Quantum compatibility optimization method for molecular Hamiltonian measurement

Abstract

The invention discloses a quantum compatibility optimization method for molecular Hamiltonian measurement. The method comprises the following steps: determining a Fouli item set and a normalized weight coefficient corresponding to each Fouli item in the Fouli item set according to a to-be-simulated target molecule; then, according to a local compatibility rule and the normalized weight coefficient, local compatibility grouping is conducted on the Fouli item set, a target group is determined, and the local compatibility rule is used for judging whether two Fouli items in the Fouli item set can be classified into the same group or not; and finally, realizing quantum compatibility optimization of molecular Hamiltonian measurement according to target grouping. Therefore, local compatibility grouping can be carried out based on the local compatibility rule and the normalized weight coefficient, and the flexibility of grouping is improved. Moreover, the relative contribution of each bubble item to the total energy of the molecular Hamiltonian can be determined according to the normalized weight coefficient, and the number of measurement times is reasonably distributed, so that the overall measurement variance is reduced, and the quantum calculation cost is reduced.

Description

Technical Field

[0001] The present application relates to the field of quantum computing, and more specifically, to a quantum compatibility optimization method for molecular Hamiltonian measurement. Background Art

[0002] In related technologies, when simulating molecular electronic structures using quantum computers, Pauli terms are typically grouped for global compatibility using a linear decoupling framework. This allows for parallel measurement of these terms, thereby improving the efficiency of quantum computing simulations. However, this linear decoupling framework requires that the Pauli matrices of all qubits within a group must be completely compatible; otherwise, the grouping cannot be performed. This grouping criterion wastes measurement resources, increasing the cost of quantum computing. Summary of the Invention

[0003] The present application provides a quantum compatibility optimization method for molecular Hamiltonian measurement.

[0004] The present application provides a method for optimizing quantum compatibility of molecular Hamiltonian measurements, the method comprising: Determining a Pauli term set and a normalized weight coefficient corresponding to each Pauli term in the Pauli term set according to a target molecule to be simulated; performing local compatibility grouping on the Pauli term set according to a local compatibility rule and the normalized weight coefficient to determine a target group, wherein the local compatibility rule is used to determine whether two Pauli terms in the Pauli term set can be classified into the same measurement group; According to the target grouping, quantum compatibility optimization of the molecular Hamiltonian measurement is achieved.

[0005] In this way, the computer device determines the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set based on the target molecule to be simulated. Then, the computer device performs local compatibility grouping on the Pauli term set according to the local compatibility rule and the normalized weight coefficient to determine the target group, wherein the local compatibility rule is used to determine whether two Pauli terms in the Pauli term set can be classified into the same measurement group. Finally, the computer device realizes quantum compatibility optimization of molecular Hamiltonian measurement based on the target grouping. In this way, compared with the linear decoupling framework requiring that the Pauli matrices of all quantum bits must be completely compatible before grouping, the quantum compatibility optimization method for molecular Hamiltonian measurement provided by the embodiment of the present application can perform local compatibility grouping based on local compatibility rules and normalized weight coefficients, thereby improving the flexibility of grouping. Moreover, the relative contribution of each Pauli term to the total energy of the molecular Hamiltonian can be determined based on the normalized weight coefficient, and the number of measurements can be reasonably allocated, thereby reducing the overall measurement variance and reducing the cost of quantum computing.

[0006] In certain embodiments, determining the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set according to the target molecule to be simulated includes: Determining, according to the target molecule, a first target quantized Hamiltonian corresponding to the target molecule, wherein the first target quantized Hamiltonian is a second quantized Hamiltonian of the target molecule; The Pauli term set and the normalized weight coefficient are determined according to the first target quantized Hamiltonian.

[0007] In this way, the computer device determines a first target quantized Hamiltonian corresponding to the target molecule, where the first target quantized Hamiltonian is the second quantized Hamiltonian of the target molecule. Next, the computer device determines a set of Pauli terms and normalized weight coefficients based on the first target quantized Hamiltonian. This construction of the first target quantized Hamiltonian accurately describes the interactions between various particles in the target molecule, providing the data foundation for the subsequent Pauli term set and normalized weight coefficients.

[0008] In certain embodiments, determining a first target quantized Hamiltonian corresponding to the target molecule based on the target molecule includes: Determining the geometric structure and basis set of the target molecule based on the acquired input parameters, wherein the input parameters include elemental composition, atomic coordinates, and basis set type of the target molecule; According to the target molecule, the geometric structure, and the basis set, a one-electron integral and a two-electron integral of the target molecule are calculated, wherein the one-electron integral is used to describe the energy integral of the motion of a single electron in the target molecule in the nuclear potential field, and the two-electron integral is used to describe the energy integral of the Coulomb repulsion energy between two electrons in the target molecule; The first target quantized Hamiltonian is constructed according to the one-electron integral and the two-electron integral.

[0009] In this way, the computer device determines the geometric structure and basis set of the target molecule based on the acquired input parameters, wherein the input parameters include the elemental composition, atomic coordinates and basis set type of the target molecule. Then, the computer device calculates the one-electron integral and two-electron integral of the target molecule based on the target molecule, geometric structure and basis set, wherein the one-electron integral is used to describe the energy integral of the motion of a single electron in the target molecule in the nuclear potential field, and the two-electron integral is used to describe the energy integral of the Coulomb repulsion energy between two electrons in the target molecule. Finally, the computer device constructs the first target quantized Hamiltonian based on the one-electron integral and the two-electron integral. In this way, the molecular geometric structure and basis set are determined by input parameters, thereby calculating the one-electron integral and the two-electron integral of the target molecule and constructing the quantized Hamiltonian, realizing the conversion from the molecular physics model to the quantized Hamiltonian, and providing the data basis for the subsequent steps.

[0010] In some embodiments, determining the Pauli term set and the normalized weight coefficient according to the first target quantized Hamiltonian includes: Performing a transformation on the fermion operator in the first target quantized Hamiltonian to obtain a second target quantized Hamiltonian; The Pauli term set and the normalized weight coefficient are determined according to the second target quantized Hamiltonian.

[0011] In this way, the computer transforms the fermion operators in the first target quantized Hamiltonian to obtain the second target quantized Hamiltonian. Next, the computer determines the Pauli term set and normalized weight coefficients based on the second target quantized Hamiltonian. In this way, by processing the fermion operators and determining the second target quantized Hamiltonian, a mapping from quantum chemical expressions to a form tractable by quantum computation is achieved, providing the data foundation for the subsequent calculation of the Pauli term set and normalized weight coefficients.

[0012] In some embodiments, the fermion operator includes a creation operator and an annihilation operator, and the transforming the fermion operator in the first target quantized Hamiltonian to obtain the second target quantized Hamiltonian includes: Based on a first preset transformation rule, transforming the generation operator into a Pauli term form to generate a first tensor product; Based on a second preset transformation rule, transforming the annihilation operator into a Pauli term form to generate a second tensor product; The second target quantized Hamiltonian is determined according to the first tensor product and the second tensor product.

