, and the Hamiltonian of each embedding includes the first-order reduced density matrix and the second-order reduced density matrix. As will be further elaborated below in conjunction with Figure 6 As further elaborated.

[0050] In addition, the chemical potential of the Hamiltonian can also be optimized; and the correlated potential of the Hamiltonian after chemical potential optimization can be optimized. In this way, the quality of the solution can be improved through self-consistent iteration, avoiding the situation where the bath region cannot include the interaction between the fragment and the environment due to the inaccuracy of the wave function under the mean-field approximation.

[0051] Exemplarily, the correlated potential optimization may include: performing correlated potential optimization on some of the plurality of fragments, where the number of some fragments is less than the number of the plurality of fragments. In this way, it is not necessary to perform correlated potential optimization for all fragments, and such a local fitting method can avoid the problem of convergence difficulties while maintaining the calculation accuracy.

[0052] Below will be further elaborated in conjunction with Figures 3 to 8 The embodiments of the present disclosure will be elaborated in more detail.

[0053] Figure 3A schematic diagram showing a processing flow using DMET according to some embodiments of the present disclosure is shown. It can be understood that DMET is a quantum embedding method that divides the system under consideration into two parts: a fragment and an environment. Considering the coupling between the fragment and the environment reasonably, a high-cost and high-precision method (such as VQE with the help of a quantum computer) is used to study the fragment, while a low-cost and relatively low-precision method (such as the Hartree-Fock method) is used to study the environment, so as to ensure reducing the calculation cost on the premise of calculation accuracy.

[0054] Exemplarily, for a periodic material, the calculation supercell (abbreviated as supercell) includes a plurality of calculation unit cells (abbreviated as unit cells), such as N k units. As Figure 3 shown, the supercell 310 includes 3*3 = 9 unit cells. For example, the numbers of the 9 unit cells are sequentially 1 to 9 from top to bottom and from left to right. Correspondingly, it can be understood that this supercell is equivalent to sampling 3*3 in the k-space.

[0055] For a unit cell in the supercell, such as the unit cell numbered 5, it can be divided into a plurality of fragments. As Figure 3 shown, it is divided into three fragments, namely a, b, and c in sequence. In some examples, different fragments may have the same size, or different fragments may also have different sizes.

[0056] For a specific fragment (such as fragment a), the rest of the supercell except this fragment is the environment. As Figure 3 shown, through the method of Schmidt decomposition, for fragment a 321, its bath region 323 (denoted as α) can be determined from the environment 322. Specifically, the "components" in the environment 322 that interact with the fragment 321 can be extracted to obtain the bath region α 323. Exemplarily, the other environmental part in the environment 322 except the bath region α 323 is called the core region. In some examples, the number of orbitals included in the bath region α 323 does not exceed the number of orbitals included in the corresponding fragment 321. For example, assuming that the number of orbitals included in the fragment 321 is N A , then the maximum number of orbitals included in the bath region α 323 is N A . The fragment and the corresponding bath region together constitute the embedding. As Figure 3 shown, fragment a 321 and bath region α 323 together constitute the embedding 331. This embedding 331 includes fragment a and the influence of the environment 322 on fragment a. Exemplarily, by performing an exact solution on the embedding 331, the properties of fragment a can be obtained, that is, 341 as Figure 3 shown.

[0057] Similarly, for the remaining segments in the unit cell, namely segment b and segment c, embeddings 332 (including segment b and bath β) and 333 (including segment b and bath γ) are constructed through similar operations, and the properties 342 of segment b and 343 of segment c are obtained by exact solution. It can be seen that since the size of the segment is smaller than the unit cell, the scale for exact solution is greatly reduced.

[0058] Furthermore, by combining the solutions of multiple embeddings, the energy (E) 350 of the unit cell can be obtained. It is understandable that the obtained result of the unit cell includes the influence of other unit cells in the supercell on it, so this result is different from the result obtained only for a 1*1 unit cell.

[0059] Figure 4 The flowchart of an exemplary process 400 for determining the energy of a unit cell according to some embodiments of the present disclosure is shown. In process 400, the input can be a supercell of a periodic material. Exemplarily, the supercell can be obtained by sampling in k-space.

