A method and apparatus for determining the ground state energy of a target molecular system

Abstract

This invention provides a method and apparatus for determining the ground state energy of a target molecular system. The method includes: determining a first Hamiltonian of the target molecular system using the Born-Oppenheimer approximation; determining a first correction term using a preset perturbation expansion based on a preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian; applying the first correction term to the first Hamiltonian to obtain a second Hamiltonian; and determining the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit.

Description

Technical Field

[0001] This invention relates to the field of quantum chemistry, and in particular to a method and apparatus for determining the ground state energy of a target molecular system. Background Technology

[0002] The Born-Oppenheimer approximation, also known as the Born-Oppenheimer hypothesis, is a crucial approximation method in quantum chemistry and molecular physics. This approximation assumes that the motion of electrons and atomic nuclei can be considered separately, because the mass of the nucleus is much greater than that of the electron, and therefore its velocity is much slower. This significant difference in mass and velocity allows electrons to rapidly reach quantum state stability against the backdrop of a relatively stationary atomic nucleus. However, under high-energy, high-temperature, or strongly correlated conditions, the quantum effects of the atomic nucleus can become significant, making the error in the Born-Oppenheimer (BOA) approximation non-negligible. Furthermore, with the increasing precision of observations of molecular systems, even small approximation errors can introduce observable biases.

[0003] Currently, on quantum devices in the Noisy Mesoscale Quantum Age (NISQ), traditional quantum algorithms typically use the Born-Oppenheimer approximation as a direct assumption, thus simplifying the analysis of the Hamiltonian and wavefunction of molecular systems. Therefore, the accuracy of this method is difficult to exceed the limitations of the Born-Oppenheimer approximation, and as the required observational precision for molecular systems increases further, the advantages of quantum algorithms over classical algorithms become less apparent.

[0004] Therefore, a method and apparatus are needed to determine the ground state energy of a target molecular system. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for determining the ground state energy of a target molecular system. By combining classical optimization problems and quantum eigenvalue solving algorithms through quantum variational methods, it is possible to achieve accurate simulation on NISQ devices and has greater operability and feasibility compared to fault-tolerant quantum algorithms.

[0006] In a first aspect, the present invention provides a method for determining the ground state energy of a target molecular system, comprising:

[0007] According to the Born-Oppenheimer approximation method, the first Hamiltonian of the target molecular system is determined; based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion, and the first correction term is applied to the first Hamiltonian to obtain the second Hamiltonian.

[0008] The ground state energy corresponding to the second Hamiltonian is determined based on the second Hamiltonian and the preset variable quantum circuit.

[0009] Specifically, the variable quantum circuit includes a first number of working qubits and a second number of auxiliary qubits; determining the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and the preset variable quantum circuit includes:

[0010] Based on preset test parameters, the working qubit is prepared into a test quantum state, and after applying a Hadma gate to the auxiliary qubit, a controllable state determined according to a second Hamiltonian is applied to the working qubit. Gate, where s is the binary representation of the quantum basis vector of the auxiliary bit, H is the second Hamiltonian, and i is the imaginary unit; apply the inverse Fourier transform (QFT) operation to the auxiliary qubit. -1 Based on the measurement results of the working qubit, the ground state energy corresponding to the second Hamiltonian is determined.

[0011] Specifically, the first correction term is expressed as:

[0012]

[0013] Where λ is the momentum term of the atomic nuclei in the target molecular system, and M is the mass matrix. For the correction matrix, To reduce Planck's constant, The imaginary unit, For quality parameters, This is the gradient operator.

[0014] Specifically, the correction matrix Represented as:

[0015]

[0016] in, Representing quantum states, This represents the first-order correction for the quantum state, where i and j represent the quantum state indices, R represents the nuclear position coordinates, and r represents the electron position coordinates. It is the first Hamiltonian. The zeroth eigenvalue of the first Hamiltonian. For volume elements in three-dimensional space, Let be the correction matrix for quantum state i and quantum state j.

[0017] Specifically, the target molecular system includes: a target molecular system within a preset first temperature range.

[0018] Preferably, the method is performed using a mesoscale quantum device.

[0019] In a second aspect, the present invention provides an apparatus for determining the ground state energy of a target molecular system, comprising:

[0020] The correction unit is configured to: determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method; determine the first correction term through a preset perturbation expansion based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian; and apply the first correction term to the first Hamiltonian to obtain the second Hamiltonian.

[0021] The computing unit is configured to determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit.

