Method and device for determining quantum system state representation, equipment and storage medium

Abstract

The embodiment of the invention relates to a method and device for determining quantum system state representation, equipment and a storage medium. The method proposed herein includes: obtaining a pseudo Hamiltonian for a quantum system, the pseudo Hamiltonian configured to approximate a true Hamiltonian of the quantum system using a local interaction between a plurality of valence electrons in a subsystem; determining the energy of the quantum system based on the pseudo Hamiltonian and the neural network representing the wave function of the quantum system; and reducing the energy of the quantum system by using a Monte Carlo algorithm, and updating the neural network.

Description

Technical Field

[0001] Example embodiments of the present disclosure generally relate to the field of computer technology, and more particularly, to a method, apparatus, device, and storage medium for determining a representation of a quantum system state. Background Art

[0002] Neural Network-based Quantum Monte Carlo (NNQMC) has become a powerful method for solving many-body quantum systems with high accuracy. However, due to its demanding computational requirements, its practical application is limited to relatively small quantum systems. Therefore, improving the computational efficiency of NNQMC is an urgent technical challenge. Summary of the Invention

[0003] In a first aspect of the present disclosure, a method for determining a state representation of a quantum system is provided. The method includes: obtaining a pseudo-Hamiltonian for the quantum system, the pseudo-Hamiltonian being configured to approximate a true Hamiltonian of the quantum system using localized interactions between a plurality of valence electrons in the quantum system; determining an energy of the quantum system based on the pseudo-Hamiltonian and a neural network representing a wave function of the quantum system; and updating the neural network by reducing the energy of the quantum system using a Monte Carlo algorithm.

[0004] In a second aspect of the present disclosure, a device for determining a state representation of a quantum system is provided. The device includes: a pseudo-Hamiltonian acquisition module configured to acquire a pseudo-Hamiltonian for the quantum system, wherein the pseudo-Hamiltonian is configured to approximate the true Hamiltonian of the quantum system using localized interactions between multiple valence electrons in the quantum system; an energy calculation module configured to determine the energy of the quantum system based on the pseudo-Hamiltonian and a neural network representing a wave function of the quantum system; and a neural network optimization module configured to reduce the energy of the quantum system by utilizing a Monte Carlo algorithm and thereby update the neural network.

[0005] In a third aspect of the present disclosure, an electronic device is provided. The device includes at least one processor; and at least one memory coupled to the at least one processor and storing instructions for execution by the at least one processor. When executed by the at least one processor, the instructions cause the device to perform the method of the first aspect.

[0006] In a fourth aspect of the present disclosure, a computer-readable storage medium is provided, wherein a computer program is stored on the computer-readable storage medium, and the computer program can be executed by a processor to implement the method of the first aspect.

[0007] In a fifth aspect of the present disclosure, a computer program product is provided, which includes computer-executable instructions, which, when executed by a processor, implement the method according to the first aspect of the present disclosure.

[0008] It should be understood that the content described in this summary section is not intended to limit the key features or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The above and other features, advantages and aspects of the embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0010] Figure 1 A schematic diagram illustrating an example environment in which embodiments of the present disclosure can be implemented;

[0011] Figure 2A A schematic diagram illustrating a framework of a neural network-based quantum Monte Carlo algorithm according to some embodiments of the present disclosure is shown;

[0012] Figure 2B A schematic diagram showing a comparison of the efficiency and accuracy of pseudo-Hamiltonian, semi-local pseudopotential and all-electron according to some embodiments of the present disclosure is shown;

[0013] Figure 3 A flowchart illustrating an example process of a method for determining a representation of a quantum system state according to some embodiments of the present disclosure;

[0014] Figure 4 A schematic structural block diagram of an apparatus for determining a quantum system state representation according to some embodiments of the present disclosure is shown; and

[0015] Figure 5 A block diagram of an electronic device is shown in which one or more embodiments of the present disclosure may be implemented. DETAILED DESCRIPTION

[0016] The following describes embodiments of the present disclosure in more detail with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying 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 described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of 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.

[0017] It should be noted that the titles of any section / subsection provided herein are not limiting. Various embodiments are described throughout this document, and any type of embodiment may be included under any section / subsection. Furthermore, the embodiments described in any section / subsection may be combined in any manner with any other embodiments described in the same section / subsection and / or in different sections / subsections.