[0060] In some embodiments, k x ×k y ×k z sampling can be performed in the first Brillouin zone, and the number of sampled k points is N k ones, which is equivalent to constructing a k x ×k y ×k z supercell. For example, for the 2D-BN shown in (2) as Figure 1 , a supercell including 3*3 = 9 unit cells can be obtained by 3*3 sampling.

[0061] At 410, a localization operation can be performed. In some embodiments, for a supercell of a periodic material, its initial atomic orbital basis set can be determined, and then a localization operation can be performed on this atomic orbital basis set to generate a set of localized orbital basis sets that are orthogonal to each other. Exemplarily, the atomic orbital (AO) basis set can be represented as Exemplarily, the localized orbital (LO) basis set can also be referred to as a set of localized and mutually orthogonal basis functions, and can be represented as Exemplarily, this localization operation can be represented by the following formula (1):

[0062]

[0063] where, in formula (1), represents the coefficient matrix for converting AO to LO in k-space.

[0064] At 420, an orbital partitioning operation can be performed. Exemplarily, the orbital partitioning operation is used to divide a unit cell into multiple segments, and this orbital partitioning operation can also be referred to as a segmentation operation. In some embodiments, a unit cell can be divided into multiple segments based on a set of localized orbital basis sets that are orthogonal to each other. Exemplarily, a segment can be determined by merging associated orbitals. Exemplarily, it can be assumed that the number of multiple segments is N (for example Figure 3 where N = 3 in LO,k ), and the i-th segment among the multiple segments can be represented as {χ frag＝i}(r). And it should be understood that any basis function in a unit cell

[0065] belongs to and only belongs to one segment. Figures 7 to 8 As can be seen, the embodiments of the present disclosure perform partitioning at the orbital level rather than at the atomic level or unit cell level, so as to divide the correlated orbitals located on different atoms into one segment, which can greatly reduce the size of the segment and the subsequent calculation scale. And through such a partitioning method, accurate results can be obtained, as described in the following combination with

[0066] This way, the embodiments of the present disclosure provide an orbital-based multi-segment partitioning scheme. It is possible to perform segment partitioning in a unit cell of a periodic system based on localized orbitals, so that the scale of each segment is small enough, which can further reduce the scale of the system required by subsequent high-precision solvers.

[0067] At 43*, an integral transformation operation can be performed. Exemplarily, the integral transformation operation can also be referred to as a space transformation operation, which can transform the k-space to the R-space. In some embodiments, a mean-field calculation can be performed, and then using the Fourier transform, the first-order reduced density matrix obtained by the mean-field method is converted from the k-space to the R-space. For example, if the reduced density matrix is represented as then this transformation can be represented as Similarly, similar integral transformation operations can also be performed on other data such as basis functions and electronic integrals.

[0068] It can be understood that due to the translational symmetry of periodic materials, calculations are generally performed in the k-space to improve calculation efficiency. However, when constructing the bath region, it is necessary to perform calculations in the R-space. Therefore, a space transformation is required before constructing the bath region. Additionally, it should be noted that k x ×k y ×k z sampling is performed in the first Brillouin zone, and the dimension of the k-space here is equal to the dimension of the R-space.

[0069] At 440, an embedded Hamiltonian (Hemb )。Exemplarily, the process of constructing the Hamiltonian may include determining the bath region corresponding to each fragment, and then each fragment and its corresponding bath region form an embedding. Further, an embedded Hamiltonian can be constructed, denoted as H emb .

[0070] Specifically, for a certain fragment i, all the other local orbitals are the environment of the fragment i. In the density matrix , the off-diagonal blocks of the fragment i and its environment can be subjected to singular value decomposition, and then the orbitals of the bath region can be obtained, denoted as B pr . Exemplarily, the bath region corresponding to the fragment can be determined by Schmidt decomposition.

