Molecular system ground state energy value output method, medium, system and related equipment

Abstract

The invention provides a molecular system ground state energy value output method, a medium, a system and related equipment, and the method comprises the steps: calculating the ground state energy value and the electron number of a fragment according to a specified chemical potential value for each fragment corresponding to a molecular system; iteratively adjusting the chemical potential value by using the total electron number calculated according to the fragments and the total electron number of the molecular system to obtain a target chemical potential value and a ground state energy value of each fragment corresponding to the target chemical potential value; and calculating and outputting the ground state energy value of the molecular system based on the ground state energy value of each fragment corresponding to the target chemical potential value. According to the method, the large molecular system is divided into the small fragments for calculation, the ground state energy value of each fragment is obtained through accurate calculation, the ground state energy value of the whole molecular system can be calculated with high precision in combination with the chemical potential value subjected to iterative adjustment, and the expandability and accuracy of the calculation result are improved.

Description

Technical Field

[0001] The present application relates to the technical field of quantum chemistry, and in particular to a method for outputting the ground state energy value of a molecular system, a computer-readable storage medium, a computer device, a quantum operating system, and a quantum computer. Background Art

[0002] In the field of quantum chemistry, accurately calculating the ground-state energy of molecular systems is crucial for understanding and predicting chemical reactions. However, as the size of the system increases, the difficulty of accurately determining its ground-state energy value increases dramatically. This is primarily due to the "exponential wall" problem, where the required computational resources increase exponentially with the size of the system. Related quantum chemical methods, such as density functional theory (DFT) and the Hartree-Fock method, are computationally expensive.

[0003] Based on this, the present application provides a method for outputting the ground state energy value of a molecular system, a computer-readable storage medium, a computer device, a quantum operating system, and a quantum computer to improve related technologies. Summary of the Invention

[0004] The purpose of this application is to provide a method for outputting the ground state energy value of a molecular system, a computer-readable storage medium, a computer device, a quantum operating system, and a quantum computer, which split the molecular system into smaller fragments and calculate the ground state energy value of each fragment separately, thereby improving the scalability and accuracy of the calculation results of the ground state energy value of the molecular system.

[0005] The purpose of this application is achieved by the following technical solutions:

[0006] In a first aspect, the present application provides a method for outputting the ground state energy value of a molecular system, for outputting the ground state energy value of a molecular system, the method comprising:

[0007] For each fragment corresponding to the molecular system, calculating the ground state energy value and the number of electrons of the fragment according to the specified chemical potential value;

[0008] Iteratively adjusting the chemical potential value using the total number of electrons calculated based on the fragments and the total number of electrons in the molecular system to obtain a target chemical potential value and a ground state energy value of each fragment corresponding to the target chemical potential value;

[0009] Based on the ground state energy value of each fragment corresponding to the target chemical potential value, the ground state energy value of the molecular system is calculated and output.

[0010] In some embodiments, the multiple fragments corresponding to the molecular system are obtained by dividing the molecular system according to a specified fragment division strategy.

[0011] In some embodiments, each fragment comprises one or more atoms.

[0012] In some embodiments, the calculating the ground state energy value and the number of electrons of the fragment according to the specified chemical potential value comprises:

[0013] constructing an embedded Hamiltonian of the fragment based on the chemical potential value;

[0014] Using the embedded Hamiltonian, calculating the ground state energy value of the fragment and the corresponding target pseudo-parameters through a variational quantum eigensolver;

[0015] The number of electrons in the fragment is calculated according to the target proposed parameters.

[0016] In some embodiments, the process of constructing the embedded Hamiltonian of the fragment includes:

[0017] The embedded Hamiltonian is constructed based on the monomer-reduced density matrix of the molecular system, the initial monomer-reduced density matrix of the fragment and the chemical potential value.

[0018] In some embodiments, the process of calculating the monomer reduced density matrix of the molecular system comprises:

[0019] The Hartree-Fock method is used to perform mean field calculation on the molecular system to obtain the monomer reduced density matrix of the molecular system.

[0020] In some embodiments, the process of calculating the initial monomer reduced density matrix of the fragment comprises:

[0021] constructing an embedded orbital matrix based on a monomer reduced density matrix of the molecular system;

[0022] Using the embedded orbital matrix, an initial monomer-reduced density matrix of the fragment is calculated.

[0023] In some embodiments, constructing the embedded Hamiltonian based on the monomer-reduced density matrix of the molecular system, the initial monomer-reduced density matrix of the fragment, and the chemical potential value comprises:

[0024] Calculating the one-electron integral and the two-electron integral of the fragment using the initial monomer reduced density matrix of the fragment, the monomer reduced density matrix of the molecular system, and the chemical potential value;

[0025] The embedded Hamiltonian is constructed based on the one-electron integral and the two-electron integral of the fragment.

[0026] In some embodiments, the using the embedded Hamiltonian to calculate the ground state energy value of the fragment and the corresponding target pseudo-parameters by a variational quantum eigensolver includes:

[0027] Calculating the eigenvalue of the embedded Hamiltonian as the initial ground state energy value by self-consistent field iterative calculation;

[0028] The initial ground state energy value and the given pseudo-parameters are used as inputs of a variational quantum eigensolver to solve the ground state energy value of the embedded Hamiltonian and the corresponding target pseudo-parameters.

[0029] In some embodiments, calculating the number of electrons in the fragment according to the target proposed parameters includes:

[0030] Based on the target proposed parameters, calculating the target monomer reduced density matrix and the two-body reduced density matrix of the fragment by calculating the expected value;

[0031] The electron number of the fragment is calculated using the target monomer-reduced density matrix and the two-body-reduced density matrix of the fragment.

[0032] In a second aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, any of the above methods is implemented.

[0033] In a third aspect, the present application provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements any one of the above methods when executing the computer program.

[0034] In a fourth aspect, the present application provides a quantum operating system, which outputs the ground state energy value of a molecular system according to any of the above methods.

[0035] In a fifth aspect, the present application provides a quantum computer, comprising a quantum chip and any one of the above-mentioned quantum operating systems, wherein the quantum chip is provided with one or more quantum bits.

[0036] The present application provides an output method for the ground state energy value of a molecular system, a computer-readable storage medium, a computer device, a quantum operating system, and a quantum computer, which decomposes the molecular system into multiple small fragments and calculates the ground state energy value and the number of electrons of these fragments respectively. The ground state energy and the number of electrons of each fragment are calculated by the specified chemical potential value, and then the chemical potential value is iteratively adjusted using the number of electrons. The iterative process is based on the total number of electrons calculated by the fragments matching the total number of electrons of the original molecular system, and is adjusted to find the target chemical potential value, which makes the sum of the number of electrons of all fragments match the number of electrons of the original system. Finally, the ground state energy value of each fragment under this target chemical potential value is used to calculate the ground state energy value of the entire molecular system. Thus, by splitting the molecular system into smaller fragments for calculation, the ground state energy value of each fragment is obtained by precise calculation. Combined with the iteratively adjusted chemical potential value, the ground state energy value of the entire molecular system can be calculated with high precision, thereby improving the scalability and accuracy of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present application is further described below with reference to the accompanying drawings and specific implementation methods.