[0018] In the description of the embodiments of the present disclosure, the term "including" and similar terms should be understood as open inclusion, that is, "including but not limited to". The term "based on" should be understood as "based at least in part on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The term "some embodiments" should be understood as "at least some embodiments". Other explicit and implicit definitions may be included below. The terms "first", "second", etc. may refer to different or the same objects. Other explicit and implicit definitions may be included below.

[0019] The embodiments of the present disclosure may involve user data, data acquisition and / or use, etc. These aspects shall comply with the corresponding laws, regulations and relevant provisions. In the embodiments of the present disclosure, all data collection, acquisition, processing, processing, forwarding, use, etc. are carried out on the premise that the user is aware of and confirms them. Accordingly, when implementing the various embodiments of the present disclosure, the types, scope of use, and usage scenarios of the data or information that may be involved should be informed to the user and the user's authorization should be obtained in an appropriate manner in accordance with the relevant laws and regulations. The specific notification and / or authorization method may vary according to the actual situation and application scenario, and the scope of the present disclosure is not limited in this respect.

[0020] If this specification and the solutions in the examples involve the processing of personal information, such processing will be done only with a legitimate basis (such as with the consent of the subject of personal information or as necessary for the performance of a contract) and only within the prescribed or agreed scope. A user's refusal to process personal information other than that required for basic functions will not affect the user's use of basic functions.

[0021] Figure 1 A schematic diagram of an example environment 100 is shown in which embodiments of the present disclosure can be implemented. Figure 1 , the example environment 100 may include a terminal device 110 and an electronic device 120 .

[0022] In example environment 100, user 130 can interact with electronic device 120 via terminal device 110 and / or its attached devices. For example, user 130 can provide electronic device 120 with information related to a quantum system to be analyzed via terminal device 110. After determining the quantum system to be analyzed, electronic device 120 can establish a wave function representation of the quantum system and continuously optimize the wave function representation to ensure that the energy estimate corresponding to the wave function representation approximates the true ground state energy of the quantum system. After optimizing the wave function representation, electronic device 120 can determine various physical properties of the quantum system based on the optimized wave function representation and provide the information to user 130 for further analysis and processing.

[0023] In the example environment 100, the terminal device 110 can be any type of mobile terminal, fixed terminal or portable terminal, including a mobile phone, a desktop computer, a laptop computer, a notebook computer, a netbook computer, a tablet computer, a media computer, a multimedia tablet, a personal communication system (PCS) device, a personal navigation device, a personal digital assistant (PDA), an audio / video player, a digital camera / camcorder, a positioning device, a television receiver, a radio broadcast receiver, an e-book device, a gaming device or any combination thereof, including accessories and peripherals of these devices or any combination thereof. In some embodiments, the terminal device 110 can also support any type of interface for the user (such as "wearable" circuitry, etc.).

[0024] The electronic device 120 may be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, content distribution networks, and big data and artificial intelligence platforms. The electronic device 120 may include, for example, a computing system / server, such as a mainframe, an edge computing node, a computing device in a cloud environment, and the like.

[0025] A communication connection may be established between the electronic device 120 and the terminal device 110. The communication connection may be established via a wired or wireless method. The communication connection may include, but is not limited to, a Bluetooth connection, a mobile network connection, a Universal Serial Bus connection, a Wi-Fi connection, etc., and the embodiments of the present disclosure are not limited in this respect. In the embodiments of the present disclosure, the electronic device 120 and the terminal device 110 may implement signaling interaction via the communication connection between them.

[0026] It should be understood that the structure and function of the various elements in the environment 100 are described for illustrative purposes only and do not imply any limitation on the scope of the present disclosure.

[0027] Because the Hilbert space grows exponentially with the size of the quantum system, it is difficult to solve the Schrödinger equation exactly for systems with many particles. Quantum Monte Carlo (QMC) methods provide a mature approximation method for solving the Schrödinger equation with high accuracy and relatively low computational cost. Based on the QMC framework, NNQMC has become a revolutionary method that uses the ability of neural networks to flexibly represent wave functions. By leveraging the expressive power of deep neural networks to represent wave functions, NNQMC provides a highly accurate and scalable method to solve many-body quantum problems. In this paper, the neural network used to represent the wave function is also referred to as the neural network wave function.