[0022] Thirdly, the present invention provides a storage medium for storing a program, wherein the program, when executed, performs the following operations:

[0023] According to the Born-Oppenheimer approximation method, the first Hamiltonian of the target molecular system is determined; based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion, and the first correction term is applied to the first Hamiltonian to obtain the second Hamiltonian.

[0024] The ground state energy corresponding to the second Hamiltonian is determined based on the second Hamiltonian and the preset variable quantum circuit.

[0025] Fourthly, the present invention provides a computing device comprising a quantum processor and a classical processor, wherein:

[0026] The classical processor is used to determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method; based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion, and the first correction term is applied to the first Hamiltonian to obtain the second Hamiltonian.

[0027] The quantum processor is used to determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit.

[0028] Compared to existing technologies, this invention has the following advantages: It uses a quantum variational algorithm for molecular dynamics simulations, employing an algorithm that surpasses the BOA approximation for the mass term of the atomic nucleus, achieving higher accuracy than conventional simulation algorithms. Furthermore, the framework used in this invention can be extended to the dynamic calculation of interactions between light and heavy nuclei, as well as the analysis of the dynamic behavior of atomic nuclei in strongly correlated systems. Attached Figure Description

[0029] Figure 1 A flowchart illustrating a method for determining the ground state energy of a target molecular system, provided in an embodiment of the present invention;

[0030] Figure 2 This is a circuit diagram of the Variational Quantum Algorithm (VQA) provided in an embodiment of the present invention;

[0031] Figure 3 This is a structural diagram of a device for determining the ground state energy of a target molecular system, provided in an embodiment of the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be described below with reference to the accompanying drawings. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0034] In the description of the embodiments of the present invention, the words "exemplary," "for example," or "for instance" are used to indicate that they are examples, illustrations, or descriptions. Any embodiment or design that is described as "exemplary," "for example," or "for instance" in the embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Rather, the use of the words "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a specific manner.

[0035] In molecular dynamics, the dynamic simulation of atomic nuclei is a crucial problem. This technique involves simulating the dynamic behavior of atomic nuclei in molecular systems, as well as calculating the ground-state energy and energy spectrum structure of molecules. This reveals the molecular structure under different conditions and helps in understanding and predicting the chemical properties of molecules. Therefore, it has broad application prospects in materials synthesis, drug development, catalyst design, and other fields. For example, calculating the ground-state energy can help predict the binding affinity between drug molecules and biomolecules, thereby guiding the direction and strategy of drug design and accelerating the development of new drugs.

[0036] In practice, the Born-Oppenheimer approximation is commonly used for molecular dynamics simulations. This approximation divides the molecular system into two parts: electrons and atomic nuclei. It treats electron motion as rapid and adiabatically fixes the electron state at each instant in the position of the atomic nucleus. This simplifies the dynamic behavior of the atomic nucleus to an evolution under a given electron density distribution, making it easy to solve using classical numerical methods. However, in some cases, especially for simulations of large molecular systems or high-precision calculations, the accuracy of the Born-Oppenheimer approximation is insufficient. Therefore, it is usually necessary to combine it with other techniques and methods to improve the accuracy and applicability of the simulation.

[0037] The Born-Oppenheimer approximation is an important approximation method in quantum chemistry used to handle the coupling relationship between electrons and atomic nuclei in molecular systems. Since the mass difference between the nucleus and electrons is approximately three orders of magnitude, this approximation assumes that the motion of the nucleus is very slow relative to the motion of the electrons. Therefore, on the one hand, the Schrödinger equation for the molecular system can be decomposed into two parts: electrons and the nucleus, and the position of the nucleus can be treated as a parameter to solve for the electron's trajectory. On the other hand, the energy spectrum of the electron depends on the position parameter of the nucleus, and can therefore be analyzed as the equivalent potential energy surface of the nucleus, thus allowing for adiabatic solutions to the nucleus's dynamics and energy spectrum. This approximation method is widely applicable to most molecular systems, especially small and medium-sized molecules and molecular systems under low-temperature conditions, where its computational accuracy is relatively good. However, for large molecules or strongly correlated systems, the quasi-classical treatment of the nucleus in the Born-Oppenheimer approximation introduces significant errors. Therefore, methods beyond the Born-Oppenheimer approximation are needed for analysis and numerical calculations. Existing exact factorization methods can formally decompose the time-dependent wave functions of atomic nuclei and electrons in molecules. Within this framework, the correction terms of the Born-Oppenheimer approximation can be handled using perturbation expansion, thus enabling theoretically more accurate numerical simulations.