[0071] It can be understood that the density matrix is in the R-space, so the obtained orbital coefficients are also in the R-space. That is, in the R-space, the localized orbitals (LO) are converted into embedding orbitals (EO), which can be expressed as

[0072] Exemplarily, constructing the fragment together with its corresponding bath region is called an embedding. And the orbital coefficients of this embedding in the R-space can be expressed as the following formula (2):

[0073]

[0074] Based on this orbital coefficient, using Fourier transform, the coefficient matrix for converting LO to EO in the k-space can be obtained, as shown in the following formula (3):

[0075]

[0076] Further, the coefficient matrix for converting AO to EO in the k-space can be obtained, as shown in the following formula (4):

[0077]

[0078] In this way, the Hamiltonian H originally based on AO with dimension N can be projected onto the embedded Hamiltonian H with dimension no greater than 2N based on EO A by the coefficient matrix emb , expressed as the following formula (5):

[0079]

[0080] At 450, calculate the Hamiltonian (H emb ). In some embodiments, the embedded Hamiltonian can be solved by a correlated wave function method. For example, the first-order reduced density matrix (denoted as ) and the second-order reduced density matrix (denoted as ). In some embodiments, the Hamiltonian can be calculated on a classical computer using high-order quantum chemistry methods. In other embodiments, the Hamiltonian can be calculated on a numerical quantum simulator or a quantum computer using methods such as VQE. Exemplarily, the Hamiltonian H emb can be solved using the VQE method, and the first-order and second-order reduced density matrices can be output. In still other embodiments, the Hamiltonian can be calculated by combining a quantum computer and a classical computer, as will be further described in connection with Figure 6 .

[0081] As Figure 4 shown, the output can be obtained based on the H emb solved at 450. In some embodiments, the energy of each of a plurality of segments can be determined, and the sum of the energies of the plurality of segments can be determined to obtain the energy of the unit cell. It is understood that the output represents the energy of the unit cell.

[0082] Optionally or additionally, as Figure 4 shown, optimization can also be performed at 460. The optimization process will be further described in connection with Figure 5 . Figure 5 FIG. shows a schematic flow chart of a process 500 for obtaining an output through optimization according to some embodiments of the present disclosure.

[0083] At 461, chemical potential optimization is performed. Specifically, the sum of the diagonal elements corresponding to the segment orbitals in the first-order reduced density matrix obtained in 450 represents the electron occupancy number on the segment orbitals. Since after solving H emb using a high-precision solver such as VQE, the electrons in the embedding will be rearranged between the segment orbitals and the bath orbitals, it is possible that the number of electrons in the segment orbitals obtained by the high-precision solver is not conserved. Based on this, in the embodiments of the present disclosure, an additional parameter (referred to as the chemical potential, denoted as μ) is introduced, and a loss function is constructed for optimization.

[0084] Exemplarily, the chemical potential loss function can be expressed as Equation (6) below, where N occ represents the number of electrons in a unit cell:

[0085] L(μ) = |∑ A N A (μ) - N occ | (6)

[0086] Further, at 462, it can be determined whether to converge based on the loss function L(μ). If not convergent, return to 450 to re-solve the Hamiltonian. If convergent, proceed to 463.

[0087] At 463, the correlation potential is optimized. Specifically, through chemical potential optimization, for fragment i, the first-order reduced density matrix of fragment i can be obtained by solving with a high-precision solver, denoted as Optionally, in some embodiments, the first-order reduced density matrix of fragment i can be based on to update the orbitals of the bath region.

[0088] Exemplarily, in 440, a low-precision solver (such as the mean-field method) can be used to determine a low-precision first-order reduced density matrix, denoted as

[0089] In an embodiment of the present disclosure, when performing correlation potential optimization in 463, an additional parameter (referred to as the correlation potential, denoted as u pq ) is introduced, and a loss function is constructed for optimization.

[0090] Exemplarily, the correlation potential loss function can be expressed as Equation (7) below, where this loss function is used to make as close as possible to

[0091]

[0092] Furthermore, at 464, it can be determined whether to converge based on the loss function L(u pq ). If not converged, return to 440 to reconstruct the Hamiltonian. If converged, output.