[0028] One of the main challenges facing QMC is achieving optimization convergence in the presence of heavy elements (such as elements of the third period and transition metals) due to the high variance of the core electrons. The introduction of pseudopotentials in QMC has been shown to significantly improve optimization stability, accelerate convergence and improve accuracy. These advantages can be naturally extended to NNQMC, where pseudopotentials also solve the convergence problem and improve the overall performance. Semilocal pseudopotentials or effective core potentials (ECP) have been widely used in QMC (for clarity, ECP is used below to refer to semilocal pseudopotentials). It introduces semilocal terms to simulate the interaction between core electrons and valence electrons. ECP uses nonlocal terms to model the interaction between core electrons and valence electrons, which helps to achieve high accuracy in QMC simulations. However, when integrated with NNQMC, these nonlocal terms quickly become new computational bottlenecks, limiting the scalability of NNQMC to larger systems.

[0029] In recent years, a new type of pseudopotential, known as the pseudo-Hamiltonian (PH), has emerged as a promising alternative. Unlike ECPs, pseudo-Hamiltonians rely solely on local information about the wave function, eliminating the need for costly semi-local calculations. While pseudo-Hamiltonians have long been proposed, recent advances in pseudopotential construction techniques have only recently extended their applicability to transition metals.

[0030] Pseudopotentials are widely used in quantum chemistry to simplify the treatment of core electrons. This is particularly important in NNQMC, where the inherent high variance of core electrons hinders optimization. NNQMC can seamlessly incorporate different pseudopotentials in a unified manner by changing the Hamiltonian used in the calculation. In this disclosure, the Hamiltonian has three forms: the all-electron (AE) Hamiltonian, the ECP Hamiltonian, and the pseudoHamiltonian.

[0031] In all-electron calculations, the potential diverges near the nucleus and needs to be handled with the correct peak conditions. Pseudopotentials address this divergence by replacing the core electrons with an effective potential that behaves well near the nucleus, while preserving the behavior of the wave function outside the core region. Pseudopotentials are indispensable for transition metals and other complex systems. Even for lighter elements such as sulfur and chlorine, pseudopotentials can significantly improve accuracy and efficiency.

[0032] NNQMC has been integrated with ECP to improve accuracy and efficiency. In early implementations of NNQMC, the main computational bottleneck came from evaluating the Laplacian operator in the kinetic energy term. Therefore, removing the core electrons with ECP can reduce the number of electrons involved, directly accelerating this calculation. However, when adopting the forward Laplacian framework, the computational cost of the Laplacian operator is significantly reduced, reducing the relative efficiency gain provided by ECP. As a result, the nonlocal terms introduced by ECP (which require integration over a 3D sphere) become a new bottleneck, especially in systems with many pseudocores.

[0033] To this end, embodiments of the present disclosure provide a scheme for determining a representation of the state of a quantum system. According to this scheme, a pseudo-Hamiltonian for the quantum system is first obtained. The pseudo-Hamiltonian is configured to approximate the true Hamiltonian of the quantum system using localized interactions between multiple valence electrons in the quantum system. The energy of the quantum system is then determined based on the pseudo-Hamiltonian and a neural network representing the wave function of the quantum system. Next, the energy of the quantum system is reduced using a Monte Carlo algorithm, and the neural network is updated. This optimizes the neural network wave function.

[0034] In this way, the pseudo-Hamiltonian can be integrated into the neural network-based quantum Monte Carlo framework. The pseudo-Hamiltonian can replace the non-local terms with computationally simpler local terms, thereby improving the efficiency and accuracy of the neural network-based quantum Monte Carlo framework.

[0035] Some advantages of the embodiments of the present disclosure are described below with reference to the accompanying drawings. PH is a local pseudopotential that alleviates this problem by replacing the non-local term with a computationally efficient local term, which involves the second-order wave function derivative. In some embodiments, it can be further combined with the forward Laplace framework, as will be described in detail below. Thanks to the forward Laplace framework, these additional local derivative calculations are seamlessly integrated into the kinetic energy calculations, introducing minimal computational overhead. Therefore, for NNQMC with PH, the number of electrons corresponds to the number of valence electrons in the pseudopotential approximation. In practice, PH does not incur significant additional cost, making it an effective solution for large-scale QMC simulations.