[0038] Quantum computers have a natural advantage in simulating quantum systems, and can be applied to the dynamics simulation of small molecular systems. However, simulating the dynamic evolution of the entire molecular Hamiltonian requires high depth and complexity of quantum circuits, which is difficult to achieve on current noisy medium-scale quantum (NISQ) quantum hardware. Therefore, variational methods are often used, employing classical algorithms to assist quantum computers in parameter optimization. Quantum computers, by providing suitable anassazals, can efficiently solve for the expectation value of quantum operators, achieving a speedup compared to classical algorithms.

[0039] To overcome the shortcomings of existing technologies, a method and apparatus for determining the ground state energy of a target molecular system are proposed. This invention employs quantum algorithms to achieve molecular dynamics simulations that surpass the Born-Oppenheimer approximation. By combining classical optimization problems and quantum eigenvalue solving algorithms (VQE) through quantum variational methods, accurate simulations can be achieved on NISQ devices. Compared to fault-tolerant quantum algorithms, it offers greater operability and feasibility, and achieves solution accuracy exceeding that of conventional methods.

[0040] Figure 1 This is a flowchart illustrating a method for determining the ground-state energy of a target molecular system, provided as an embodiment of the present invention. Figure 1 As shown, the method includes at least the following steps:

[0041] S101: Determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method; based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, determine the first correction term through a preset perturbation expansion, apply the first correction term to the first Hamiltonian, and obtain the second Hamiltonian.

[0042] In one embodiment, the first correction term can be expressed as:

[0043]

[0044] Where λ is the momentum term of the atomic nuclei in the target molecular system, and M is the mass matrix. For the correction matrix, To reduce Planck's constant, The imaginary unit, For quality parameters, This is the gradient operator.

[0045] In one specific embodiment, the correction matrix It can be represented as:

[0046]

[0047] in Representing quantum states, This represents the first-order correction for the quantum state, where i and j represent the quantum state indices, R represents the nuclear position coordinates, and r represents the electron position coordinates. It is the first Hamiltonian. The zeroth eigenvalue of the first Hamiltonian. For volume elements in three-dimensional space, Let be the correction matrix for quantum state i and quantum state j.

[0048] For example, embodiments of the present invention, based on perturbation expansion using exact factorization, achieve ground-state energy eigenvalue solutions with accuracy exceeding that of the Born-Oppenheimer approximation. In exact factorization, the total wavefunction of the system is expressed as a product of the electron and nucleus degrees of freedom, and the expressions for the Hamiltonian and wavefunction are constructed through precise mathematical relationships. Unlike the BO approximation, which treats the motions of electrons and nuclei separately, exact factorization emphasizes the overall correlation of the system and can handle electron-nucleus interactions without strict separation. In the Born-Oppenheimer approximation, it is assumed that the mass of the nucleus is much greater than the mass of the electron, therefore the kinetic energy of the nucleus can be neglected. In perturbation methods, for example, small quantities can be used... To reduce the mass of the atomic nucleus, specifically, it can be expressed as the mass ratio of electrons to the atomic nucleus, that is, when... When the mass of the atomic nucleus approaches infinity, a rigorous and precise decomposition reverts to the lowest-order result given by the Born-Oppenheimer approximation; however, when the atomic nucleus has a finite mass, the relationship between energy and the wave function... Expanding by different powers yields the results of the perturbation expansion. After retaining the lowest-order correction, substituting... This is equivalent to the atomic nucleus taking on its actual physical value. The correction calculated by this perturbation expansion method consists of two parts: the diagonal Born-Oppenheimer correction term (DBOC) and the correction term for the atomic nucleus mass. The correction for the atomic nucleus mass is brought about by the non-zero electron mass in the molecule, and its lowest-order correction can be expressed as:

[0049]

[0050] Where λ is the momentum term of the atomic nuclei in the target molecular system, and M is the mass matrix. For the correction matrix, To reduce Planck's constant, The imaginary unit, For quality parameters, This is the gradient operator.

[0051] Correction matrix It can be represented as:

[0052]

[0053] in, Representing quantum states, This represents the first-order correction for the quantum state, where i and j represent the quantum state indices, R represents the nuclear position coordinates, and r represents the electron position coordinates. It is the first Hamiltonian. The zeroth eigenvalue of the first Hamiltonian. For volume elements in three-dimensional space, Let be the correction matrix for quantum states i and j. The corrected second Hamiltonian can be obtained by calculating using the above formula.

[0054] S102: Determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and the preset variable quantum circuit.