[0093] In some embodiments of the present disclosure, the correlation potential optimization can also be referred to as correlation potential fitting, and in 463, the correlation potential fitting can be performed only for fragments among multiple fragments, without performing it for all fragments. Thus, the present disclosure realizes the "local fitting" of the correlation potential. In this way, the problem of difficult convergence of the correlation potential can be suppressed while maintaining the calculation accuracy as much as possible, thereby improving the overall energy calculation efficiency.

[0094] It can be understood that when performing Schmidt decomposition to determine the bath region, only when the exact wave function is known can the obtained bath region truly contain a complete characterization of the fragment-environment interaction. However, in practical applications, when initially determining the bath region, it is based on an approximate wave function (such as a wave function under mean-field approximation), so the initially determined bath region may be inaccurate. In the embodiments of the present disclosure, by optimizing 460 (including chemical potential optimization 461 and correlation potential optimization 463), the quality of the solution can be improved through self-consistent iteration, so that the accuracy of the energy of the obtained unit cell is higher.

[0095] In addition, as described above in combination with Figure 4As described in 450, in the embodiments of the present disclosure, the embedded Hamiltonian can be determined by VQE on a quantum computer or a numerical quantum simulator. It can be understood that for a quite long period of time, the number of qubits that a quantum computer can handle (currently dozens of qubits) far from meets the requirements of quantum simulation of periodic systems (hundreds or even thousands of qubits). In the embodiments of the present disclosure, since a unit cell is divided into multiple segments, the scale of a single segment is greatly reduced, so that the current quantum computer has the ability to handle the simulation problem of periodic material systems.

[0096] Figure 6 FIG. shows a schematic flowchart of a process 450 for determining an embedded Hamiltonian according to some embodiments of the present disclosure. Exemplarily, the process 450 can be executed on a quantum computer, or as Figure 6 shown, can be executed on a combination of a quantum computer and a classical computer.

[0097] At 451, quantum state preparation can be performed based on the Hamiltonian H constructed at 440 emb . In some embodiments, the Hamiltonian H emb is represented in the form of a fermionic operator and can be converted into a Pauli operator representation for simulation on a quantum computer. Exemplarily, based on the Hamiltonian H in the form of Pauli operators emb , a quantum initial state can be prepared on a quantum computer, and the quantum initial state can be, for example, a Hartree - Fock (HF) state.

[0098] At 452, a quantum circuit is executed. In some embodiments, a parameter - containing quantum circuit can be constructed based on the Pauli operator representation and the quantum circuit is executed.

[0099] At 453, an observable measurement is performed. Specifically, by executing the quantum circuit at 452, the energy of the simulated system can be measured.

[0100] At 454, parameter update is performed. Specifically, the parameters can be optimized on a classical computer. Exemplarily, according to the optimized parameters, the quantum state can be prepared again on the quantum computer (such as when not converging at 455), the quantum circuit can be constructed and measured, and the parameters are re - optimized until the energy converges (such as when converging at 455).

[0101] Furthermore, based on the parameters when converging at 455, a quantum circuit can be constructed on the quantum computer and the first - order reduced density matrix and the second - order reduced density matrix can be measured as the result of 450.

[0102] The embodiments of the present disclosure can be applied to various periodic materials, as described below in conjunction with Figure 7 and Figure 8Fragmentations of two-dimensional single-layer boron nitride and three-dimensional transition metal oxide nickel oxide are respectively shown.

[0103] As Figure 7 shows a schematic diagram of the supercell of two-dimensional single-layer boron nitride (2D-BN). When performing fragmentation, the unit cell 701 can be divided into three fragments. The first fragment 710 includes the 2s orbital, 2p x orbital and 2p y orbital of B. The second fragment 720 includes the 2s orbital, 2p x orbital and 2p y orbital of N. The third fragment 730 includes the remaining orbitals of the unit cell. Exemplarily, the embedded Hamiltonian can be determined for the first fragment 710 and the second fragment 720 using the VQE method on a quantum computer, and the embedded Hamiltonian can be determined for the third fragment 730 on a classical computer.

[0104] Exemplarily, the unit cell of 2D-BN includes one B atom and one N atom, and the equation of state of 2D-BN can be calculated. By constructing supercells of different sizes and comparing them using the scheme of the present disclosure, the results are shown in Table 2.