[0036] Figure 2A FIG. 2 shows a schematic diagram of a framework 200A of NNQMC according to some embodiments of the present disclosure. Figure 2A As shown, framework 200A includes a chemical system under investigation 205 and Hamiltonian options 210. Hamiltonian options 210 include pH, ECP, and AE. Framework 200A also includes an NNQMC workflow 215, in which the wave function is represented by a neural network-based anatomy (e.g., a Laplace network) and optimized toward lower energies, ultimately converging to the ground state. Energy differences between different systems, such as ionization energies 216, excitation energies 217, and atomization energies 218, can be analyzed for chemical properties 220.

[0037] Figure 2B 200B is a schematic diagram showing a comparison of the efficiency and accuracy of PH, ECP, and AE according to some embodiments of the present disclosure. Figure 2B As shown, using PH can achieve higher accuracy with less computational effort. Pseudopotentials eliminate the wave function fluctuations in the core region caused by the nuclear Coulomb singularity in AE, thus making PH and ECP more accurate. The bottleneck in computational time is the energy calculation, which includes kinetic and potential energy calculations. The combination of accelerated kinetic energy calculations and the avoidance of the semi-local spherical integral required by ECP gives PH its unique efficiency.

[0038] In order to better describe the embodiments of the present disclosure, NNQMC with different Hamiltonian forms will be introduced first.

[0039] NNQMC is a class of high-precision methods for solving the time-independent Schrödinger equation, which can be expressed as follows:

[0040]

[0041] in represents the Hamiltonian operator corresponding to the energy of the quantum system, and ψ represents the wave function of the quantum system. Under the Born-Oppenheimer approximation, the Hamiltonian of the all-electron can be given by the following expression:

[0042]

[0043] Where i and j are subscripts for electrons, I and J are subscripts for nuclei, and Z I Represents the charge. i and R I represent the positions of electrons and nuclei respectively.

[0044] For heavy atoms, the complex interplay of core electron dynamics can lead to significant computational challenges. However, predicting chemical properties often depends more critically on handling valence electrons. In such cases, a simplified form of the effective Hamiltonian can be used that eliminates the core electrons and adds an additional potential energy term to model the interaction between the core and valence electrons. Such a Hamiltonian can be expressed as follows:

[0045]

[0046] in Keep the form of formula (2), but include only valence electrons. vI =|r v -R I | represents the radial distance between the valence electron and atom I.

[0047] The additional potential energy term about atom I is given by It is shown in detail in formula (4). and V l It is usually expanded in a Gaussian basis set with the parameters to be optimized, where |lm> represents the spherical harmonics. However, the non-local nature of the second term in Equation (4) significantly increases the cost of NNQMC calculations.

[0048] Figure 3 FIG. 3 is a flow chart illustrating an example process 300 of a method for determining a representation of a quantum system state according to some embodiments of the present disclosure. The process 300 may be implemented at the electronic device 120 .

[0049] Reference Figure 3 At block 310 , the electronic device 120 obtains a pseudo-Hamiltonian for the quantum system. The pseudo-Hamiltonian is configured to approximate a true Hamiltonian of the quantum system using local interactions between multiple valence electrons in the quantum system.

[0050] As another form of Hamiltonian, the pseudo-Hamiltonian not only approximates the interaction between the ion nucleus and the electron, but also modifies the kinetic energy term using the effective Hamiltonian. Under spherical symmetry around each atom, the general form of the pseudo-Hamiltonian is given by:

[0051]

[0052] in represents the momentum operator, represents the angular momentum operator. a, and is a parameterized function that needs to be optimized. In addition to the kinetic energy, the contains a second-order differential operator, which may have a high computational cost. Using the modified forward Laplace framework, the computational cost of this term can be neglected. In the initial stage of constructing the pseudo-Hamiltonian, all the parameters in Equation (6) are unknown.

[0053] NNQMC provides a unified framework for all three Hamiltonian forms. According to the requirements of Fermi-Dirac statistics, NNQMC solves the Schrödinger equation by modeling the wave function with an antisymmetric neural network. In variational Monte Carlo, according to the variational principle, the total energy is used as the training loss to obtain the first eigenstate (i.e., the ground state) in formula (1). Given a many-body wave function ψ(x), where x = concat(r1,…,r n ) represents the coordinates of the electron, and the total energy can be calculated by the following formula:

[0054]

[0055] in represents the square of the normalized wave function, Denotes the local energy function. The energy results can be further improved by using the Diffusion Monte Carlo method.