[0038] Figure 1 This is a flow chart of a method for outputting the ground state energy value of a molecular system provided in an embodiment of the present application.

[0039] Figure 2 This is a flow chart of a method for calculating the ground state energy value and the number of electrons of a fragment provided in an embodiment of the present application.

[0040] Figure 3 It is a flow chart of a process of constructing an embedded Hamiltonian of a fragment provided in an embodiment of the present application.

[0041] Figure 4 This is a schematic diagram of a process for calculating the initial monomer reduced density matrix of a fragment provided in an embodiment of the present application.

[0042] Figure 5 This is a schematic diagram of a process for constructing an embedded track matrix provided in an embodiment of the present application.

[0043] Figure 6 This is a flow chart of a method for calculating the ground state energy value of a fragment and the corresponding target simulated parameters through a variational quantum eigensolver provided in an embodiment of the present application.

[0044] Figure 7 This is a flow chart of calculating the number of electrons in a fragment provided in an embodiment of the present application.

[0045] Figure 8 This is a structural block diagram of a computer device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making any creative work are within the scope of protection of this application.

[0047] In the description of the embodiments of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly indicate the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0048] In recent years, a variety of quantum computing methods have been developed to harness the potential of quantum computing to solve computational problems in large systems. The variational quantum eigensolver (VQE) is a typical quantum-classical hybrid algorithm that solves the ground-state energy of a system by optimizing parameterized quantum circuits. It has demonstrated high computational accuracy for small molecular systems. However, the scalability of the VQE algorithm is limited by the performance of current quantum hardware.

[0049] Density Matrix Embedding Theory (DMET), on the other hand, offers a strategy for decomposing a large system into multiple smaller ones. By solving the ground-state energies of these smaller systems separately and integrating them appropriately, the properties of the larger system can be approximated. DMET offers good scalability for large systems, but suffers from low computational accuracy.

[0050] The DMET-VQE hybrid algorithm combines the advantages of both approaches: the high-precision computational power of VQE and the scalability of DMET. This algorithm divides a large system into multiple small fragments, accurately solves each fragment using the VQE algorithm, and then integrates these results within the DMET framework to achieve high-precision and efficient calculation of the ground-state energy of the large system. This approach not only addresses the computational challenges of related algorithms when dealing with large systems, but also overcomes the scalability and accuracy limitations of single quantum algorithms.

[0051] See also Figure 1 , Figure 1 This is a flow chart of a method for outputting the ground state energy value of a molecular system provided in an embodiment of the present application.

[0052] An embodiment of the present application provides a method for outputting the ground state energy value of a molecular system, which is used to output the ground state energy value of a molecular system. The method includes steps S101 to S103.

[0053] Step S101: for each fragment corresponding to the molecular system, the ground state energy value and the number of electrons of the fragment are calculated according to a specified chemical potential value.

[0054] The ground state energy value of a molecular system refers to the energy value when the molecule is in the lowest energy state (or approximate lowest energy state). Fragment refers to the smaller molecular units into which the original macromolecular system is decomposed according to certain rules, for example, the molecular system can be divided into multiple fragments by the DMET algorithm. Chemical potential is a thermodynamic quantity, which represents the change in free energy when a particle is added to a molecular system at constant temperature and pressure. By adjusting the chemical potential value, the number of electrons in the fragment system can be made close to the number of electrons in the original molecular system. It should be noted that in each iterative process of DMET, the chemical potential value is specified, and the embodiment of the application does not limit the specified method, for example, it can be set automatically by manual specification or according to a preset algorithm. As an example, the specified chemical potential value can be, for example, 0, 0.0001, -0.0019674, etc.

[0055] Step S102: using the total number of electrons calculated based on the fragments and the total number of electrons in the molecular system, iteratively adjusting the chemical potential value to obtain a target chemical potential value and a ground state energy value of each fragment corresponding to the target chemical potential value.

[0056] Among them, the total number of electrons calculated based on the fragments is the sum of the number of electrons of all the calculated fragments. The total number of electrons of a molecular system refers to the true total number of electrons of the molecular system, for example, the total number of electrons of the H4 molecular system is 4. In the DMET algorithm, the chemical potential value can be used to adjust the total number of electrons in the molecular system calculated based on the fragments. In this step, the chemical potential value is continuously adjusted until the total number of electrons calculated based on the fragments matches the total number of electrons of the molecular system, and the chemical potential value at this time is used as the target chemical potential value. The matching of the total number of electrons N1 calculated based on the fragments and the total number of electrons N0 of the molecular system means, for example, |N1-N0|<preset value, or, |N1-N0| / N0<preset ratio. The preset value or preset ratio can be a very small positive number.

[0057] Step S103: Calculate and output the ground state energy value of the molecular system based on the ground state energy value of each fragment corresponding to the target chemical potential value.

[0058] For example, the sum of the ground state energy values ​​of each fragment corresponding to the target chemical potential value is calculated, and then added to the repulsive energy value of the molecular system to obtain the ground state energy value of the molecular system and output it.

[0059] In the above embodiment, a complex molecular system is decomposed into multiple fragments, and the ground state energy values ​​and electron numbers of these fragments are calculated separately. The ground state energy and electron number of each fragment are calculated by a specified chemical potential value, and then the chemical potential value is iteratively adjusted using the electron number. The iterative process is aimed at matching the total number of electrons calculated by the fragments with the total number of electrons of the original molecular system, and is adjusted to find a target chemical potential value, which makes the sum of the number of electrons of all fragments match the number of electrons of the original system. Finally, the ground state energy value of the entire molecular system is calculated using the ground state energy value of each fragment under this target chemical potential value. This method effectively converts the complex problem of a large system into a collection of multiple small problems, making the calculation of the ground state energy more feasible and accurate. Thus, by splitting the molecular system into smaller fragments for calculation, the ground state energy value of each fragment is obtained by accurate calculation. Combined with the iteratively adjusted chemical potential value, the ground state energy value of the entire molecular system can be calculated with high precision, thereby improving the scalability and accuracy of the calculation results. This method is applicable to molecular systems of varying sizes and complexities, exhibiting excellent versatility and adaptability, enabling efficient and high-precision calculations of the ground-state energy values ​​of molecular systems. When applied to large molecular systems, the method can significantly reduce the overall computational effort.

[0060] In some embodiments, the multiple fragments corresponding to the molecular system can be obtained by dividing the molecular system according to a specified fragment division strategy.

[0061] Fragmentation strategies are rules used to determine how to cut a large molecular system into small fragments, which can be based on various principles, such as the nature of chemical bonds, the distance between atoms, or the requirements of computational efficiency and accuracy.

[0062] In some embodiments, each fragment may include one or more atoms. As an example, each fragment may include one atom. For example, the H10 molecular system may be split into 10 fragments, each of which includes one H atom. As another example, each fragment may include multiple atoms.