[0013] In this manner, based on the first preset transformation rule, the computer device transforms the generation operator into a Pauli term, generating a first tensor product. Next, based on the second preset transformation rule, the computer device transforms the annihilation operator into a Pauli term, generating a second tensor product. Finally, the computer device determines a second target quantized Hamiltonian based on the first and second tensor products. In this way, by transforming the fermion generation and annihilation operators, the quantized Hamiltonian is converted into a form that can be processed by quantum computing.

[0014] In some embodiments, determining the Pauli term set and the normalized weight coefficient according to the second target quantized Hamiltonian includes: processing the second target quantized Hamiltonian based on a linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine a third target quantized Hamiltonian; performing a Pauli term extraction process on the third target quantized Hamiltonian to determine the Pauli term set and a weight coefficient corresponding to each Pauli term in the Pauli term set; The weight coefficient is normalized to determine the normalized weight coefficient.

[0015] In this way, the computer device processes the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine the third target quantized Hamiltonian. Next, the computer device performs Pauli term extraction on the third target quantized Hamiltonian, determining a set of Pauli terms and the corresponding weight coefficients for each Pauli term in the set. Finally, the computer device normalizes the weight coefficients to determine the normalized weight coefficients. In this way, through linear relationship simplification and Hamiltonian transformation, the Pauli terms are organized and weighted, providing a data foundation for subsequent measurement optimization.

[0016] In some embodiments, processing the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine the third target quantized Hamiltonian includes: Simplifying the second target quantized Hamiltonian according to the commutation relation of the first temporary Pauli term to determine a fourth target quantized Hamiltonian; The second temporary Pauli terms in the fourth target quantized Hamiltonian are merged to determine the third target quantized Hamiltonian.

[0017] In this way, the computer simplifies the second target quantized Hamiltonian based on the commutation relation of the first provisional Pauli term to determine the fourth target quantized Hamiltonian. Next, the computer combines the second provisional Pauli terms in the fourth target quantized Hamiltonian to determine the third target quantized Hamiltonian. In this way, through commutation relation simplification and Pauli term merging, the Hamiltonian is structurally optimized and standardized, providing a data foundation for subsequent measurement optimization.

[0018] In certain embodiments, performing local compatibility grouping on the Pauli term set according to the local compatibility rule and the normalized weight coefficient to determine the target group includes: Performing descending processing on the normalized weight coefficients to determine a target weight coefficient of a preset proportion and a target Pauli term corresponding to the target weight coefficient, wherein the Pauli term set includes the target Pauli term; According to the local compatibility rule, the target Pauli items are grouped according to local compatibility to determine the target group.

[0019] In this manner, the computer device processes the normalized weight coefficients in descending order to determine a target weight coefficient with a preset percentage and a target Pauli term corresponding to the target weight coefficient, wherein the Pauli term set includes the target Pauli term. Next, the computer device performs local compatibility grouping on the target Pauli terms based on the local compatibility rule to determine the target group. In this way, by screening the target Pauli terms in descending order of weight and combining the grouping with the local compatibility rule, precise allocation of measurement resources and improved measurement efficiency are achieved.

[0020] In certain embodiments, the step of optimizing the quantum compatibility of the molecular Hamiltonian measurement according to the target grouping comprises: Determining a quantum compatibility relationship between Pauli terms in the target group based on a preset quantum compatibility rule; Grouping the Pauli terms in the target group according to the quantum compatibility relationship and the obtained measurement requirements to determine a target measurement group; The target measurement group is measured in parallel to achieve quantum compatibility optimization of the molecular Hamiltonian measurement.

[0021] In this way, the computer device determines the quantum compatibility relationship between the Pauli terms in the target group based on the preset quantum compatibility rules. Next, the computer device groups the target groups according to the quantum compatibility relationship and the acquired measurement requirements, determining target measurement groups. Finally, the computer device performs parallel measurements on the target measurement groups to optimize the quantum compatibility of the molecular Hamiltonian measurement. In this way, by determining local compatibility based on quantum compatibility rules and grouping based on measurement requirements, measurement efficiency is improved.

[0022] In some embodiments, grouping the Pauli terms in the target group according to the quantum compatibility relationship and the acquired measurement requirements to determine the target measurement group includes: Constructing a compatibility graph model corresponding to the target group according to the quantum compatibility relationship and the target group; The Pauli items in the target group are grouped according to the measurement requirement and the compatibility graph model to determine the target measurement group.

[0023] In this manner, the computer device determines a compatibility graph model corresponding to the target group based on the quantum compatibility relationship and the target group. Next, the target group is grouped according to the measurement requirements and the compatibility graph model to determine the target measurement group. In this way, by constructing a compatibility graph model and grouping based on measurement requirements, the Pauli term compatibility relationship is visualized and the grouping strategy is personalized.

[0024] Additional aspects and advantages of the embodiments of the present application will be given in part in the description below, and in part will become obvious from the description below, or will be learned through practice of the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which: Figure 1 This is one of the flow diagrams of the optimization method according to the embodiment of the present application; Figure 2 This is the second flow chart of the optimization method according to the embodiment of the present application; Figure 3 This is the third flow chart of the optimization method according to the embodiment of the present application; Figure 4 This is the fourth flow chart of the optimization method according to the embodiment of the present application; Figure 5 This is the fifth flow chart of the optimization method according to the embodiment of the present application; Figure 6 This is the sixth flow chart of the optimization method according to the embodiment of the present application; Figure 7 This is the seventh flow chart of the optimization method according to the embodiment of the present application; Figure 8 This is the eighth flow chart of the optimization method according to the embodiment of the present application; Figure 9 Schematic diagram of target grouping of LiH molecules according to an embodiment of the present application; Figure 10This is the ninth flow chart of the optimization method according to the embodiment of the present application; Figure 11 This is the tenth flow chart of the optimization method according to the embodiment of the present application; Figure 12 is a schematic diagram of a compatibility diagram model of a LiH molecule according to an embodiment of the present application; Figure 13 This is one of the schematic diagrams of grouping of LiH molecules according to an embodiment of the present application; Figure 14 This is the second schematic diagram of the grouping of LiH molecules according to the embodiment of the present application; Figure 15 This is the third schematic diagram of the grouping of LiH molecules according to the embodiment of the present application; Figure 16 This is the fourth schematic diagram of the grouping of LiH molecules according to the embodiment of the present application. DETAILED DESCRIPTION

[0026] The embodiments of the present application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the embodiments of the present application, and should not be understood as limiting the embodiments of the present application.