[0056] In some embodiments, a pseudoHamiltonian can be constructed. For example, various parameters of the pseudoHamiltonian can be initialized. The pseudoHamiltonian can then be optimized by reducing the difference between the pseudoHamiltonian and a reference pseudopotential for the quantum system. In some examples, the reference pseudopotential can include a semilocal pseudopotential, a norm-conserving pseudopotential, an ultrasoft pseudopotential, or the like.

[0057] When optimizing the pseudo-Hamiltonian, the radial effective mass of the electron is fixed to be equal to its actual mass by setting a(r) = 0 in Equation (6). Under this constraint, the kinetic energy term of the Hamiltonian is simplified to the standard form, shifting the focus to the potential energy term in the construction. Excluding the kinetic energy term, the pseudo-Hamiltonian can be expressed in the following expanded form using the spherical harmonics |lm>:

[0058]

[0059] By exploiting the similarity with the ECP, the parameterized functions in the pseudo-Hamiltonian are assigned so that the matrix elements match those of the ECP:

[0060] <lm|V PH (r)|lm>= <lm|V ECP (r)|lm> (9)

[0061] (l=0,1,2,…,M-1; m=-l,-l+1,…,+l)

[0062] where M-1 represents the maximum nonlocal angular momentum channel in a given semilocal pseudopotential.

[0063] In one example, a pseudoHamiltonian for sulfur, a common element in nature, can be constructed. First, the pseudoHamiltonian can be preliminarily optimized using the Hartree-Fock (HF) method. Properties of a quantum system containing sulfur (e.g., a binding curve) are evaluated based on the preliminarily optimized pseudoHamiltonian and a reference pseudopotential. This yields an error that characterizes the difference between the pseudoHamiltonian and the reference pseudopotential. The pseudoHamiltonian can then be reoptimized based on this error.

[0064] The pseudo-Hamiltonian construction process described above is merely exemplary and is not intended to be limiting. Any suitable method may be used to construct the pseudo-Hamiltonian. In some embodiments, an already constructed pseudo-Hamiltonian may be obtained. The embodiments of the present disclosure are not limited in this respect.

[0065] At block 320, electronic device 120 determines the energy of the quantum system based on the pseudo-Hamiltonian and a neural network representing the wave function of the quantum system. A quantum system may be a microscopic system described by quantum mechanics. The wave function represents the state of the quantum system and can indicate the probability distribution of particles in space. The neural network can capture complex electron correlation effects and provide an accurate representation of the wave function.

[0066] In some examples, the neural network representing the wave function can include a Laplace network, a Fermi network, or the like. By inputting the pseudo-Hamiltonian into the neural network, the energy of the quantum system can be determined. The pseudo-Hamiltonian is designed to overcome the localization errors of pseudopotential diffusion Monte Carlo, making it naturally compatible not only with diffusion Monte Carlo but also with variational Monte Carlo.

[0067] In some embodiments, determining the energy of a quantum system can be based on the total Hamiltonian of the quantum system. Based on the pseudo-Hamiltonian and the Coulomb interactions between the multiple valence electrons, a representation of the total Hamiltonian can be constructed. The representation includes second-order derivative terms related to the respective positions of the multiple valence electrons. In one example, the total Hamiltonian can be expressed as follows:

[0068]

[0069] where α,β∈{x,y,z}, Denotes the α-axis momentum operator of the i-th electron, A(r), b(r) and V all (r1,r2,…,r N ) is derived from formula (5). The first term in formula (10), namely The need for second-order operator calculations of neural networks becomes the computational bottleneck of the NNVMC method.

[0070] The total Hamiltonian is then determined by obtaining the computational results of the second-order derivative terms using a forward Laplace algorithm, wherein the forward Laplace algorithm is configured to compute the second-order derivative terms in a single forward pass. In some examples, the forward Laplace algorithm (also known as a forward Laplace framework) can be applied to accelerate the computation of the second-order derivative terms. The forward Laplace algorithm is designed for Laplace computations but can be generalized to any second-order operator.