[0105] Table 2

[0106]

[0107]

[0108] As can be seen from Table 2, using the scheme in the present disclosure, only two calculations of 12 qubits are required, which is much easier than one calculation of 24 qubits.

[0109] As Figure 8 shows a schematic diagram of the supercell of three-dimensional transition metal oxide nickel oxide (3D-NiO). When performing fragmentation, the unit cell 801 can be divided into three fragments. The first fragment 810 includes the e g orbital of Ni1 and the 2p orbitals of O1 (including 2p x , 2p y and 2p z ). The second fragment 820 includes the e g orbital of Ni2 and the 2p orbitals of O2 (including 2p x , 2p y and 2p z ). The third fragment 830 includes the remaining orbitals of the unit cell. Exemplarily, the embedded Hamiltonian can be determined for the first fragment 810 and the second fragment 820 using the VQE method on a quantum computer, and the embedded Hamiltonian can be determined for the third fragment 830 on a classical computer.

[0110] Exemplarily, the unit cell of 3D-NiO includes two Ni atoms and two O atoms, and the magnetic order of 3D-NiO, i.e., the energy difference between the ferromagnetic phase and the antiferromagnetic phase, can be calculated. By constructing supercells of different sizes and comparing them using the scheme of the present disclosure, the results are shown in Table 3.

[0111] Table 3

[0112]

[0113] As can be seen from Table 3, using the scheme in the present disclosure, only two calculations of 20 qubits are required, and the requirements for the processing resources of the quantum computer are relatively low.

[0114] It should be understood that in the embodiments of the present disclosure, "first", "second", "third", etc. are only used to indicate that multiple objects may be different, but at the same time do not exclude that two objects are the same, and should not be construed as any limitation to the embodiments of the present disclosure.

[0115] It should also be understood that the division of the manners, situations, categories, and embodiments in the embodiments of the present disclosure is only for the convenience of description and should not constitute a special limitation. The features in various manners, categories, situations, and embodiments can be combined with each other under logical conditions.

[0116] It should also be understood that the above content is only to help those skilled in the art better understand the embodiments of the present disclosure, rather than to limit the scope of the embodiments of the present disclosure. Those skilled in the art can make various modifications, changes, or combinations according to the above content. The solutions after such modifications, changes, or combinations are also within the scope of the embodiments of the present disclosure.

[0117] It should also be understood that the above description focuses on emphasizing the differences between the various embodiments, and the same or similar parts can be referred to or borrowed from each other. For the sake of brevity, they will not be elaborated here.

[0118] Figure 9 FIG. shows a schematic block diagram of an exemplary device 900 according to some embodiments of the present disclosure. The device 900 can be implemented by software, hardware, or a combination of both.

[0119] As Figure 9As shown, the device 900 includes an acquisition module 910, a partitioning module 920, a bath region determination module 930, and an energy determination module 940. The acquisition module 910 is configured to acquire the atomic orbital basis set of the unit cell in the supercell of the periodic material. The partitioning module 920 is configured to partition the unit cell into multiple segments based on the atomic orbital basis set of the unit cell. The bath region determination module 930 is configured to determine multiple bath regions in the supercell corresponding to the multiple segments respectively. The energy determination module 940 is configured to determine the energy of the unit cell based on the multiple segments and the multiple bath regions.

[0120] In some embodiments, the partitioning module 920 may include a localized orbital basis set determination sub-module, an orbital subgroup partitioning sub-module, and a multi-segment determination sub-module. The localized orbital basis set determination sub-module is configured to determine a set of mutually orthogonal localized orbital basis sets based on the atomic orbital basis set of the unit cell. The orbital subgroup partitioning sub-module is configured to partition the set of mutually orthogonal localized orbital basis sets into multiple orbital subgroups. The multi-segment determination sub-module is configured to determine multiple segments based on the multiple orbital subgroups.

[0121] In some embodiments, the bath region determination module 930 may include a transformation sub-module and a bath region determination sub-module. The transformation sub-module is configured to transform from the reciprocal space to the real space through a space transformation operation. The bath region determination sub-module is configured to determine multiple bath regions in the real space corresponding to the multiple segments respectively.