[0063] In the above embodiment, the molecular system is divided by a specified fragment partitioning strategy to obtain multiple fragments, which can contain one or more atoms, so as to achieve more detailed and flexible processing of complex molecular systems. For each independent fragment, its ground state energy value and electron number are calculated according to a specific chemical potential value. Then, using the calculation results of these fragments, the chemical potential value is iteratively adjusted so that the total number of electrons calculated matches the total number of electrons in the original molecular system. Thus, the macromolecular system is divided into fragments that are easier to manage and calculate, each fragment including one or more atoms, which can significantly reduce the complexity and time required for calculation, especially when computing resources are limited. According to the characteristics of the molecular system and the computing requirements, the fragment partitioning strategy can be flexibly selected, which has a wide range of applications and can handle various systems from small molecules to macromolecular complexes.

[0064] See also Figure 2 , Figure 2 This is a flow chart of a method for calculating the ground state energy value and the number of electrons of a fragment provided in an embodiment of the present application.

[0065] In some embodiments, the step of calculating the ground state energy value and the number of electrons of the fragment according to the specified chemical potential value (ie, step S101 ) may include steps S201 to S203 .

[0066] Step S201: constructing the embedded Hamiltonian of the fragment based on the chemical potential value.

[0067] The embedded Hamiltonian is a special Hamiltonian that describes a fragment of a molecular system while taking into account the influence of the rest of the system. By introducing the influence of the external environment, a portion of the molecular system can be studied in isolation without losing the overall physical properties, allowing for precise quantum calculations on this fragment. Embedded Hamiltonians can be constructed using specialized methods, such as density matrix embedding theory.

[0068] Step S202: using the embedded Hamiltonian, calculating the ground state energy value of the segment and the corresponding target hypothetical parameters through a variational quantum eigensolver.

[0069] The variational quantum eigensolver minimizes the expectation value of the embedded Hamiltonian by optimizing a parameterized quantum circuit, thereby finding the ground-state energy value and the corresponding quantum state of the embedded Hamiltonian. When using the variational quantum eigensolver, the pseudo parameters are the parameters adjusted during the optimization process, defining the specific form of the parameterized quantum circuit used to solve for the ground-state energy value of the molecular system. The target pseudo parameters are the pseudo parameters corresponding to the ground-state energy value of the fragment.

[0070] Step S203: Calculate the number of electrons in the fragment according to the target proposed parameters.

[0071] In the above embodiment, the process of calculating the ground state energy value and electron number of the fragment first involves constructing an embedded Hamiltonian based on the specified chemical potential value. By embedding the external environmental effects of the fragment into the Hamiltonian of the fragment, the fragment can be calculated independently while taking into account the influence of other parts of the molecular system. Next, using the constructed embedded Hamiltonian, the ground state energy and corresponding target pseudo-parameters of the fragment are calculated by the variational quantum eigensolver. The variational quantum eigensolver solves the ground state energy value by optimizing the parameterized quantum circuit. The target pseudo-parameters obtained in this process reflect the quantum state configuration required to achieve the ground state energy value. Finally, based on the target pseudo-parameters, the electron number of the fragment is calculated, thereby achieving an accurate assessment of the ground state energy value and electron number of each fragment of the molecular system. Therefore, by constructing the embedded Hamiltonian and using the VQE algorithm, the ground state energy value of the fragment can be accurately calculated while taking into account the overall environmental influence of the molecular system, thereby greatly improving the accuracy of the overall calculation. As a quantum-classical hybrid algorithm, VQE utilizes the advantages of quantum computing in processing quantum state superposition and entanglement. It can find the ground state energy value of a fragment in a shorter time, which is more efficient than completely classical computing methods.

[0072] See also Figure 3 , Figure 3 It is a flow chart of a process of constructing an embedded Hamiltonian of a fragment provided in an embodiment of the present application.

[0073] In some embodiments, the process of constructing the embedded Hamiltonian of the fragment may include step S301.

[0074] Step S301: constructing the embedded Hamiltonian based on the monomer-reduced density matrix of the molecular system, the initial monomer-reduced density matrix of the fragment and the chemical potential value.

[0075] The one-body reduced density matrix (1-RDM) of a molecular system is used to approximate the average distribution of individual electrons in the molecular system. The initial one-body reduced density matrix of a fragment is used to approximate the distribution of individual electrons in the fragment. The purpose of calculating the initial one-body reduced density matrix of a fragment is to provide a starting point or reference value for subsequent quantum calculations using classical quantum chemical methods (such as the Hartree-Fock method). This initial one-body reduced density matrix is ​​based on classical approximations and is used to construct the embedded Hamiltonian, reflecting a preliminary estimate of the electron distribution in the fragment.

[0076] In the above embodiment, first, the monomer reduced density matrix of the entire molecular system and the initial monomer reduced density matrix of the fragment are calculated. The purpose of this step is to obtain the electron distribution information of the overall system and the specific fragment. Next, based on the monomer reduced density matrix of the overall molecular system, the initial monomer reduced density matrix of the fragment, and the given chemical potential value, an embedded Hamiltonian is constructed for the fragment. This embedded Hamiltonian not only reflects the properties of the fragment itself, but also includes the influence of the overall molecular system on the fragment. In this way, the properties of the fragment in the overall system, such as the ground state energy value and the number of electrons, can be more accurately simulated and calculated. Therefore, for each fragment, by combining the electron distribution information of the entire molecular system and the fragment to construct an embedded Hamiltonian, the properties of the fragment in the overall molecular system can be more accurately reflected. Using the embedded Hamiltonian construction method based on the chemical potential value, the chemical potential value is iteratively adjusted with the goal of matching the total electron number calculated based on the fragment with the total electron number of the molecular system, so that the properties of the fragment are correctly simulated, thereby increasing the reliability and applicability of the calculation results.

[0077] In some embodiments, the process of calculating the monomer reduced density matrix of the molecular system may include: performing a mean field calculation on the molecular system using the Hartree-Fock method to obtain the monomer reduced density matrix of the molecular system.

[0078] The Hartree-Fock method predicts the electronic structure of molecules and atoms by solving an approximate solution to the Schrödinger equation. It uses the mean-field approximation to simplify the multi-electron problem to a single-electron problem, where each electron moves in the average potential field generated by the other electrons.

[0079] In the above embodiment, the process of calculating the monomer-reduced density matrix of the molecular system is achieved by performing a mean-field calculation on the molecular system using the Hartree-Fock method. The Hartree-Fock method gradually adjusts the electron wave function by constructing and solving a set of self-consistent field equations until a specified end adjustment condition is met. In this process, each electron is considered to move independently in the average electric potential field generated by other electrons. In this way, the electron distribution of the molecular system can be calculated and expressed in the form of a monomer-reduced density matrix, reflecting the average electron occupancy in the molecular system.