[0027] In the field of quantum chemistry simulations, the Linear Decoupling Framework (LDF) is a commonly used measurement optimization technique in traditional techniques for molecular electronic structure simulations using quantum computers. This framework decomposes the molecular Hamiltonian into Pauli terms (such as the tensor product of the X, Y, and Z operators), constructs a conflict graph with Pauli terms as nodes and qubit operator conflicts as edges, and then uses a graph coloring algorithm to group globally compatible Pauli terms into the same group, enabling parallel measurement and improving quantum computing simulation efficiency.

[0028] However, the linear decoupling framework strictly requires that the Pauli matrices of all qubits within the same group must be fully compatible. For any two Pauli terms within the same group, the operators at all qubit positions must either be identical or one of them must be the identity matrix I; otherwise, grouping is prohibited. This "all-or-nothing" grouping criterion severely restricts the efficient use of measurement resources. For example, when two Pauli terms have compatible bases only on some qubits (e.g., X⊗I and I⊗X both have X in the first bit), the traditional framework cannot meet the full bit compatibility requirement and must forcibly split them into different groups, resulting in a surge in the number of groups.

[0029] Based on the above questions, please refer to Figure 1, the embodiment of the present application provides a quantum compatibility optimization method for molecular Hamiltonian measurement, the method comprising: 01: According to the target molecule to be simulated, determine the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set; 02: Based on the local compatibility rule and normalized weight coefficient, the Pauli term set is grouped by local compatibility to determine the target group; 03: Optimize quantum compatibility of molecular Hamiltonian measurements based on target grouping.

[0030] The present application also provides a computer device including a memory and a processor. The quantum compatibility optimization method for molecular Hamiltonian measurement of the present application can be implemented by the computer device of the present application. Specifically, a computer program is stored in the memory, and the processor is used to determine the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set based on the target molecule to be simulated. And based on the local compatibility rule and the normalized weight coefficient, the Pauli term set is grouped for local compatibility to determine the target group. And based on the target group, the quantum compatibility optimization of molecular Hamiltonian measurement is achieved.

[0031] The embodiment of the present application also provides a molecular Hamiltonian measurement device. The quantum compatibility optimization method for molecular Hamiltonian measurement of the embodiment of the present application can be implemented by the molecular Hamiltonian measurement device of the embodiment of the present application. Specifically, the molecular Hamiltonian measurement device includes a determination module. The determination module is used to determine the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set according to the target molecule to be simulated. And according to the local compatibility rule and the normalized weight coefficient, the Pauli term set is locally grouped for compatibility and the target group is determined. And according to the target group, the quantum compatibility optimization of the molecular Hamiltonian measurement is achieved.

[0032] Specifically, the molecular Hamiltonian refers to the quantum mechanical operator that describes the interactions between electrons and atomic nuclei in a molecule. In other words, the molecular Hamiltonian is a physical model simulated by quantum chemistry, encompassing interactions such as electron kinetic energy, nuclear attraction, and repulsion between electrons.

[0033] Molecular Hamiltonian measurement involves performing quantum measurements on a molecular Hamiltonian to obtain physical quantities such as its energy eigenvalue. This is achieved by measuring Pauli terms in groups and combining the results. This means that Hamiltonian measurements cannot be performed directly on a quantum computer. Instead, they must be decomposed into linear combinations of Pauli terms, measured in parallel, and then their weighted sum is calculated to obtain the expected value of the Hamiltonian. Molecular Hamiltonian measurement is a key step in quantum chemical simulations, and measurement efficiency and accuracy directly impact the reliability of the simulation results.

[0034] Quantum compatibility refers to the compatibility relationship between Pauli terms in quantum measurement, which can be categorized as global compatibility or local compatibility. Global compatibility means that to be grouped together, all qubit operators between any two Pauli terms within that group must be completely compatible. Local compatibility means that to be grouped together, at least one qubit operator between any two Pauli terms within that group must be identical or contain the identity matrix I. For example, Pauli terms X⊗Y and Z⊗I are locally compatible, and Pauli terms X⊗Y and X⊗Z are locally compatible, but Pauli terms X⊗Y and Z⊗Z are not locally compatible.

[0035] The target molecule refers to the specific molecule to be simulated, such as the LiH (lithium hydride) molecule, whose geometric structure and basis set need to be determined. The number and weight distribution of Pauli terms for different target molecules are different.

[0036] The Pauli term set is the set of tensor products of Pauli operators obtained by decomposing the molecular Hamiltonian through the Jordan-Wigner transformation, such as 、 Each Pauli term in the Pauli term set represents an interaction term in the Hamiltonian. The Jordan-Wigner transformation is a mapping method that can map fermion operators to combinations of Pauli operators for quantum bits, thereby achieving a mapping from quantum chemical expressions to quantum computationally tractable forms.

[0037] The normalized weight coefficient refers to the percentage of the absolute value of each Pauli term coefficient to the sum of the absolute values ​​of the total coefficients, that is, ,in, is the Pauli term weight coefficient corresponding to each Pauli term, In the quantum compatibility optimization method for molecular Hamiltonian measurement provided in the embodiments of the present application, the normalized weight coefficient can quantify the importance of the Pauli term (the higher the normalized weight coefficient of the Pauli term, the greater its impact on the molecular energy and the greater its importance). High-weight terms have a greater impact on molecular energy, and measurement accuracy should be prioritized (i.e., the number of measurements of Pauli terms with high normalized weight coefficients should be increased). In this way, the normalized weight coefficient can be used to reasonably allocate the number of measurements, maximizing measurement accuracy when resources are limited.

[0038] The local compatibility rule, also known as the local compatibility judgment rule, determines whether Pauli terms can be grouped together. This rule requires that the operators on at least one qubit in the group be compatible (either identical or containing I). In molecular Hamiltonian measurements, due to the hardware limitations of quantum computers, if the quantum circuit used for measurement (determined by factors such as the number and complexity of the Pauli terms being measured) is too deep, this can lead to significant deviations in the results. By using the local compatibility rule to group Pauli terms together, the depth of the quantum circuit can be reduced, improving measurement accuracy.

[0039] The target grouping refers to the grouping results determined by the local compatibility rule. The Pauli terms with the potential for parallel measurement are preliminarily determined in the target grouping. Whether parallel measurement can be performed still needs to be determined by the preset quantum compatibility rule.

[0040] It should be noted that the quantum compatibility optimization method for molecular Hamiltonian measurements provided in the embodiments of this application primarily targets the grouping stage of molecular Hamiltonian measurements. Specifically, Pauli terms are grouped based on local compatibility rules (breaking through the traditional global compatibility constraint by allowing grouping only if some qubits are compatible). A normalized weight coefficient is introduced to filter high-contribution Pauli terms by descending order, prioritizing the allocation of measurement resources to key terms. Furthermore, a compatibility graph model can be constructed to dynamically adjust grouping based on measurement requirements, maximizing parallel measurement efficiency.

[0041] First, a molecular Hamiltonian is constructed based on the target molecule to be simulated, a set of Pauli terms is obtained by decomposition, and the normalized weight coefficients are calculated to quantify the importance of different Pauli terms.