[0122] Exemplarily, the bath region determination sub-module may include an environment determination sub-unit and a bath region determination sub-unit. The environment determination sub-unit is configured to determine the rest of the supercell except the first segment as the environment of the first segment in the real space. The bath region determination sub-unit is configured to perform singular value decomposition on the non-diagonal block of the first-order reduced density matrix of the first segment and the environment to determine the first bath region corresponding to the first segment, where the first segment may be any one of the multiple segments.

[0123] In some embodiments, the energy determination module 940 may include an embedding construction sub-module, a Hamiltonian determination sub-module, a segment energy determination sub-module, and a unit cell energy determination sub-module. The embedding construction sub-module is configured to construct multiple embeddings based on the multiple segments and the multiple bath regions. The Hamiltonian determination sub-module is configured to determine the Hamiltonian of each embedding in the multiple embeddings. The segment energy determination sub-module is configured to determine the energy of each segment in the multiple segments based on the Hamiltonian of each embedding in the multiple embeddings. The unit cell energy determination sub-module is configured to determine the sum of the energies of the multiple segments as the energy of the unit cell.

[0124] Exemplarily, the apparatus 900 may further include a construction module configured to determine the orbital coefficients embedded in real space; determine a coefficient matrix for converting from atomic orbitals to embedded orbitals in reciprocal space based on the orbital coefficients embedded in real space; and construct an embedded Hamiltonian based on the coefficient matrix.

[0125] Exemplarily, the Hamiltonian determination sub-module is configured to be specifically configured to solve for the Hamiltonian of each embedding among multiple embeddings on a numerical quantum simulator or a quantum computer through a variational quantum eigensolver or other quantum chemistry methods, and the Hamiltonian of each embedding includes a first-order reduced density matrix and a second-order reduced density matrix.

[0126] Exemplarily, the apparatus 900 may further include an optimization module configured to: perform chemical potential optimization on the Hamiltonian; and perform correlation potential optimization on the Hamiltonian after chemical potential optimization.

[0127] Optionally, the optimization module may be configured to: perform correlation potential optimization on some of the multiple segments, where the number of some segments is less than the number of the multiple segments.

[0128] In some examples, the apparatus 900 may further include an input module configured to determine a supercell by sampling in reciprocal space.

[0129] In some embodiments, the periodic material includes any one of the following: a one-dimensional hydrogen structure, a two-dimensional single-layer boron nitride, or a three-dimensional transition metal oxide nickel oxide.

[0130] Figure 9 The apparatus 900 can be used to implement the above-mentioned combination Figures 2 to 6 The process described above, for the sake of brevity, will not be elaborated here.

[0131] The division of modules or units in the embodiments of the present disclosure is illustrative, merely a logical function division. In actual implementation, there may be other division methods. In addition, the functional units in the disclosed embodiments may be integrated into one unit, may exist separately physically, or two or more units may be integrated into one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.

[0132] Figure 10 The block diagram of an example device 1000 that can be used to implement the embodiments of the present disclosure is shown. It should be understood that Figure 10 The shown device 1000 is merely exemplary and should not constitute any limitation to the functions and scopes of the implementation manners described herein. For example, the device 1000 can be used to execute the above-described Figures 2 to 6The processes described above. For example, device 1000 may be implemented as a classical computer and / or a quantum computer.

[0133] As Figure 10 shown, device 1000 is in the form of a general-purpose computing device. The components of computing device 1000 may include, but are not limited to, one or more processors or processing units 1010, a memory 1020, a storage device 1030, one or more communication units 1040, one or more input devices 1050, and one or more output devices 1060. Processing unit 1010 may be an actual or virtual processor and is capable of performing various processes according to programs stored in memory 1020. In a multi-processor system, multiple processing units execute computer-executable instructions in parallel to improve the parallel processing ability of computing device 1000.