[0080] The Hartree-Fock method is used to calculate the monomer-reduced density matrix of a molecular system, providing a reliable basis for calculating the electronic structure of the molecular system. The resulting monomer-reduced density matrix accurately describes the average distribution of electrons. Although the Hartree-Fock method is an approximate method based on the mean field, it can provide relatively fast information on the electronic structure of a molecular system without sacrificing much accuracy.

[0081] See also Figure 4 , Figure 4 This is a schematic diagram of a process for calculating the initial monomer reduced density matrix of a fragment provided in an embodiment of the present application.

[0082] In some embodiments, the process of calculating the initial monomer reduced density matrix of the fragment may include steps S401 to S402.

[0083] Step S401: constructing an embedded orbital matrix based on the monomer reduced density matrix of the molecular system.

[0084] For a fragment in a molecular system, the embedded orbital matrix is ​​used to describe the electronic structure of the fragment and its bath region, and can be constructed by combining the fragment orbital matrix and the bath region orbital matrix.

[0085] Step S402: Calculate the initial monomer reduced density matrix of the fragment using the embedded orbital matrix.

[0086] See also Figure 5 , Figure 5 This is a schematic diagram of a process for constructing an embedded track matrix provided in an embodiment of the present application.

[0087] In some embodiments, constructing the embedded orbital matrix based on the monomer reduced density matrix of the molecular system (ie, step S401 ) may include steps S501 to S503 .

[0088] Step S501: Determine the bath area corresponding to the fragment from the environment through the monomer reduced density matrix of the molecular system.

[0089] For a fragment in a molecular system, the remainder of the system excluding the fragment is referred to as the environment. For example, the bath region corresponding to the fragment can be determined from the environment using methods such as Schmidt decomposition. For example, the "components" in the environment that interact with the fragment can be extracted to obtain the bath region corresponding to the fragment. The remaining portion of the environment excluding the bath region can be referred to as the core region. The monomer-reduced density matrix of the molecular system, as a form of mean-field information, can be used to determine the bath region corresponding to the fragment.

[0090] Step S502: constructing a bath area orbital matrix bath_orb of the bath area.

[0091] The bath orbital matrix bath_orb is a matrix that describes the electronic structure of the bath. For example, it can be calculated from the monomer reduced density matrix of the molecular system, reflecting the influence of the environment on the fragment.

[0092] Step S503: Construct the embedded orbital matrix E using the identity matrix I and the bath orbital matrix bath_orb.

[0093] Among them, E can be expressed as

[0094] The identity matrix I is a square matrix with all 1s on the main diagonal and all 0s elsewhere. It is used to preserve the electronic structure information of the fragment itself when constructing the embedded orbital matrix.

[0095] In the above-described embodiment, when calculating the initial monomer-reduced density matrix for a fragment in a molecular system, the following steps are first performed: based on the monomer-reduced density matrix of the entire molecular system, a method such as Schmidt decomposition is used to determine the bath region interacting with the fragment from the environment, so that the bath region can accurately simulate the interaction between the fragment and its surroundings. Next, a bath region orbital matrix is ​​constructed, and then an embedded orbital matrix is ​​constructed using the bath region orbital matrix, and the initial monomer-reduced density matrix for the fragment is further calculated. Thus, by determining the bath region interacting with the fragment and performing calculations based on this, the electronic structure of the fragment and its interaction with the environment can be more accurately simulated, thereby improving the accuracy of the overall calculation results.

[0096] In some embodiments, constructing the embedded Hamiltonian based on the monomer reduced density matrix of the molecular system, the initial monomer reduced density matrix of the fragment and the chemical potential value (i.e., step S301) includes: calculating the single-electron integral and the double-electron integral of the fragment using the initial monomer reduced density matrix of the fragment, the monomer reduced density matrix of the molecular system and the chemical potential value; and constructing the embedded Hamiltonian based on the single-electron integral and the double-electron integral of the fragment.

[0097] Single-electron integrals include the kinetic energy integral and the nuclear attraction integral, which are used to calculate the kinetic energy of a single electron and the interaction between the electron and the nucleus, respectively. Because these integrals involve the coordinates of a single electron, they are called single-electron integrals. In contrast, two-electron integrals involve the coordinates of two electrons and are used to calculate Coulomb repulsion. For example, they are composed of different orbital wave functions, operators involving the coordinates of the two electrons, and two sets of electron coordinates.

[0098] In the above example, the process of constructing the embedded Hamiltonian for a fragment involves calculating the one-electron integral and two-electron integral for the fragment using the monomer-reduced density matrix of the entire molecular system, the fragment's initial monomer-reduced density matrix, and the current chemical potential. The embedded Hamiltonian is then constructed based on the one-electron and two-electron integrals. This allows for precise construction of the embedded Hamiltonian for the fragment during the fragment calculation, enabling more accurate simulation of the fragment's electronic structure and energy state, improving the accuracy of predictions of the molecular system's electronic properties.

[0099] See also Figure 6 , Figure 6 This is a flow chart of a method for calculating the ground state energy value of a fragment and the corresponding target simulated parameters through a variational quantum eigensolver provided in an embodiment of the present application.

[0100] In some embodiments, the step of using the embedded Hamiltonian to calculate the ground state energy value of the fragment and the corresponding target hypothetical parameter by a variational quantum eigensolver (ie, step S202 ) may include steps S601 to S602 .

[0101] Step S601: Calculate the eigenvalue of the embedded Hamiltonian as the initial ground state energy value by self-consistent field iterative calculation.

[0102] Self-consistent field iterative calculations repeatedly update the electron wave function until a stable solution is reached that minimizes the ground state energy, obtaining the initial ground state energy value. For example, the Hartree-Fock method can be used for self-consistent field iterative calculations.

[0103] Step S602: using the initial ground state energy value and given pseudo-parameters as inputs of a variational quantum eigensolver to solve the ground state energy value of the embedded Hamiltonian and the corresponding target pseudo-parameters.

[0104] In the VQE algorithm, the pseudo-parameter is an adjustable parameter in the quantum circuit. By optimizing the pseudo-parameter, the minimum expected value of the embedded Hamiltonian corresponding to the fragment can be found as the ground state energy value of the fragment.

[0105] In the above embodiment, first, the self-consistent field iterative calculation method is used to calculate the eigenvalue of the embedded Hamiltonian to obtain the initial ground state energy value. This step provides a starting point for the variational quantum eigensolver, which helps to guide the subsequent quantum optimization process. Next, the initial ground state energy value and the given hypothetical parameters are used as input, and the variational quantum eigensolver (VQE) is used to accurately solve the ground state energy value of the embedded Hamiltonian and optimize the corresponding target hypothetical parameters. The VQE algorithm minimizes the expected value of the embedded Hamiltonian by adjusting the hypothetical parameters in the quantum circuit, thereby finding a more accurate ground state energy value. Therefore, by combining the self-consistent field iterative calculation and the VQE algorithm, it is possible to start the optimization from a more accurate initial ground state energy value, and then find a more accurate ground state energy value through VQE, thereby improving the accuracy of the overall calculation.