[0042] Then, based on the local compatibility rule and the normalized weight coefficient, the Pauli terms are grouped according to local compatibility to obtain the target grouping.

[0043] Ultimately, the efficiency and accuracy of molecular Hamiltonian measurements are optimized by processing the target groups and performing parallel measurements.

[0044] The following describes the quantum compatibility optimization method for molecular Hamiltonian measurement provided by the embodiment of the present application by taking the target molecule LiH (lithium hydride) molecule as an example.

[0045] First, based on the LiH molecule, determine the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set. For example, some of the Pauli terms in the Pauli term set are 、 、 、 and Among them, The corresponding normalized weight coefficient is 0.260636; The corresponding normalized weight coefficient is 0.066069; The corresponding normalized weight coefficient is 0.066069; The corresponding normalized weight coefficient is 0.026910; The corresponding normalized weight coefficient is 0.026910.

[0046] Then, according to the preset quantum compatibility rules and normalized weight coefficients, the Pauli term set is grouped according to local compatibility to determine the target group.

[0047] Finally, computer devices are grouped according to their objectives to achieve quantum compatibility optimization of molecular Hamiltonian measurements.

[0048] In summary, in the quantum compatibility optimization method for molecular Hamiltonian measurement provided by the embodiment of the present application, the computer device determines the Pauli term set and the normalized weight coefficient corresponding to each Pauli term in the Pauli term set based on the target molecule to be simulated. Then, the computer device performs local compatibility grouping on the Pauli term set according to the local compatibility rule and the normalized weight coefficient to determine the target group, wherein the local compatibility rule is used to determine whether two Pauli terms in the Pauli term set can be classified into the same measurement group. Finally, the computer device implements quantum compatibility optimization for molecular Hamiltonian measurement based on the target grouping. In this way, compared with the linear decoupling framework requiring that the Pauli matrices of all quantum bits must be completely compatible before grouping, the quantum compatibility optimization method for molecular Hamiltonian measurement provided by the embodiment of the present application can perform local compatibility grouping based on the local compatibility rule and the normalized weight coefficient, thereby improving the flexibility of grouping. Moreover, the relative contribution of each Pauli term to the total energy of the molecular Hamiltonian can be determined based on the normalized weight coefficient, and the number of measurements can be reasonably allocated, thereby reducing the overall measurement variance and reducing the quantum computing cost.

[0049] See also Figure 2 In certain embodiments, step 01 (determining a Pauli term set and a normalized weight coefficient corresponding to each Pauli term in the Pauli term set based on a target molecule to be simulated) includes: 011: According to the target molecule, determining a first target quantized Hamiltonian corresponding to the target molecule; 012: Based on the first objective quantized Hamiltonian, determine the Pauli term set and normalized weight coefficients.

[0050] In certain embodiments, the determination module is further configured to determine a first target quantized Hamiltonian corresponding to the target molecule based on the target molecule, and determine a Pauli term set and a normalized weight coefficient based on the first target quantized Hamiltonian.

[0051] In certain embodiments, the processor is further configured to determine, based on the target molecule, a first target quantized Hamiltonian corresponding to the target molecule, and determine, based on the first target quantized Hamiltonian, a set of Pauli terms and a normalized weight coefficient.

[0052] Specifically, the first target quantized Hamiltonian refers to the second quantized Hamiltonian of the target molecule (i.e., the second quantized Hamiltonian of the target molecule), which is the quantum mechanical operator that describes the interaction between electrons and atomic nuclei in the molecule. The first target quantized Hamiltonian H is expressed as:

[0053] in, and They are the creation operator and annihilation operator of fermions, respectively, and are used to describe the creation and annihilation of electrons between quantum states. is an electron integral, representing the electron's kinetic energy and the energy of attraction with the nucleus; It describes the kinetic energy of electrons and the energy of attraction between electrons and the nucleus; It represents the process of electron transition from state q to state p. is the two-electron integral, representing the repulsive energy between electrons; Describes the repulsive energy between electrons; It represents the process of two electrons jumping at the same time, that is, one electron jumps from state r to state p, and the other electron jumps from state s to state q; and by introducing , to avoid double counting of electron pairs.

[0054] The second quantized Hamiltonian transforms the quantum state and interaction of electrons into computable operator expressions through a combination of fermion operators, which can accurately describe the energy and electron distribution of molecules.

[0055] Continuing with the above example, based on the LiH molecule to be simulated, a first target quantized Hamiltonian corresponding to the LiH molecule can be obtained. Specifically, through a combination of fermion operators, the quantum states of each electron in the LiH molecule and the interactions between them are transformed into a computable second quantized Hamiltonian.

[0056] Then, through certain processing, the first target quantized Hamiltonian is converted into a set of Pauli terms that can be processed by a quantum computer, thereby determining the set of Pauli terms and normalized weight coefficients.

[0057] In this way, the computer device determines a first target quantized Hamiltonian corresponding to the target molecule, where the first target quantized Hamiltonian is the second quantized Hamiltonian of the target molecule. Next, the computer device determines a set of Pauli terms and normalized weight coefficients based on the first target quantized Hamiltonian. This construction of the first target quantized Hamiltonian accurately describes the interactions between various particles in the target molecule, providing the data foundation for the subsequent Pauli term set and normalized weight coefficients.

[0058] See also Figure 3 In certain embodiments, step 011 (determining a first target quantized Hamiltonian corresponding to the target molecule based on the target molecule) includes: 0111: Determine the geometric structure and basis set of the target molecule based on the obtained input parameters; 0112: Calculate the one-electron integral and two-electron integral of the target molecule based on the target molecule, geometric structure and basis set; 0113: Based on one-electron integral and two-electron integral, construct the first target quantized Hamiltonian.

[0059] In certain embodiments, the determination module is further configured to determine the geometry and basis set of the target molecule based on the acquired input parameters, calculate the one-electron integral and the two-electron integral of the target molecule based on the target molecule, the geometry, and the basis set, and construct a first target quantized Hamiltonian based on the one-electron integral and the two-electron integral.

[0060] In certain embodiments, the processor is further configured to determine the geometry and basis set of the target molecule based on the acquired input parameters; calculate the one-electron integral and the two-electron integral of the target molecule based on the target molecule, the geometry, and the basis set; and construct a first target quantized Hamiltonian based on the one-electron integral and the two-electron integral.

[0061] Specifically, input parameters refer to the initial data provided by the user or the system to describe the physical properties of the target molecule and are a prerequisite for constructing the Hamiltonian. Input parameters typically include the elemental composition of the target molecule (e.g., LiH, which is composed of Li and H atoms), atomic coordinates (specific parameters of the geometric structure), and basis set type (e.g., STO-3G, 6-31G, etc.), which can be obtained through user input or default configuration.