[0134] Computing device 1000 generally includes multiple computer storage media. Such media may be any available media accessible to computing device 1000, including but not limited to volatile and non-volatile media, removable and non-removable media. Memory 1020 may be volatile memory (such as registers, caches, random access memory (RAM)), non-volatile memory (such as read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory), or some combination thereof. Storage device 1030 may be removable or non-removable media and may include machine-readable media, such as a flash drive, a magnetic disk, or any other media that can be used to store information and / or data (such as training data for training) and can be accessed within computing device 1000.

[0135] Computing device 1000 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not shown in Figure 10 it, a disk drive for reading from or writing to a removable, non-volatile magnetic disk (such as a "floppy disk") and an optical disk drive for reading from or writing to a removable, non-volatile optical disk may be provided. In these cases, each drive may be connected to a bus (not shown) by one or more data media interfaces. Memory 1020 may include a computer program product 1025 having one or more program modules that are configured to perform the various methods or actions of the various implementations of the present disclosure.

[0136] The communication unit 1040 enables communication with other computing devices via a communication medium. Additionally, the functionality of the components of the computing device 1000 can be implemented with a single computing cluster or multiple computing machines that are capable of communicating via a communication link. Thus, the computing device 1000 can operate in a networked environment using a logical connection to one or more other servers, network personal computers (PCs), or another network node.

[0137] The input device 1050 can be one or more input devices such as a mouse, keyboard, trackball, etc. The output device 1060 can be one or more output devices such as a display, speaker, printer, etc. The computing device 1000 can also communicate with one or more external devices (not shown) as needed via the communication unit 1040, such as storage devices, display devices, etc., communicate with one or more devices that enable a user to interact with the computing device 1000, or communicate with any device that enables the computing device 1000 to communicate with one or more other computing devices (e.g., network card, modem, etc.). Such communication can be performed via an input / output (I / O) interface (not shown).

[0138] According to an exemplary implementation of the present disclosure, a computer-readable storage medium is provided, on which computer-executable instructions are stored, and the computer-executable instructions are executed by a processor to implement the method described above. According to an exemplary implementation of the present disclosure, a computer program product is also provided, the computer program product being tangibly stored on a non-transitory computer-readable medium and including computer-executable instructions, and the computer-executable instructions being executed by a processor to implement the method described above. According to an exemplary implementation of the present disclosure, a computer program product is provided, on which a computer program is stored, and the program, when executed by a processor, implements the method described above.

[0139] Aspects of the present disclosure are described herein with reference to the flowcharts and / or block diagrams of methods, apparatuses, devices, and computer program products according to the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and the combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.

[0140] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that the instructions, when executed by the processing unit of the computer or other programmable data processing apparatus, result in an apparatus that implements the functions / actions specified in one or more boxes of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer-readable medium storing the instructions comprises a manufacture including instructions that implement various aspects of the functions / actions specified in one or more boxes of the flowchart and / or block diagram.

[0141] The computer-readable program instructions may be loaded onto a computer, other programmable data processing apparatus, or other device, such that a series of operational steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes of the flowchart and / or block diagram.

[0142] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various implementations of the present disclosure. In this regard, each box in the flowchart or block diagram may represent a module, a segment of code, or a portion of an instruction, and the module, segment of code, or portion of an instruction may include one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions noted in the boxes may occur out of the order noted in the figures. For example, two consecutive boxes may in fact be executed substantially in parallel, or they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each box in the block diagrams and / or flowcharts, and combinations of boxes in the block diagrams and / or flowcharts, can be implemented by a dedicated hardware-based system that performs the specified functions or actions, or by a combination of dedicated hardware and computer instructions.

[0143] The implementations of the present disclosure have been described above. The description is illustrative, not exhaustive, and is not limited to the disclosed implementations. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described implementations. The choice of terms used herein is intended to best explain the principles of the implementations, the practical application, or the improvement of the technology in the market, or to enable other ordinary skill in the art to understand the various implementations disclosed herein.

Claims

1. A data processing method, comprising: Obtaining an atomic orbital basis set of a unit cell in a supercell of a periodic material; Dividing the unit cell into a plurality of segments based on the atomic orbital basis set of the unit cell; Determining a plurality of bath regions in the supercell respectively corresponding to the plurality of segments; And Determining the energy of the unit cell based on the plurality of segments and the plurality of bath regions.