[0071] The forward Laplace framework calculates the Laplace operator (for example, second-order derivative terms) associated with the neural network through an efficient forward propagation process. Traditional methods calculate the Hessian matrix through automatic differentiation and then take its trace to obtain the Laplace operator, which requires multiple forward and backward propagations, greatly reducing the training speed. The forward Laplace method directly calculates the Laplace operator, avoiding unnecessary calculations and propagations. Specifically, in the forward propagation of each layer, in addition to calculating the hidden state value, the first-order derivative and intermediate Laplace terms are also calculated. In this way, all terms can be calculated iteratively from the first layer to the last layer, thereby calculating the Laplace operator in a single forward propagation.

[0072] In some embodiments, the second-order derivative term may include a plurality of coefficient matrices (denoted as A) corresponding to a plurality of valence electrons, each of which may be determined based on the position of the corresponding valence electron. One or more input terms in the input triple of the forward Laplace algorithm may be determined based on the coefficient matrix. The triple may be represented as

[0073] In some embodiments, the electronic device 120 may perform matrix decomposition on the coefficient matrix corresponding to each valence electron in the plurality of valence electrons to obtain a transformation matrix corresponding to the valence electron. In some examples, since the bounded energy constraint requires that the symmetric coefficient matrix A(r) be positive definite, there exists a matrix The following conditions are met:

[0074] A(r)=Q T (r)Q(r) (11)

[0075] Where Q(r) represents the transformation matrix.

[0076] After determining the transformation matrix, the total transformation matrix for multiple valence electrons can be determined based on the transformation matrices obtained for multiple valence electrons. Based on the total transformation matrix, the first-order input terms in the input triples are generated. The total transformation matrix can be expressed as In determining the total transformation matrix Q tot Afterwards, the first-order input terms can be generated where ψ represents the wave function of the quantum system.

[0077] In some embodiments, the electronic device 120 may construct a second-order operator corresponding to a second-order derivative term based on a plurality of coefficient matrices. Based on the second-order operator, a second-order input term in the input triple is generated. In one example, represents the second-order operator associated with the first term in formula (10), based on which the first-order input term can be generated

[0078] Since the transformation matrix Q tot is a block diagonal matrix, so the triplet The evaluation of can exploit the intrinsic sparse derivative structure in Laplace networks and other neural network-based transforms, making the additional computational cost associated with the pseudo-Hamiltonian negligible.

[0079] At block 330, electronic device 120 updates the neural network by reducing the energy of the quantum system using a Monte Carlo algorithm. By updating the neural network, the wave function can be optimized. The optimized wave function can be used to determine properties of the quantum system, such as energy, momentum, spectral properties, thermodynamic properties, and the like.

[0080] In some examples, the Monte Carlo algorithm may include variational Monte Carlo (VMC), diffusion Monte Carlo, projection Monte Carlo, etc. The embodiments of the present disclosure are not limited to specific updates.

[0081] The embodiments of the present disclosure also provide corresponding devices for implementing the above methods or processes. Figure 4 FIG4 is a schematic block diagram of an apparatus 400 for determining a quantum system state representation according to some embodiments of the present disclosure. The apparatus 400 may be implemented as or included in the electronic device 120. Each module / component in the apparatus 400 may be implemented by hardware, software, firmware, or any combination thereof.

[0082] Reference Figure 4 The apparatus 400 includes a pseudo-Hamiltonian acquisition module 410, an energy calculation module 420, and a neural network optimization module 430. The pseudo-Hamiltonian acquisition module 410 is configured to acquire a pseudo-Hamiltonian for the quantum system. The pseudo-Hamiltonian is configured to approximate the true Hamiltonian of the quantum system using localized interactions between multiple valence electrons in the quantum system. The energy calculation module 420 is configured to determine the energy of the quantum system based on the pseudo-Hamiltonian and a neural network representing the wave function of the quantum system. The neural network optimization module 430 is configured to reduce the energy of the quantum system by using a Monte Carlo algorithm and update the neural network.

[0083] In some embodiments, determining the energy of the quantum system is based on a total Hamiltonian of the quantum system. The energy calculation module 420 is further configured to construct a representation of the total Hamiltonian based on the pseudo-Hamiltonian and the Coulomb interaction between the plurality of valence electrons, the representation including a second-order derivative term associated with the respective positions of the plurality of valence electrons; and determine the total Hamiltonian by obtaining a calculation result of the second-order derivative term using a forward Laplace algorithm, wherein the forward Laplace algorithm is configured to calculate the second-order derivative term in a single forward propagation.