[0055] In one embodiment, the variable quantum circuit may include a first number of working qubits and a second number of auxiliary qubits. Furthermore, the specific method for determining the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and the preset variable quantum circuit may include the following process: preparing the working qubits into a test quantum state based on preset test parameters; and, after applying a Hadma gate to the auxiliary qubits, applying a controllable energy determined according to the second Hamiltonian to the working qubits. Gate, where s is the binary representation of the quantum basis vector of the auxiliary bit, H is the second Hamiltonian, and i is the imaginary unit; apply the inverse Fourier transform (QFT) operation to the auxiliary qubit. -1 The ground state energy corresponding to the second Hamiltonian is determined by classical optimization based on the measurement results of the working qubit.

[0056] Figure 2 This is a circuit diagram of the Variational Quantum Algorithm (VQA) provided in an embodiment of the present invention. Figure 2 As shown, this quantum circuit consists of two parts: n working bits and t auxiliary bits. This is achieved through parameterized Ansatz... To construct and test quantum states. Here... It is a parameter-dependent The unitary operation is used to generate specific quantum states, which will be used for subsequent energy calculations. Auxiliary bits: The initial state is typically... This is used to store phase information. First, a Hadamard gate is applied to the t auxiliary bits. ), will from State transforms into uniform superposition state Substituting the corrected second Hamiltonian calculated from S101 into the controllable... Door. Controllable. Door (Controlled- A gate is an extension of a basic quantum gate. In this embodiment, controllability... The gate is defined as follows: s is the binary representation of the quantum basis vectors of the auxiliary bit portion, H is the second Hamiltonian, and i is the imaginary unit. Then, a quantum phase estimation (QPE) operation is performed. This involves performing a quantum phase estimation operation on each... State application controlled Operation, among which This involves parameterization operations on the working bit. This process encodes phase information related to the working bit state onto the auxiliary bit. Finally, a quantum inverse Fourier transform (QFT) is applied to the auxiliary bit. This operation converts the auxiliary bit state into a binary representation of the phase, from which phase information can be extracted. Through quantum phase estimation, phase information related to the test quantum state can be obtained. This phase information can be further converted into an energy expectation value. After obtaining the energy expectation value, a classical algorithm is used to optimize Ansatz. parameters The optimization goal is to minimize the expected energy value. This is achieved through multiple iterations (i.e., repeatedly adjusting the parameters). (And recalculate the expected energy value), and finally the ground state energy corresponding to the second Hamiltonian can be calculated, which is the lowest energy state of the system.

[0057] In different scenarios, the target molecular system can be a target molecular system under conditions of high temperature, high energy, or other conditions where atomic nuclei and electrons are strongly correlated. In a specific embodiment, the target molecular system may include a target molecular system within a preset first temperature range.

[0058] In different embodiments, the specific quantum device used to perform the method can be different. In one specific embodiment, the method can be performed using a mesoscale quantum device (NISQ).

[0059] According to another embodiment, an apparatus for determining the ground state energy of a target molecular system is provided. Figure 3 A structural diagram of a device for determining the ground state energy of a target molecular system provided in an embodiment of the present invention is shown below. Figure 3 As shown, the device 300 includes:

[0060] The correction unit 301 is configured to: determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method; determine the first correction term through a preset perturbation expansion based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian; and apply the first correction term to the first Hamiltonian to obtain the second Hamiltonian.

[0061] The calculation unit 302 is configured to determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit.

[0062] In one embodiment, the present invention provides a storage medium for storing a program, wherein the program, when executed, performs the following operations:

[0063] According to the Born-Oppenheimer approximation method, the first Hamiltonian of the target molecular system is determined; based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion, and the first correction term is applied to the first Hamiltonian to obtain the second Hamiltonian.

[0064] The ground state energy corresponding to the second Hamiltonian is determined based on the second Hamiltonian and the preset variable quantum circuit.

[0065] In one embodiment, the present invention provides a computing device comprising a quantum processor and a classical processor, wherein:

[0066] The classical processor is used to determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method; based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion, and the first correction term is applied to the first Hamiltonian to obtain the second Hamiltonian.

[0067] The quantum processor is used to determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit.