2. The method according to claim 1, wherein dividing the unit cell into a plurality of segments based on the atomic orbital basis set of the unit cell comprises: Determining a localized orbital basis set that is orthogonal to each other based on the atomic orbital basis set of the unit cell; Dividing the mutually orthogonal localized orbital basis set into a plurality of orbital subgroups; And Determining the plurality of segments based on the plurality of orbital subgroups.

3. The method according to claim 1, wherein determining a plurality of bath regions in the supercell respectively corresponding to the plurality of segments comprises: Performing a space transformation operation to transform from reciprocal space to real space; And Determining the plurality of bath regions respectively corresponding to the plurality of segments in the real space.

4. The method according to claim 3, wherein determining the plurality of bath regions respectively corresponding to the plurality of segments in the real space comprises determining a first bath region corresponding to a first segment among the plurality of segments by the following formula: Determining the remaining part of the supercell except the first segment as the environment of the first segment in the real space; and Performing singular value decomposition on the non-diagonal block of the first-order reduced density matrix of the first segment and the environment to determine the first bath region corresponding to the first segment.

5. The method according to any one of claims 1 to 4, wherein determining the energy of the unit cell based on the plurality of segments and the plurality of bath regions comprises: Constructing a plurality of embeddings based on the plurality of segments and the plurality of bath regions; Determining the Hamiltonian of each embedding among the plurality of embeddings; Determining the energy of each segment among the plurality of segments based on the Hamiltonian of each embedding among the plurality of embeddings; And Determining the sum of the energies of the plurality of segments as the energy of the unit cell.

6. The method according to claim 5, further comprising: Determining the orbital coefficients of the embedding in real space; Determining a coefficient matrix for converting from atomic orbitals to embedding orbitals in reciprocal space based on the orbital coefficients of the embedding in real space; and Constructing the Hamiltonian of the embedding based on the coefficient matrix.

7. The method according to claim 5, wherein determining the Hamiltonian of each embedding among the plurality of embeddings comprises: Solving for the Hamiltonian of each embedding among the plurality of embeddings through a variational quantum eigensolver on a numerical quantum simulator or a quantum computer, and the Hamiltonian of each embedding includes a first-order reduced density matrix and a second-order reduced density matrix.

8. The method according to claim 5, further comprising: Performing chemical potential optimization on the Hamiltonian; And Performing correlation potential optimization on the Hamiltonian after chemical potential optimization.

9. The method according to claim 8, wherein performing correlation potential optimization comprises: Performing correlation potential optimization on some of the plurality of segments, wherein the number of the some segments is less than the number of the plurality of segments.

10. The method according to any one of claims 1 to 4 further comprises: Determining the supercell by sampling in reciprocal space.

11. The method according to any one of claims 1 to 4, wherein the periodic material comprises any one of the following: One-dimensional hydrogen structure, Two-dimensional monolayer boron nitride, or Three-dimensional transition metal oxide nickel oxide.

12. An electronic device comprising: At least one processing unit; At least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions when executed by the at least one processing unit causing the electronic device to perform actions, the actions comprising: Obtaining an atomic orbital basis set of a unit cell in a supercell of a periodic material; Dividing the unit cell into a plurality of segments based on the atomic orbital basis set of the unit cell; Determining a plurality of bath regions in the supercell respectively corresponding to the plurality of segments; and Determining the energy of the unit cell based on the plurality of segments and the plurality of bath regions.

13. A data processing device comprising: An obtaining module configured to obtain an atomic orbital basis set of a unit cell in a supercell of a periodic material; A dividing module configured to divide the unit cell into a plurality of segments based on the atomic orbital basis set of the unit cell; A bath region determining module configured to determine a plurality of bath regions in the supercell respectively corresponding to the plurality of segments; And An energy determining module configured to determine the energy of the unit cell based on the plurality of segments and the plurality of bath regions.

14. A computer-readable storage medium having stored thereon a computer program, which when executed by a processor implements the method according to any one of claims 1 to 11.

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