[0084] In some embodiments, the second-order derivative term includes multiple coefficient matrices corresponding to multiple valence electrons, each coefficient matrix is determined based on the position of the corresponding valence electron, and one or more input terms in the input triplet of the forward Laplace algorithm are determined based on the coefficient matrix.

[0085] In some embodiments, the device 400 also includes a first-order input term generation module, which is configured to perform matrix decomposition on the corresponding coefficient matrix for each valence electron in a plurality of valence electrons to obtain a transformation matrix corresponding to the valence electron; determine a total transformation matrix for the plurality of valence electrons based on the transformation matrices obtained respectively for the plurality of valence electrons; and generate a first-order input term in the input triplet based on the total transformation matrix.

[0086] In some embodiments, the apparatus 400 further includes a second-order input term generation module configured to construct a second-order operator corresponding to a second-order derivative term based on multiple coefficient matrices; and to generate a second-order input term in an input triplet based on the second-order operator.

[0087] In some embodiments, the pseudo-Hamiltonian acquisition module 410 is further configured to initialize various parameters of the pseudo-Hamiltonian; and optimize the pseudo-Hamiltonian by reducing the difference between the pseudo-Hamiltonian and a reference pseudo-potential for the quantum system.

[0088] Figure 5 1 is a block diagram of an electronic device 500 in which one or more embodiments of the present disclosure may be implemented. The electronic device 500 may be used to implement, for example, Figure 1 The electronic device 120 or Figure 4 The device 400 shown. It should be understood that Figure 5 The illustrated electronic device 500 is merely exemplary and should not be construed as limiting the functionality and scope of the embodiments described herein.

[0089] Reference Figure 5, electronic device 500 is in the form of a general electronic device. Components of electronic device 500 may include, but are not limited to, one or more processors 510, memory 520, storage device 530, one or more communication units 540, one or more input devices 550, and one or more output devices 560. Processor 510 may be a real or virtual processor and is capable of performing various processes according to a program stored in memory 520. In a multi-processor system, multiple processors execute computer-executable instructions in parallel to increase the parallel processing capabilities of electronic device 500.

[0090] The electronic device 500 typically includes a plurality of computer storage media. Such media can be any available media accessible to the electronic device 500, including but not limited to volatile and non-volatile media, removable and non-removable media. The memory 520 can be a volatile memory (e.g., registers, cache, random access memory (RAM)), a non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. The storage device 530 can be a removable or non-removable medium and can include a machine-readable medium, such as a flash drive, a disk, or any other medium that can be used to store information and / or data and can be accessed within the electronic device 500.

[0091] The electronic device 500 may further include additional removable / non-removable, volatile / non-volatile storage media. Figure 5 As shown in FIG, a magnetic disk drive for reading from or writing to a removable, non-volatile magnetic disk (e.g., 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 520 may include a computer program product 525 having one or more program modules configured to perform various methods or actions of various embodiments of the present disclosure.

[0092] The communication unit 540 enables communication with other electronic devices via a communication medium. Additionally, the functions of the components of the electronic device 500 can be implemented in a single computing cluster or multiple computing machines that can communicate via a communication connection. Thus, the electronic device 500 can operate in a networked environment using a logical connection with one or more other servers, a network personal computer (PC), or another network node.

[0093] Input device 550 may be one or more input devices, such as a mouse, keyboard, or trackball. Output device 560 may be one or more output devices, such as a display, a speaker, or a printer. Electronic device 500 may also communicate with one or more external devices (not shown) via communication unit 540 as needed, such as a storage device, a display device, or the like, with one or more devices that allow a user to interact with electronic device 500, or with any device that allows electronic device 500 to communicate with one or more other electronic devices (e.g., a network card, a modem, etc.). Such communication may be performed via an input / output (I / O) interface (not shown).

[0094] According to an exemplary implementation of the present disclosure, a computer-readable storage medium is provided, on which computer-executable instructions are stored, wherein 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, which is tangibly stored on a non-transitory computer-readable medium and includes computer-executable instructions, and the computer-executable instructions are executed by a processor to implement the method described above.

[0095] Various aspects of the present disclosure are described herein with reference to flowcharts and / or block diagrams of methods, apparatuses, devices, and computer program products implemented according to the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.