[0106] See also Figure 7 , Figure 7 This is a flow chart of calculating the number of electrons in a fragment provided in an embodiment of the present application.

[0107] In some embodiments, the step of calculating the number of electrons in the fragment according to the target proposed parameters (ie, step S203 ) may include steps S701 to S702 .

[0108] Step S701: Based on the target simulated parameters, the target monomeric reduced density matrix and the target binary reduced density matrix of the fragment are calculated by calculating expected values.

[0109] It is important to note that the target monomer-reduced density matrix for the fragment obtained from the VQE calculation is different from the initial monomer-reduced density matrix for the fragment obtained from the aforementioned calculation. After obtaining the target pseudo-parameters, the fragment's monomer-reduced density matrix is ​​calculated again, this time utilizing the results of the VQE algorithm. The resulting monomer-reduced density matrix reflects a more accurate electron distribution after quantum optimization and serves as the target monomer-reduced density matrix. This step, performed within the quantum computing framework and taking into account quantum state optimization, aims to provide electron distribution information that is closer to the true ground state than the initial calculation. The initial calculation provides an approximate electron distribution used to construct the embedding Hamiltonian and initiate the optimization process. Subsequent calculations based on the target pseudo-parameters utilize the results of the VQE algorithm, revealing deeper physical information, such as electron correlation effects, which may be overlooked or under-addressed in classical approximations. Using the target pseudo-parameters obtained from VQE optimization to calculate the target monomer-reduced density matrix ensures that the target monomer-reduced density matrix reflects the latest understanding based on quantum optimization, providing more reliable results.

[0110] The two-body reduced density matrix of the fragment describes the average distribution between the two electrons in the fragment, provides relevant information about the interaction between electron pairs, and can be used to calculate the interaction energy between electrons and the number of electrons.

[0111] Step S702: Calculate the number of electrons in the fragment using the target monomer-reduced density matrix and the two-body-reduced density matrix of the fragment.

[0112] As an alternative to step S702 , in other embodiments, the electron number of the fragment can be directly calculated using only the target monomer reduced density matrix of the fragment.

[0113] In the above embodiment, based on the optimized target hypothetical parameters, the target single-body reduced density matrix and two-body reduced density matrix for the fragment are first obtained by calculating the expected value using a parameterized quantum circuit. These density matrices provide information about the electron distribution and electron pair interactions within the fragment. Next, these density matrices are used to calculate the electron count of the fragment. The two-body reduced density matrix of the fragment provides additional information about electron pairs, facilitating a more accurate assessment of the fragment's properties, such as the electron count.

[0114] Therefore, using the hypothetical parameters optimized based on quantum computing (i.e., target hypothetical parameters) to calculate the density matrix of the fragment (including the target monomer-reduced density matrix and the two-body-reduced density matrix) makes the calculation results of the electron number of the fragment more reliable, especially when dealing with complex molecular systems or highly correlated systems.

[0115] The present application also provides another method for outputting the ground state energy value of a molecular system, which is used to output the ground state energy value of a molecular system. The method includes:

[0116] For each fragment corresponding to the molecular system, the one-electron integral and the two-electron integral of the fragment are calculated using the initial monomer reduced density matrix of the fragment, the monomer reduced density matrix of the molecular system, and the chemical potential value; based on the one-electron integral and the two-electron integral of the fragment, the embedded Hamiltonian is constructed; the multiple fragments corresponding to the molecular system are obtained by dividing the molecular system according to a specified fragment partitioning strategy; each fragment includes one or more atoms;

[0117] Calculating the eigenvalue of the embedded Hamiltonian as the initial ground state energy value by self-consistent field iterative calculation; using the initial ground state energy value and the given pseudo-parameters as inputs of a variational quantum eigensolver to solve the ground state energy value of the embedded Hamiltonian (as the ground state energy value of the corresponding segment) and the corresponding target pseudo-parameters;

[0118] Based on the target hypothetical parameters, a target monomer-reduced density matrix and a two-body-reduced density matrix of the fragment are calculated by calculating expected values; the number of electrons of the fragment is calculated using the target monomer-reduced density matrix and the two-body-reduced density matrix of the fragment; and the sum of the number of electrons of all fragments is calculated as the total number of electrons calculated based on the fragments;

[0119] Iteratively adjusting the chemical potential value with the goal of matching the total electron number calculated based on the fragments with the total electron number of the molecular system to obtain a target chemical potential value and a ground state energy value of each fragment corresponding to the target chemical potential value;

[0120] Based on the ground state energy value of each fragment corresponding to the target chemical potential value, the ground state energy value of the molecular system is calculated and output.

[0121] The process of calculating the monomer reduced density matrix of the molecular system includes: performing mean field calculation on the molecular system using the Hartree-Fock method to obtain the monomer reduced density matrix of the molecular system.

[0122] The process of calculating the initial monomer reduced density matrix of the fragment includes: constructing an embedded orbital matrix based on the monomer reduced density matrix of the molecular system; and calculating the initial monomer reduced density matrix of the fragment using the embedded orbital matrix.

[0123] Taking the H4 molecular system as an example, the DMET+VQE hybrid algorithm is used to calculate the ground state energy value of the molecular system. Assuming the bond length of the H4 molecular system is 1, the coordinates of its four H atoms are as follows:

[0124]

[0125] The fragment partitioning strategy used in the following calculations is to divide each H atom into a fragment independently. The monomer reduced density matrix (1-RDM) of the original molecular system is as follows:

[0126] 1-RDM=array([[0.51702108,0.49970984,0.51702108,0.49971055],

[0127] [0.49970984,1.48297892,0.49971055,0.51702108],

[0128] [0.51702108,0.49971055,0.51702108,0.49970984],

[0129] [0.49971055,0.51702108,0.49970984,1.48297892]]).

[0130] For the first H-atom fragment, the first step in the fragment calculation process can be to construct the bath orbital matrix (bath_orb). Assume that the bath orbital matrix (bath_orb) corresponding to the first H-atom fragment is as follows:

[0131] bath_orb=array([[1,0,0,0],

[0132] [0,5.70684783e-01,7.07107024e-01,-4.17514714e-01],

[0133] [0,5.90454768e-01,5.01452742e-07,8.07070732e-01],

[0134] [0,5.70685593e-01,7.07106539e-01,-4.17514427e-01]]).

[0135] Based on the bath orbital matrix (bath_orb), the corresponding embedded orbital matrix of the fragment is constructed, and the initial monomer reduced density matrix (onerdm_high) of the fragment can be calculated as follows:

[0136] onerdm_high=array([[0,0,0,0],

[0137] [0,1.00000069e+00,7.09161511e-07,-1.00000000e+00],

[0138] [0,7.09161511e-07,5.02909704e-13,-7.09161025e-07],

[0139] [0,-1.00000000e+00,-7.09161025e-07,9.99999315e-01]]).

[0140] Next, the one-electron integral (one_ele, matrix), two-electron integral (two_ele, fourth-order tensor) and Fock matrix of the fragment are calculated as follows:

[0141] one_ele=array([[-1.60064922,-0.29919877],

[0142] [-0.29919877,-1.95468773]]).