[0062] Geometric structure refers to the spatial distribution of atomic nuclei within a target molecule, typically expressed as atomic coordinates (e.g., three-dimensional Cartesian coordinates). Geometric structure determines physical properties of a molecule, such as the type, length, and angle of chemical bonds. It serves as the basis for calculating molecular interactions and can be used to calculate the Coulomb attraction between electrons and nuclei, as well as the repulsion between nuclei. For example, the geometric structure of the LiH molecule is linear, with the distance between the Li and H atoms being approximately 1.59 angstroms.

[0063] A basis set is a collection of mathematical functions (basis functions) used to expand the electron wave function. It approximates the electron wave function through a linear combination of a finite number of basis functions. Common types include STO-3G, 6-31G, and cc-pVDZ. It's important to note that the type of basis set determines the accuracy and complexity of the calculations. Specifically, the larger the basis set, the more accurate the integral calculations, and the more accurately the Hamiltonian reflects the true electronic structure of the molecule. For example, the STO-3G basis set, which stands for Slater-Type Orbital - 3 Gaussians, approximates a single Slater-type orbital (STO) with three Gaussians. This approach offers high computational efficiency but limited accuracy. The 6-31G basis set, which stands for 6-31 Gaussian split-valence basis set, describes the valence and inner-shell electron orbitals of an atom using different numbers of Gaussians to more precisely capture the behavior of valence electrons. The cc-pVDZ basis set, short for correlation-consistent polarized Valence Double-Zeta, systematically adds basis functions (such as polarization functions and higher angular momentum functions) to ensure that the calculation results converge to the exact value as the basis set size increases.

[0064] An electron integral refers to the energy integral describing the motion of a single electron in the nuclear potential field, which is recorded as Where p and q are basis function indices. One electron integral can form a single electron term of the second quantized Hamiltonian ( ), this single-electron term describes the kinetic energy of the electron and its interaction with the nucleus, and is a basic component of the Hamiltonian.

[0065] The two-electron integral refers to the integral describing the Coulomb repulsion energy between two electrons, which is recorded as , where p, q, r, and s are basis function indices. The two-electron integral can form the two-electron term of the second quantized Hamiltonian ( ), this two-electron term is used to describe the mutual repulsion energy between electrons and plays a decisive role in the chemical properties of molecules (such as bond energy or reactivity).

[0066] Continuing with the previous example, the geometry and basis set are determined based on the user-entered input parameters. Specifically, based on the user-entered "LiH molecule" and "STO-3G," the system generates the corresponding atomic coordinates and basis function set (basis set).

[0067] Next, the geometry and basis set jointly determine the results of the one-electron and two-electron integrals, which reflect the kinetic energy, nuclear attraction energy, and inter-electron repulsion energy of the electrons in the LiH molecule.

[0068] Finally, according to the one-electron integral and the two-electron integral determined above, the first target quantized Hamiltonian (the second quantized Hamiltonian) is constructed, that is, .

[0069] In this way, the computer device determines the geometric structure and basis set of the target molecule based on the acquired input parameters, wherein the input parameters include the elemental composition, atomic coordinates and basis set type of the target molecule. Then, the computer device calculates the one-electron integral and two-electron integral of the target molecule based on the target molecule, geometric structure and basis set, wherein the one-electron integral is used to describe the energy integral of the motion of a single electron in the target molecule in the nuclear potential field, and the two-electron integral is used to describe the energy integral of the Coulomb repulsion energy between two electrons in the target molecule. Finally, the computer device constructs the first target quantized Hamiltonian based on the one-electron integral and the two-electron integral. In this way, the molecular geometric structure and basis set are determined by input parameters, thereby calculating the one-electron integral and the two-electron integral of the target molecule and constructing the quantized Hamiltonian, realizing the conversion from the molecular physics model to the quantized Hamiltonian, and providing the data basis for the subsequent steps.

[0070] See also Figure 4 In some embodiments, step 012 (determining a set of Pauli terms and normalized weight coefficients based on the first target quantized Hamiltonian) includes: 0121: Transform the fermion operator in the first target quantized Hamiltonian to obtain the second target quantized Hamiltonian; 0122: Based on the second objective quantized Hamiltonian, determine the Pauli term set and normalized weight coefficients.

[0071] In certain embodiments, the determination module is further configured to transform the fermion operator in the first target quantized Hamiltonian to obtain a second target quantized Hamiltonian, and determine a Pauli term set and a normalized weight coefficient based on the second target quantized Hamiltonian.

[0072] In certain embodiments, the processor is further configured to transform the fermion operator in the first target quantized Hamiltonian to obtain a second target quantized Hamiltonian, and determine a Pauli term set and a normalized weight coefficient based on the second target quantized Hamiltonian.

[0073] Specifically, fermion operators refer to operators that describe the creation and annihilation of fermion (such as electron) quantum states, and are the basis for constructing molecular Hamiltonians, including the creation operator and annihilation operator .

[0074] The second target quantized Hamiltonian refers to the Hamiltonian obtained by mapping the fermion operators in the first target quantized Hamiltonian to Pauli operators (such as X, Y, and Z) on the quantum bit through methods such as Jordan-Wigner transformation. It is in the form of ,in, For Pauli terms, The second target quantized Hamiltonian is an equivalent representation of the first target quantized Hamiltonian in quantum bit space. It transforms complex combinations of fermion operators into tensor products of Pauli operators, enabling measurements of the molecular Hamiltonian on a quantum computer. Pauli operators are a set of Hermitian operators used to describe the state of a single quantum bit, including three fundamental operators and a unit operator.

[0075] Through quantum bit mapping of fermion operators, the molecular Hamiltonian is converted from the field of quantum chemistry to the field of quantum computing (i.e., from the first target quantized Hamiltonian to the second target quantized Hamiltonian).

[0076] Then, according to the second target quantized Hamiltonian, a set of Pauli terms and normalized weight coefficients for subsequent measurement processes are determined.

[0077] Continuing with the above example, the Jordan-Wigner transformation is performed on the first target quantized Hamiltonian corresponding to the LiH molecule to map the fermion operator to the qubit state, ultimately obtaining the Hamiltonian of the target chemical molecule (i.e., the second target quantized Hamiltonian). The original coefficients of some Pauli terms and the qubit mapping are shown in Table 1 below: Table 1

[0078] Then, the Pauli term set and the normalized weight coefficient are determined according to the second target quantized Hamiltonian.

[0079] In this way, the computer transforms the fermion operators in the first target quantized Hamiltonian to obtain the second target quantized Hamiltonian. Next, the computer determines the Pauli term set and normalized weight coefficients based on the second target quantized Hamiltonian. In this way, by processing the fermion operators and determining the second target quantized Hamiltonian, a mapping from quantum chemical expressions to a form tractable by quantum computation is achieved, providing the data foundation for the subsequent calculation of the Pauli term set and normalized weight coefficients.