[0096] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine such that when these instructions are executed by the processor of the computer or other programmable data processing device, a device is generated that implements the functions / actions specified in one or more blocks in the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium, where these instructions cause the computer, programmable data processing device, and / or other device to operate in a specific manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing various aspects of the functions / actions specified in one or more blocks in the flowchart and / or block diagram.

[0097] Computer-readable program instructions can be loaded onto a computer, other programmable data processing apparatus, or other device so 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 in the flowchart and / or block diagram.

[0098] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple implementations of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part for a module, program segment or instruction, and a part for a module, program segment or instruction comprises one or more executable instructions for realizing the logical function of the specification. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be realized by a special hardware-based system that performs the function or action of the specification, or can be realized by a combination of special hardware and computer instructions.

[0099] While various implementations of the present disclosure have been described above, the foregoing description is intended to be illustrative, non-exhaustive, and not limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is intended to best explain the principles of the implementations, their practical applications, or improvements to existing technologies, or to enable others skilled in the art to understand the various implementations disclosed herein.

Claims

1. A method for determining a representation of a state of a quantum system, comprising: obtaining a pseudo-Hamiltonian for a quantum system, wherein the pseudo-Hamiltonian is configured to approximate a true Hamiltonian of the quantum system using local interactions between a plurality of valence electrons in the quantum system; determining an energy of the quantum system based on the pseudo-Hamiltonian and a neural network representing a wave function of the quantum system; as well as The neural network is updated by reducing the energy of the quantum system using a Monte Carlo algorithm.

2. The method of claim 1 , wherein determining the energy of the quantum system is based on a total Hamiltonian of the quantum system, and the total Hamiltonian is determined by: constructing a representation of the total Hamiltonian based on the Coulombic interaction between the pseudo-Hamiltonian and the plurality of valence electrons, the representation including second-order derivative terms related to respective positions of the plurality of valence electrons; and The total Hamiltonian is determined by obtaining a calculation result of the second-order derivative term using a forward Laplace algorithm, wherein the forward Laplace algorithm is configured to calculate the second-order derivative term in a single forward propagation.

3. The method according to claim 2, wherein the second-order derivative term includes a plurality of coefficient matrices corresponding to the plurality of valence electrons, each coefficient matrix is determined based on the position of the corresponding valence electron, and one or more input terms in the input triplet of the forward Laplace algorithm are determined based on the coefficient matrix.

4. The method according to claim 3, further comprising: For each valence electron in the plurality of valence electrons, performing matrix decomposition on a coefficient matrix corresponding to the valence electron to obtain a transformation matrix corresponding to the valence electron; determining a total transformation matrix for the plurality of valence electrons based on the transformation matrices respectively obtained for the plurality of valence electrons; as well as Based on the total transformation matrix, first-order input terms in the input triplet are generated.

5. The method according to claim 3, further comprising: constructing a second-order operator corresponding to the second-order derivative term based on the multiple coefficient matrices; as well as Based on the second-order operator, second-order input terms in the input triple are generated.

6. The method of claim 1 , wherein constructing the pseudo-Hamiltonian for the quantum system comprises: Initializing various parameters of the pseudo-Hamiltonian; as well as The pseudo-Hamiltonian is optimized by reducing the difference between the pseudo-Hamiltonian and a reference pseudo-potential for the quantum system.

7. An apparatus for determining a representation of a state of a quantum system, comprising: a pseudo-Hamiltonian acquisition module, configured to acquire a pseudo-Hamiltonian for a quantum system, wherein the pseudo-Hamiltonian is configured to approximate a true Hamiltonian of the quantum system using a local interaction between a plurality of valence electrons in the quantum system; an energy calculation module configured to determine the energy of the quantum system based on the pseudo-Hamiltonian and a neural network representing a wave function of the quantum system; and The neural network optimization module is configured to update the neural network by reducing the energy of the quantum system using a Monte Carlo algorithm.

8. An electronic device comprising: at least one processor; as well as At least one memory is coupled to the at least one processor and stores instructions for execution by the at least one processor, the instructions causing the electronic device to perform the method according to any one of claims 1 to 6 when executed by the at least one processor.

9. A computer-readable storage medium having computer-executable instructions stored thereon, wherein the computer-executable instructions can be executed by a processor to implement the method according to any one of claims 1 to 6.

10. A computer program product comprising computer executable instructions, wherein the computer executable instructions, when executed by a processor, implement the method according to any one of claims 1 to 6.

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