[0143] two_ele=array([[[[0.87846902,-0.00372507],

[0144] [-0.00372507,0.40671628]],

[0145] [[-0.00372507,0.00640914],

[0146] [0.00640914,0.00202643]]],

[0147] [[[-0.00372507,0.00640914],

[0148] [0.00640914,0.00202643]],

[0149] [[0.40671628,0.00202643],

[0150] [0.00202643,0.56923383]]]]).

[0151] fock=array([[-0.72649644,-0.29721169],

[0152] [-0.29721169,-1.05116894]]).

[0153] A self-consistent field iterative calculation is performed on the fragment to obtain the initial ground-state energy value. The VQE method is then used to iteratively optimize the target pseudo-parameters and the corresponding ground-state energy value. Based on the target pseudo-parameters, the target one-body reduced density matrix (fragment_onerdm) and two-body reduced density matrix (fragment_twordm) corresponding to the fragment are calculated.

[0154] fragment_onerdm=array([[1.9862813,0.02473714],

[0155] [0.02473714,0.0137187]]).

[0156] fragment_twordm=array([[[[1.98591566e+00,2.69467501e-02],

[0157] [2.69467501e-02,3.65638560e-04]],

[0158] [[2.69467501e-02,-1.62843656e-01],

[0159] [3.65638560e-04,-2.20961413e-03]]],

[0160] [[[2.69467501e-02,3.65638560e-04],

[0161] [-1.62843656e-01,-2.20961413e-03]],

[0162] [[3.65638560e-04,-2.20961413e-03],

[0163] [-2.20961413e-03,1.33530626e-02]]]]).

[0164] The ground state energy value (fragment_energy) and number of electrons (number_of_electron) of this fragment are as follows:

[0165] fragment_energy=-0.7621532837700722.

[0166] number_of_electron=0.5453075749373857.

[0167] The H4 molecular system has a total of four fragments. The above calculations are related to the first fragment. The calculation process of the remaining three fragments is similar to that of the first fragment, so the calculation process will not be repeated here. Only the calculation results are provided as follows:

[0168] Second snippet:

[0169] bath_orb=array([[0,-5.70684783e-01,4.17514714e-01,-7.07107024e-01],

[0170] [1.00000000e+00,0.00000000e+00,0.00000000e+00,0.00000000e+00],

[0171] [0.00000000e+00,-5.70685593e-01,4.17514427e-01,7.07106539e-01],

[0172] [0.00000000e+00,5.90454768e-01,8.07070732e-01,5.01452741e-07]]).

[0173] onerdm_high=array([[0.34863707,0,0.34863683,0.67392781],

[0174] [0,0,0,0],

[0175] [0.34863683,0,0.34863659,0.67392735],

[0176] [0.67392781,0,0.67392735,1.30272633]]).

[0177] one_ele=array([[-1.60064922,0.31750836],

[0178] [0.31750836,-1.2264124]]).

[0179] two_ele=array([[[[0.87846902,0.00864192],

[0180] [0.00864192,0.4068046]],

[0181] [[0.00864192,0.00584206],

[0182] [0.00584206,0.00545694]]],

[0183] [[[0.00864192,0.00584206],

[0184] [0.00584206,0.00545694]],

[0185] [[0.4068046,0.00545694],

[0186] [0.00545694,0.5882485]]]])。

[0187] fock=array([[-0.86699546,0.32255413],

[0188] [0.32255413,-0.20814619]])。

[0189] fragment_onerdm=array([[1.98733041,-0.02152897],

[0190] [-0.02152897,0.01266959]])。

[0191] fragment_twordm=array([[[[1.98705544e+00,-2.33751126e-02],

[0192] [-2.33751126e-02,2.74977678e-04]],

[0193] [[-2.33751126e-02,-1.56935568e-01],

[0194] [2.74977678e-04,1.84614204e-03]]],

[0195] [[[-2.33751126e-02,2.74977678e-04],

[0196] [[-1.56935568e-01,1.84614204e-03]],

[0197] [[2.74977678e-04,1.84614204e-03],

[0198] [1.84614204e-03,1.23946076e-02]]]])。

[0199] fragment_energy = -1.5527304185025463。

[0200] number_of_electron = 1.4580083006616313。

[0201] The third fragment:

[0202] bath_orb = array([[0.00000000e+00,5.90454768e-01,5.01452741e-07,8.07070732e-01],

[0203] [0.00000000e+00,5.70685593e-01,-7.07106539e-01,-4.17514427e-01],

[0204] [1.00000000e+00,0.00000000e+00,0.00000000e+00,0.00000000e+00],

[0205] [0.00000000e+00,5.70684783e-01,7.07107024e-01,-4.17514714e-01]])。

[0206] onerdm_high = array([[5.02909704e-13,-7.09161025e-07,0.00000000e+00,7.09161511e-07],[-7.09161025e-07,9.99999315e-01,0.00000000e+00,-1.00000000e+00],

[0207] [0.00000000e+00,0.00000000e+00,0.00000000e+00,0.00000000e+00],

[0208] [7.09161511e-07,-1.00000000e+00,0.00000000e+00,1.00000069e+00]])。

[0209] one_ele=array([[-1.60064922,-0.29919877],

[0210] [-0.29919877,-1.95468773]])。

[0211] two_ele=array([[[[0.87846902,-0.00372507],

[0212] [-0.00372507,0.40671628]],

[0213] [[-0.00372507,0.00640914],

[0214] [0.00640914,0.00202643]]],

[0215] [[[-0.00372507,0.00640914],

[0216] [0.00640914,0.00202643]],

[0217] [[0.40671628,0.00202643],

[0218] [0.00202643,0.56923383]]]])。

[0219] fock=array([[-0.72649644,-0.29721169],

[0220] [-0.29721169,-1.05116894]])。

[0221] fragment_onerdm=array([[1.9862813,0.02473714],

[0222] [0.02473714,0.0137187]])。

[0223] fragment_twordm=array([[[[1.98591566e+00,2.69467503e-02],

[0224] [2.69467503e-02,3.65638564e-04]],

[0225] [[2.69467503e-02,-1.62843656e-01],

[0226] [3.65638564e-04,-2.20961414e-03]]],

[0227] [[[2.69467503e-02,3.65638564e-04],

[0228] [-1.62843656e-01,-2.20961414e-03]],

[0229] [[3.65638564e-04,-2.20961414e-03],

[0230] [-2.20961414e-03,1.33530626e-02]]]])。

[0231] fragment_energy = -0.76215328387842。

[0232] number_of_electron = 0.5453075750413725。

[0233] The fourth fragment:

[0234] bath_orb = array([[0.00000000e+00,5.70685593e-01,-4.17514427e-01,7.07106539e-01],[0.00000000e+00,-5.90454768e-01,-8.07070732e-01,5.01452741e-07],