[0080] See also Figure 5In some embodiments, the fermion operator includes a generation operator and an annihilation operator. Step 0121 (transforming the fermion operator in the first target quantized Hamiltonian to obtain a second target quantized Hamiltonian) includes: 01211: Based on a first preset transformation rule, transform the generation operator into a Pauli term form to generate a first tensor product; 01212: Based on the second preset transformation rule, the annihilation operator is transformed into a Pauli term form to generate a second tensor product; 01213: Determine a second target quantized Hamiltonian based on the first tensor product and the second tensor product.

[0081] In certain embodiments, the determination module is further configured to transform the generation operator into a Pauli term form based on a first preset transformation rule to generate a first tensor product; and to transform the annihilation operator into a Pauli term form based on a second preset transformation rule to generate a second tensor product; and to determine a second target quantized Hamiltonian based on the first tensor product and the second tensor product.

[0082] In some embodiments, the processor is further configured to transform the generation operator into a Pauli term form based on a first preset transformation rule to generate a first tensor product; transform the annihilation operator into a Pauli term form based on a second preset transformation rule to generate a second tensor product; and determine a second target quantized Hamiltonian based on the first tensor product and the second tensor product.

[0083] Specifically, the first preset transformation rule refers to the transformation rule for mapping the fermion generation operator to the tensor product of the Pauli operators on the quantum bit, specifically the transformation formula for the generation operator in the Jordan-Wigner transformation: , which means that an electron is generated in the quantum state p, where is the Pauli-Z operator, which is used to calculate the parity of the electron occupation number; and The Pauli-X and Pauli-Y operators of the p-th qubit are used to update the value of the qubit; represents the tensor product of the Pauli-Z operators of the first p-1 qubits; Used to create electronic states on the target qubit.

[0084] The first tensor product refers to the tensor product of the Pauli operators corresponding to the fermion generation operator after applying the first preset transformation rule, which is in the form of The first tensor product is the specific representation of the operator in the quantum bit space. For example, when p=2, the operator Transformed into , which means that before generating electrons on the second qubit, the parity of the first qubit is detected first.

[0085] The second preset transformation rule refers to the transformation rule that maps the fermion annihilation operator to the tensor product of Pauli operators on the quantum bit. Specifically, it is the transformation formula of the annihilation operator in the Jordan-Wigner transformation: , which means to eliminate the electron in quantum state q. The difference from the generation operator transformation is that the molecule is , which corresponds to the operation of annihilating the electronic state.

[0086] The second tensor product refers to the tensor product of the Pauli operators corresponding to the fermion annihilation operator after applying the second preset transformation rule, which is in the form of The second tensor product is the specific representation of the annihilation operator in the quantum bit space. For example, when p=2, the operator Transformed into , which means that before annihilating the electron on the second qubit, the parity of the first qubit is detected first.

[0087] Continuing with the above example, based on the first preset transformation rule and the second preset transformation rule, the generation operator and the annihilation operator are transformed to generate a first tensor product and a second tensor product, which are substituted into the first target quantized Hamiltonian to determine the second target quantized Hamiltonian.

[0088] In this manner, based on the first preset transformation rule, the computer device transforms the generation operator into a Pauli term, generating a first tensor product. Next, based on the second preset transformation rule, the computer device transforms the annihilation operator into a Pauli term, generating a second tensor product. Finally, the computer device determines a second target quantized Hamiltonian based on the first and second tensor products. In this way, by transforming the fermion generation and annihilation operators, the quantized Hamiltonian is converted into a form that can be processed by quantum computing.

[0089] See also Figure 6 In some embodiments, step 0122 (determining a set of Pauli terms and normalized weight coefficients based on the second target quantized Hamiltonian) includes: 01221: Based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian, the second target quantized Hamiltonian is processed to determine the third target quantized Hamiltonian; 01222: Perform Pauli term extraction processing on the third target quantized Hamiltonian to determine the Pauli term set and the weight coefficient corresponding to each Pauli term in the Pauli term set; 01223: Normalize the weight coefficient and determine the normalized weight coefficient.

[0090] In certain embodiments, the determination module is further configured to process the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine a third target quantized Hamiltonian, perform Pauli term extraction on the third target quantized Hamiltonian to determine a Pauli term set and a weight coefficient corresponding to each Pauli term in the Pauli term set, and perform normalization on the weight coefficient to determine a normalized weight coefficient.

[0091] In certain embodiments, the processor is further configured to process the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine a third target quantized Hamiltonian, perform Pauli term extraction on the third target quantized Hamiltonian to determine a Pauli term set and a weight coefficient corresponding to each Pauli term in the Pauli term set, and perform normalization on the weight coefficient to determine a normalized weight coefficient.

[0092] Specifically, the first temporary Pauli term refers to the intermediate Pauli term (not the final normalized Pauli term) generated in the process of mapping the first target quantized Hamiltonian (second quantized Hamiltonian) to the second target quantized Hamiltonian through the Jordan-Wigner transformation. The first temporary Pauli term may include redundant identity matrices I, repeated operator combinations, or tensor products that do not conform to the simplest form. For example, during the transformation process, the following may be generated: Such items, where is the identity matrix, which can be simplified to ,at this time This is the first temporary Pauli term.

[0093] The linear relationship of the first temporary Pauli terms refers to the quantum mechanical commutation relationship or linear combination relationship satisfied by the first temporary Pauli terms, which is used to simplify the second target quantized Hamiltonian, eliminate redundant terms or merge similar terms. By simplifying the linear relationship, the second target quantized Hamiltonian can be converted into a simplified form ,in, is the non-redundant normalized Pauli term, is the combined coefficient. For example, if the second target quantized Hamiltonian contains X⊗Y+X⊗Y, it is combined into 2X⊗Y through a linear relationship, improving subsequent computational efficiency. This linear relationship of the first temporary Pauli term eliminates redundant terms, reduces the number of Pauli terms in the quantized Hamiltonian, and reduces grouping complexity.

[0094] The third target quantized Hamiltonian refers to the simplest form of Hamiltonian obtained by analyzing the linear relationship (such as commutation relationship, linear combination relationship) of the first temporary Pauli term in the second target quantized Hamiltonian, simplifying the second target quantized Hamiltonian and merging similar terms. Its expression is: The third objective, the quantized Hamiltonian, is the direct basis for determining the Pauli term set and normalized weight coefficients. It eliminates the redundant terms generated during the intermediate transformation process, ensures the uniqueness of the Pauli terms and the accuracy of the coefficients, and provides an accurate physical model and data foundation for subsequent group measurement optimization based on local compatibility.

[0095] Firstly, the second target quantized Hamiltonian is processed through the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine the third target quantized Hamiltonian.

[0096] Then, all independent Pauli terms are directly extracted from the third target quantized Hamiltonian , forming the Pauli term set { 、 、 、…、 Then, the coefficients of all Pauli terms in the third objective quantized Hamiltonian are Take the absolute value and sum it up to get S=∑| Finally, the normalized weight coefficient of each Pauli term is , reflecting the relative contribution of the Pauli term to the total energy.