[0068] It is understood that the method steps in the embodiments of the present invention can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0069] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0070] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the ground state energy of a target molecular system, wherein, include: The first Hamiltonian of the target molecular system is determined according to the Born-Oppenheimer approximation method. Based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion. The first correction term is then applied to the first Hamiltonian to obtain a second Hamiltonian. The first correction term is expressed as: Where λ is the momentum term of the atomic nuclei in the target molecular system, and M is the mass matrix. For the correction matrix, To reduce Planck's constant, The imaginary unit, For quality parameters, The gradient operator; the correction matrix Represented as: in, Representing quantum states, This represents the first-order correction for the quantum state, where i and j represent the quantum state indices, R represents the nuclear position coordinates, and r represents the electron position coordinates. It is the first Hamiltonian. The zeroth eigenvalue of the first Hamiltonian. For volume elements in three-dimensional space, Let be the correction matrix for quantum state i and quantum state j; The ground state energy corresponding to the second Hamiltonian is determined based on the second Hamiltonian and a preset variable quantum circuit; the variable quantum circuit includes a first number of working qubits and a second number of auxiliary qubits; the determination of the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and the preset variable quantum circuit includes: Based on preset test parameters, the working qubit is prepared into a test quantum state, and after applying a Hadma gate to the auxiliary qubit, a controllable state determined according to a second Hamiltonian is applied to the working qubit. Gate, where s is the binary representation of the quantum basis vector of the auxiliary bit, H is the second Hamiltonian, and i is the imaginary unit; apply the inverse Fourier transform (QFT) operation to the auxiliary qubit. -1 Based on the measurement results of the working qubit, the ground state energy corresponding to the second Hamiltonian is determined.

2. The method according to claim 1, wherein, The target molecular system includes: a target molecular system within a preset first temperature range.

3. The method according to claim 1, wherein, The method is performed using a mesoscale quantum device.

4. An apparatus for determining the ground state energy of a target molecular system, wherein, include: The correction unit is configured to determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method. Based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion. The first correction term is then applied to the first Hamiltonian to obtain a second Hamiltonian. The first correction term is expressed as: Where λ is the momentum term of the atomic nuclei in the target molecular system, and M is the mass matrix. For the correction matrix, To reduce Planck's constant, The imaginary unit, For quality parameters, The gradient operator; the correction matrix Represented as: in, Representing quantum states, This represents the first-order correction for the quantum state, where i and j represent the quantum state indices, R represents the nuclear position coordinates, and r represents the electron position coordinates. It is the first Hamiltonian. The zeroth eigenvalue of the first Hamiltonian. For volume elements in three-dimensional space, Let be the correction matrix for quantum state i and quantum state j; The computing unit is configured to determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit; the variable quantum circuit includes a first number of working qubits and a second number of auxiliary qubits; the determination of the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and the preset variable quantum circuit includes: Based on preset test parameters, the working qubit is prepared into a test quantum state, and after applying a Hadma gate to the auxiliary qubit, a controllable state determined according to a second Hamiltonian is applied to the working qubit. Gate, where s is the binary representation of the quantum basis vector of the auxiliary bit, H is the second Hamiltonian, and i is the imaginary unit; apply the inverse Fourier transform (QFT) operation to the auxiliary qubit. -1 Based on the measurement results of the working qubit, the ground state energy corresponding to the second Hamiltonian is determined.

5. A computing device comprising a quantum processor and a classical processor, wherein: The classical processor is used to determine the first Hamiltonian of the target molecular system according to the Born-Oppenheimer approximation method. Based on the preset mass ratio parameter of electrons to atomic nuclei in the target molecular system and the first Hamiltonian, a first correction term is determined through a preset perturbation expansion. The first correction term is then applied to the first Hamiltonian to obtain a second Hamiltonian. The first correction term is expressed as: Where λ is the momentum term of the atomic nuclei in the target molecular system, and M is the mass matrix. For the correction matrix, To reduce Planck's constant, The imaginary unit, For quality parameters, The gradient operator; the correction matrix Represented as: in, Representing quantum states, This represents the first-order correction for the quantum state, where i and j represent the quantum state indices, R represents the nuclear position coordinates, and r represents the electron position coordinates. It is the first Hamiltonian. The zeroth eigenvalue of the first Hamiltonian. For volume elements in three-dimensional space, Let be the correction matrix for quantum state i and quantum state j; The quantum processor is used to determine the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and a preset variable quantum circuit; the variable quantum circuit includes a first number of working qubits and a second number of auxiliary qubits; determining the ground state energy corresponding to the second Hamiltonian based on the second Hamiltonian and the preset variable quantum circuit includes: Based on preset test parameters, the working qubit is prepared into a test quantum state, and after applying a Hadma gate to the auxiliary qubit, a controllable state determined according to a second Hamiltonian is applied to the working qubit. Gate, where s is the binary representation of the quantum basis vector of the auxiliary bit, H is the second Hamiltonian, and i is the imaginary unit; apply the inverse Fourier transform (QFT) operation to the auxiliary qubit. -1 Based on the measurement results of the working qubit, the ground state energy corresponding to the second Hamiltonian is determined.

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