[0235] [0.00000000e+00,5.70684783e-01,-4.17514714e-01,-7.07107024e-01],

[0236] [1.00000000e+00,0.00000000e+00,0.00000000e+00,0.00000000e+00]])。

[0237] onerdm_high = array([[0.34863659,0.67392735,0.34863683,0],

[0238] [0.67392735,1.30272633,0.67392781,0],

[0239] [0.34863683,0.67392781,0.34863707,0],

[0240] [0,0,0,0]])。

[0241] one_ele=array([[-1.60064922,-0.31750836],

[0242] [-0.31750836,-1.2264124]])。

[0243] two_ele=array([[[[0.87846902,-0.00864192],

[0244] [-0.00864192,0.4068046]],

[0245] [[-0.00864192,0.00584206],

[0246] [0.00584206,-0.00545694]]],

[0247] [[[-0.00864192,0.00584206],

[0248] [0.00584206,-0.00545694]],

[0249] [[0.4068046,-0.00545694],

[0250] [-0.00545694,0.5882485]]]])。

[0251] fock=array([[-0.86699546,-0.32255413],

[0252] [-0.32255413,-0.20814619]])。

[0253] fragment_onerdm=array([[1.98732955,0.02154504],

[0254] [0.02154504,0.01267045]])。

[0255] fragment_twordm=array([[[[1.98705416e+00,2.33926000e-02],

[0256] [2.33926000e-02,2.75389440e-04]],

[0257] [[2.33926000e-02,-1.56938375e-01],

[0258] [2.75389440e-04,-1.84755740e-03]]],

[0259] [[[2.33926000e-02,2.75389440e-04],

[0260] [-1.56938375e-01,-1.84755740e-03]],

[0261] [[2.75389440e-04,-1.84755740e-03],

[0262] [-1.84755740e-03,1.23950589e-02]]]]).

[0263] fragment_energy=-1.5527232353094433.

[0264] number_of_electron=1.4579938106635985.

[0265] After all four fragments are calculated, the ground state energy and total electron number of the original molecular system can be calculated. When calculating the ground state energy of the molecular system, the repulsive energy of the original molecular system can be added, assuming it is 2.865078432259999.

[0266] fragment_energy=-0.7621532837700722-1.5527304185025463-0.76215328387842-1.5527232353094433+2.865078432259999=-1.7646817892004828.

[0267] number_of_electron=0.5453075749373857+1.4580083006616313+0.5453075750413725+1.4579938106635985=4.006617261303988.

[0268] In DMET iterative calculations, chemical potential values ​​can be iteratively optimized to ensure that the total electron count calculated from the fragments is as close as possible to the total electron count of the original molecular system. The above calculation process is a single DMET iteration. The complete DMET iteration process is shown in Table 1.

[0269] Table 1

[0270] Number of iterations Chemical potential The total number of electrons calculated from the fragments The ground state energy value of the molecular system 1 0 4.006617261303988 -1.7646817892004 2 0.0001 4.006953602520262 -1.7649403798910 3 -0.0019674250385606864 4.000000388389687 -1.7595921932437

[0271] In this embodiment, the calculated ground state energy value of the H4 molecular system with a bond length of 1 is -1.7595921932437, which is within 4e-5 of the calculated result of -1.7595580712796703 by DM ET-FCI.

[0272] As a classical algorithm, the DMET algorithm is scalable but lacks computational precision. As a quantum-classical hybrid algorithm, the VQE algorithm offers high computational precision but lacks scalability, making it difficult to apply to large-scale calculations. DMET-VQE, as a hybrid algorithm, mitigates the shortcomings of both while retaining their respective advantages, and can be applied to high-precision calculations of the ground-state energy of large systems.

[0273] When performing mean-field calculations on molecular systems, in addition to using the Hartree-Fock method, more advanced electron correlation methods (such as MP2, CCSD, or DFT) can also be introduced to improve the accuracy of the monomer reduced density matrix. To further improve computational efficiency and accuracy, machine learning algorithms can be combined with existing quantum chemical calculation methods. For example, machine learning models can be used to predict the chemical potential value of the next DMET iteration or the ground state energy value of a fragment, thereby reducing the number of computational iterations and complexity.

[0274] An embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, any of the above methods is implemented.

[0275] An embodiment of the present application further provides a computer program product, which includes a computer program, and when the computer program is executed by a processor, implements any of the above methods.

[0276] The computer program product may be a portable compact disc read-only memory (CD-ROM) and include program code, and may be run on a terminal device, such as a personal computer. However, the computer program product of the present application is not limited thereto, and the computer program product may be any combination of one or more computer-readable media.

[0277] An embodiment of the present application further provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements any of the above methods when executing the computer program.

[0278] See also Figure 8 , Figure 8 This is a structural block diagram of a computer device provided in an embodiment of the present application.

[0279] The embodiments of the present application do not limit the computer device, which may be, for example, a local computer device, a cloud computer device, a distributed computer device, etc.

[0280] As an example, a quantum computer device can be used to calculate the ground state energy value of a fragment, a classical computer device can be used to calculate the number of electrons in the fragment, iteratively adjust the chemical potential value, and calculate and output the ground state energy value of the molecular system.

[0281] like Figure 8 As shown, the computer device may include: a memory 110, a processor 120, and a communication interface 130. The memory 110, the processor 120, and the communication interface 130 are connected via an internal connection path.

[0282] The memory 110 is used to store computer programs. In some implementations, the computer programs may include codes for implementing the methods of the embodiments of the present application.

[0283] The processor 120 is configured to execute the computer program stored in the memory 110 to control the communication interface 130 to receive input data and information and output data such as operation results. In some implementations, when the solutions of the embodiments of the present application are implemented through software or firmware, the computer program for implementing the solutions of the embodiments of the present application may be stored in the processor 120 and executed by the processor 120.

[0284] The memory 110 may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (Programmable ROM, PROM), an erasable programmable read-only memory (Erasable PROM, EPROM), an electrically erasable programmable read-only memory (EEPROM) or a flash memory. The volatile memory may be a random access memory (RAM). It should be noted that the memory 110 described herein is intended to include, but is not limited to, any memory of these and other suitable types. As an example, the memory 110 includes a random access memory (RAM), a cache memory and a read-only memory (ROM). Among them, the memory 110 stores a computer program, and the computer program can be executed by the processor 120 so that the processor 120 implements the steps of any of the above methods.

[0285] The processor 120 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. A general-purpose processor may be a microprocessor, or the processor 120 may be any conventional processor.

[0286] During implementation, each step of the above method can be completed by an integrated logic circuit of the hardware in the processor 120 or by instructions in the form of software. The method disclosed in conjunction with the embodiments of the present application can be directly embodied as being executed by a hardware processor, or can be executed by a combination of hardware and software modules in the processor 120. The software module can be located in a mature storage medium in the art, such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory 110, and the processor 120 reads the information in the memory 110 and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0287] In some implementations, in addition to the hardware units described above, the computer device may also include software modules, where the software modules may be, for example, an operating system, a basic input and output system (BIOS), application software, etc.