[0097] Continuing with the above example, after processing the LiH molecule, some normalized weight coefficients are shown in Table 2: Table 2

[0098] In this way, the computer device processes the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine the third target quantized Hamiltonian. Next, the computer device performs Pauli term extraction on the third target quantized Hamiltonian, determining a set of Pauli terms and the corresponding weight coefficients for each Pauli term in the set. Finally, the computer device normalizes the weight coefficients to determine the normalized weight coefficients. In this way, through linear relationship simplification and Hamiltonian transformation, the Pauli terms are organized and weighted, providing a data foundation for subsequent measurement optimization.

[0099] See also Figure 7 In some embodiments, step 01221 (processing the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine the third target quantized Hamiltonian) includes: 012211: According to the commutation relation of the first temporary Pauli term, the second target quantized Hamiltonian is simplified to determine the fourth target quantized Hamiltonian; 012212: Merge the second temporary Pauli term in the fourth target quantized Hamiltonian to determine the third target quantized Hamiltonian.

[0100] In some embodiments, the determining module is further configured to simplify the second target quantized Hamiltonian based on the commutation relation of the first temporary Pauli term to determine a fourth target quantized Hamiltonian, and to combine the second temporary Pauli term in the fourth target quantized Hamiltonian to determine a third target quantized Hamiltonian.

[0101] In some embodiments, the processor is further configured to simplify the second target quantized Hamiltonian based on the commutation relation of the first temporary Pauli term to determine a fourth target quantized Hamiltonian, and to combine the second temporary Pauli term in the fourth target quantized Hamiltonian to determine a third target quantized Hamiltonian.

[0102] Specifically, the simplification process refers to performing algebraic operations on the Pauli terms in the second target quantized Hamiltonian based on the commutation relation of the first temporary Pauli terms to obtain a fourth target quantized Hamiltonian with a simpler structure. In this way, the Pauli terms in the second target quantized Hamiltonian that do not conform to the simplest form (such as those containing redundant unit matrices, repeated operator combinations, or reducible phases) are transformed into independent tensor product forms (such as 、 etc.) to facilitate subsequent grouping and measurement.

[0103] The fourth target quantized Hamiltonian refers to the intermediate Hamiltonian obtained after simplifying the second target quantized Hamiltonian, in which the first temporary Pauli term has been simplified to a more basic Pauli operator tensor product through the commutation relation, but there may still be multiple Pauli terms of the same form (only the coefficients are different).

[0104] The merging process refers to merging the coefficients of the Pauli terms with exactly the same form (i.e., the same operator tensor product on the same quantum bit) in the fourth target quantized Hamiltonian to obtain the final third target quantized Hamiltonian.

[0105] In this way, the computer simplifies the second target quantized Hamiltonian based on the commutation relation of the first provisional Pauli term to determine the fourth target quantized Hamiltonian. Next, the computer combines the second provisional Pauli terms in the fourth target quantized Hamiltonian to determine the third target quantized Hamiltonian. In this way, through commutation relation simplification and Pauli term merging, the Hamiltonian is structurally optimized and standardized, providing a data foundation for subsequent measurement optimization.

[0106] See also Figure 8In some embodiments, step 02 (grouping the Pauli term set by local compatibility according to the local compatibility rule and the normalized weight coefficient to determine the target group) includes: 021: Process the normalized weight coefficients in descending order to determine the target weight coefficient of the preset proportion and the target Pauli term corresponding to the target weight coefficient; 022: According to the local compatibility rule, the target Pauli items are grouped according to local compatibility to determine the target group.

[0107] In certain embodiments, the determination module is further configured to perform descending processing on the normalized weight coefficients to determine a target weight coefficient with a preset proportion and a target Pauli term corresponding to the target weight coefficient, and to perform local compatibility grouping on the target Pauli terms according to a local compatibility rule to determine a target group.

[0108] In certain embodiments, the processor is further configured to perform descending processing on the normalized weight coefficients to determine a target weight coefficient with a preset proportion and a target Pauli term corresponding to the target weight coefficient, and to perform local compatibility grouping on the target Pauli terms according to a local compatibility rule to determine a target group.

[0109] Specifically, descending processing involves sorting the normalized weight coefficients of the Pauli terms from largest to smallest to prioritize them. This descending order prioritizes the Pauli terms that contribute most to the total energy, providing a basis for subsequent prioritization of high-weight terms and optimizing the allocation of measurement resources (high-weight terms receive more measurements, reducing redundant measurements of low-weight terms).

[0110] The preset percentage refers to a preset percentage value that can be set manually and is used to select the portion of the Pauli terms with the largest energy contribution from the Pauli terms arranged in descending order as the target Pauli term. In some embodiments, the preset percentage can be "the top 10%."

[0111] The target Pauli term refers to the high-weight Pauli term with a preset percentage selected after descending order processing. This term is called the target Pauli term. It is the core subset of the Pauli term set and plays a dominant role in the energy calculation of the molecular Hamiltonian. The target Pauli term is the core object of the local compatibility grouping.

[0112] The local compatibility rule states that there must be at least one qubit such that the Pauli operators of the two Pauli terms on this qubit are the same, or the Pauli operator on the qubit of one Pauli term is the identity matrix I, and the Pauli operator on the qubit of the other Pauli term is an arbitrary Pauli operator. This rule can be used to determine whether two Pauli terms can be grouped into the same group. That is, if for the Pauli terms and , check its component on the i-th quantum bit ( ), if there is at least one qubit Make (e.g., both are X operators), or one of the components is the identity matrix I (e.g., and ), then the two are partially compatible. Among them, and are two Pauli terms; represents the Pauli term In the basis on qubits; is the identity matrix; is the total number of qubits.

[0113] See also Figure 9 , Figure 9 Schematic diagram of target grouping of LiH molecules. Figure 9 The graphical model of only some Pauli terms of LiH molecules, Figure 9 in 、 、 、 、 、 and , which is consistent with the above Table 1, Table 2, and Table 3 、 、 、 and are the Pauli terms of the LiH molecule. And, to improve readability, Figure 9 The identity matrix I map in the Pauli term is omitted. For example, the Pauli term Can be simplified to , since I is compatible with any operator, it does not affect the compatibility judgment. Figure 9 It can be found that the target group only includes Pauli terms, there is no quantum compatibility relationship between the Pauli terms, and it is also impossible to determine whether these Pauli terms can be measured in parallel.

[0114] In this way, the computer device processes the normalized weight coefficients in descending order to determine a target weight coefficient with a preset percentage and a target Pauli item corresponding to the target weight coefficient. The Pauli item set includes the target Pauli item. Next, the computer device performs local compatibility grouping on the target Pauli items based on local compatibility rules to determine a target group. This method, by screening the target Pauli items in descending order of weight and combining them with the local compatibility rules for grouping, achieves precise allocation of measurement resources and improves measurement efficiency.