[0288] An operating system manages the hardware and / or software resources of a computer device and is the core and cornerstone of the computer. It handles basic tasks such as managing and allocating memory, prioritizing the supply and demand of system resources, controlling input and output devices, operating the network, and managing the file system. To facilitate user operation, most operating systems provide an interface for users to interact with the system.

[0289] The BIOS is used to run hardware initialization during the power-on boot phase and provide runtime services for the operating system and applications. In some implementations, the BIOS can also monitor and display the processor temperature and execute functions such as adjusting temperature protection strategies.

[0290] Application software, also known as an application program, is software written for a specific user purpose. It is a major category of computer software. For example, application software might be a program used for power control, temperature management, and other purposes.

[0291] An embodiment of the present application also provides a quantum operating system, which outputs the ground state energy value of a molecular system according to any of the above methods.

[0292] An embodiment of the present application further provides a quantum computer, comprising a quantum chip and any one of the above-mentioned quantum operating systems, wherein the quantum chip is provided with one or more quantum bits.

[0293] In some embodiments, the quantum computer may be a superconducting quantum computer, and accordingly, the quantum chip may be a superconducting quantum chip, which may be provided with one or more superconducting quantum bits.

[0294] The embodiments of the present application do not limit the number of quantum bits on the quantum chip, which can be, for example, 32, 72, 100, 200, etc.

[0295] It should be noted that although some embodiments of this application take quantum chips as an example, this application can be applied to other quantum computer devices, such as quantum computer simulation devices, etc., and this application is not limited to this.

[0296] It should be understood that the specific examples in this specification are only intended to help those skilled in the art better understand the implementation methods of the present application, rather than to limit the scope of protection of the present application.

[0297] It can be understood that in the various implementations of this specification, the size of the serial number of each process does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of this application.

[0298] It can be understood that the various implementation methods described in this specification can be implemented individually or in combination, and this application is not limited to this.

[0299] Unless otherwise indicated, all technical and scientific terms used in this specification have the same meaning as commonly understood by those skilled in the art in the technical field of this specification. The terms used in this specification are only for the purpose of describing specific embodiments and are not intended to limit the scope of this specification. The term "and / or" used in this specification includes any and all combinations of one or more of the relevant listed items. The singular forms "a", "above", and "the" used in this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0300] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this specification.

[0301] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described embodiments may refer to the corresponding processes in other embodiments and will not be repeated here.

[0302] In the several embodiments provided in this specification, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0303] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected according to actual needs to achieve the objectives of the technical solutions of this application.

[0304] In addition, each functional unit in each embodiment of this specification may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0305] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this specification, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of this specification. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, and other media that can store program code.

[0306] The above are only specific embodiments of this specification, but the scope of protection of this application is not limited to them. Any changes or substitutions that can be easily conceived by any person skilled in the art within the technical scope disclosed in this specification should be included in the scope of protection of this specification. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A method for outputting the ground state energy value of a molecular system, characterized in that: For outputting the ground state energy value of a molecular system, the method comprises: For each fragment corresponding to the molecular system, calculating the ground state energy value and the number of electrons of the fragment according to the specified chemical potential value; Iteratively adjusting the chemical potential value using the total number of electrons calculated based on the fragments and the total number of electrons in the molecular system to obtain a target chemical potential value and a ground state energy value of each fragment corresponding to the target chemical potential value; Based on the ground state energy value of each fragment corresponding to the target chemical potential value, the ground state energy value of the molecular system is calculated and output.

2. The method for outputting the ground state energy value of a molecular system according to claim 1, characterized in that: The multiple fragments corresponding to the molecular system are obtained by dividing the molecular system according to a specified fragment division strategy.

3. The method for outputting the ground state energy value of a molecular system according to claim 2, characterized in that: Each fragment consists of one or more atoms.

4. The method for outputting the ground state energy value of a molecular system according to claim 1, wherein: Calculating the ground state energy value and the number of electrons of the fragment according to the specified chemical potential value includes: constructing an embedded Hamiltonian of the fragment based on the chemical potential value; Using the embedded Hamiltonian, calculating the ground state energy value of the fragment and the corresponding target pseudo-parameters through a variational quantum eigensolver; The number of electrons in the fragment is calculated according to the target proposed parameters.

5. The method for outputting the ground state energy value of a molecular system according to claim 4, characterized in that: The process of constructing the embedded Hamiltonian of the fragment includes: The embedded Hamiltonian is constructed based on the monomer-reduced density matrix of the molecular system, the initial monomer-reduced density matrix of the fragment and the chemical potential value.

6. The method for outputting the ground state energy value of a molecular system according to claim 5, characterized in that: The process of calculating the monomer reduced density matrix of the molecular system includes: The Hartree-Fock method is used to perform mean field calculation on the molecular system to obtain the monomer reduced density matrix of the molecular system.

7. The method for outputting the ground state energy value of a molecular system according to claim 5, characterized in that: The process of calculating the initial monomer reduced density matrix of the fragment includes: constructing an embedded orbital matrix based on a monomer reduced density matrix of the molecular system; Using the embedded orbital matrix, an initial monomer-reduced density matrix of the fragment is calculated.

8. The method for outputting the ground state energy value of a molecular system according to claim 5, characterized in that: The constructing of the embedded Hamiltonian based on the monomer reduced density matrix of the molecular system, the initial monomer reduced density matrix of the fragment and the chemical potential value comprises: Calculating the one-electron integral and the two-electron integral of the fragment using the initial monomer reduced density matrix of the fragment, the monomer reduced density matrix of the molecular system, and the chemical potential value; The embedded Hamiltonian is constructed based on the one-electron integral and the two-electron integral of the fragment.

9. The method for outputting the ground state energy value of a molecular system according to claim 4, characterized in that: The method of using the embedded Hamiltonian to calculate the ground state energy value of the fragment and the corresponding target hypothetical parameters through a variational quantum eigensolver includes: Calculating the eigenvalue of the embedded Hamiltonian as the initial ground state energy value by self-consistent field iterative calculation; The initial ground state energy value and the given pseudo-parameters are used as inputs of a variational quantum eigensolver to solve the ground state energy value of the embedded Hamiltonian and the corresponding target pseudo-parameters.

10. The method for outputting the ground state energy value of a molecular system according to claim 4, characterized in that: Calculating the number of electrons in the fragment according to the target proposed parameters includes: Based on the target proposed parameters, calculating the target monomer reduced density matrix and the two-body reduced density matrix of the fragment by calculating the expected value; The electron number of the fragment is calculated using the target monomer-reduced density matrix and the two-body-reduced density matrix of the fragment.

11. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 10 is implemented.

12. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and the processor implements the method according to any one of claims 1 to 10 when executing the computer program.

13. A quantum operating system, characterized in that: The quantum operating system outputs the ground state energy value of the molecular system according to the method according to any one of claims 1 to 10.

14. A quantum computer, characterized in that The quantum computer includes a quantum chip and the quantum operating system according to claim 13, and one or more quantum bits are arranged on the quantum chip.

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