[0115] See also Figure 10In certain embodiments, step 03 (optimizing quantum compatibility of molecular Hamiltonian measurements according to target grouping) includes: 031: Based on the preset quantum compatibility rules, determine the quantum compatibility relationship between the Pauli terms in the target group; 032: According to the quantum compatibility relationship and the obtained measurement requirements, the Pauli terms in the target group are grouped to determine the target measurement group; 033: Parallel measurement of target measurement groups to achieve quantum compatibility optimization of molecular Hamiltonian measurements.

[0116] In certain embodiments, the determination module is further configured to determine quantum compatibility relationships between Pauli terms in a target group based on a preset quantum compatibility rule. The module is further configured to group the Pauli terms in the target group based on the quantum compatibility relationships and the acquired measurement requirements to determine a target measurement group. Furthermore, the module is configured to perform parallel measurements on the target measurement group to achieve quantum compatibility optimization for molecular Hamiltonian measurements.

[0117] In certain embodiments, the processor is further configured to determine a quantum compatibility relationship between Pauli terms in a target group based on a preset quantum compatibility rule, group the Pauli terms in the target group based on the quantum compatibility relationship and the acquired measurement requirements to determine a target measurement group, and perform parallel measurements on the target measurement group to achieve quantum compatibility optimization of molecular Hamiltonian measurements.

[0118] Specifically, the default quantum compatibility rule is that the operators of two Pauli terms on any quantum bit do not conflict, that is, if for all and If not established, and Compatible, among them, and are two Pauli terms; represents the Pauli term In the basis on qubits; is the identity matrix; is the total number of qubits. Or, is any operator, is 1, and Not true (m is 1-n except the qubits), then and Compatible. The preset quantum compatibility rules can determine whether the Pauli terms in the target group can be measured in parallel in the same measurement group. See Table 3 below: Table 3

[0119] Quantum compatibility refers to the logical relationship between the Pauli terms in the target group, which determines whether they satisfy the pre-set quantum compatibility rules. If two Pauli terms have a quantum compatibility relationship, it means that they can be measured in parallel.

[0120] Measurement requirements guide the dynamic adjustment of grouping strategies, adapting grouping results to the optimization goals of different scenarios (such as focusing on efficiency or accuracy), and improving the versatility and practicality of the method. Different measurement requirements require different grouping methods.

[0121] The target measurement group refers to a set of Pauli terms that can be measured in parallel, divided from the target group according to the quantum compatibility relationship and measurement requirements. The Pauli terms in each target measurement group meet the preset compatibility rules and data can be obtained simultaneously in the same round of measurement.

[0122] In this way, the computer device determines the quantum compatibility relationship between the Pauli terms in the target group based on the preset quantum compatibility rules. Next, the computer device groups the target groups according to the quantum compatibility relationship and the acquired measurement requirements, determining target measurement groups. Finally, the computer device performs parallel measurements on the target measurement groups to optimize the quantum compatibility of the molecular Hamiltonian measurement. In this way, by determining local compatibility based on quantum compatibility rules and grouping based on measurement requirements, measurement efficiency is improved.

[0123] See also Figure 11 In some embodiments, step 032 (grouping the Pauli terms in the target group according to the quantum compatibility relationship and the obtained measurement requirements to determine the target measurement group) includes: 0321: Based on the quantum compatibility relationship and target grouping, a compatibility graph model corresponding to the target grouping is constructed; 0322: Group the Pauli items in the target group according to the measurement requirements and the compatibility graph model to determine the target measurement group.

[0124] In certain embodiments, the confirmation module is further configured to construct a compatibility graph model corresponding to the target group based on the quantum compatibility relationship and the target group, and to group the Pauli terms in the target group based on the measurement requirements and the compatibility graph model to determine the target measurement group.

[0125] In certain embodiments, the processor is further configured to construct a compatibility graph model corresponding to the target group based on the quantum compatibility relationship and the target group, and to group the Pauli terms in the target group based on the measurement requirements and the compatibility graph model to determine a target measurement group.

[0126] Specifically, the compatibility graph model is represented as an undirected graph (G = (V, E)), where each node V represents a Pauli term (e.g. 、 If two Pauli terms have a quantum compatibility relationship, then an edge E is connected between the corresponding two nodes, indicating that the two Pauli terms can be measured in parallel.

[0127] Continuing with the above example, see Figure 12 , Figure 12 This is a schematic diagram of the compatibility graph model of LiH. Figure 12 and Figure 9 It can be found that the quantum compatibility relationship between the Pauli terms has been indicated by the connecting lines.

[0128] See also Figure 13 、 Figure 14 、 Figure 15 and Figure 16 , Figure 13 、 Figure 14 、 Figure 15 and Figure 16 The following are schematic diagrams of different groups of LiH molecules, and the Pauli terms are divided into different groups by rectangular boxes. In this way, according to different measurement requirements, Figure 12 The quantized Hamiltonian shown is subjected to local compatibility grouping processing to obtain different target groups.

[0129] In this way, the computer device determines the compatibility graph model corresponding to the target group based on the quantum compatibility relationship and the target group. Then, based on the measurement requirements and the compatibility graph model, the target group is grouped to determine the target measurement group. By constructing the compatibility graph model and grouping based on the measurement requirements, the Pauli term compatibility relationship can be visualized and the grouping strategy can be customized.

[0130] The present application also provides a computer-readable storage medium containing a computer program. When the computer program is executed by one or more processors, the one or more processors execute the method of the present application.

[0131] It is understood that a computer program includes computer program code. The computer program code may be in source code form, object code form, executable file, or some intermediate form. Computer-readable storage media may include any entity or device capable of carrying computer program code, recording media, USB flash drives, removable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), and software distribution media.

[0132] In the description of this specification, the descriptions with reference to the terms "particularly", "further", "particularly", "understandably", etc. are intended to mean that the specific features, structures, materials or characteristics described in conjunction with the embodiments or examples are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms are not intended to refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0133] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0134] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A quantum compatibility optimization method for molecular Hamiltonian measurement, characterized in that: The method comprises: Determining a Pauli term set and a normalized weight coefficient corresponding to each Pauli term in the Pauli term set according to a target molecule to be simulated; performing local compatibility grouping on the Pauli term set according to a local compatibility rule and the normalized weight coefficient to determine a target group, wherein the local compatibility rule is used to determine whether two Pauli terms in the Pauli term set can be classified into the same group; According to the target grouping, quantum compatibility optimization of the molecular Hamiltonian measurement is achieved.

2. The method according to claim 1, characterized in that The step of determining a Pauli term set and a normalized weight coefficient corresponding to each Pauli term in the Pauli term set according to a target molecule to be simulated includes: Determining, according to the target molecule, a first target quantized Hamiltonian corresponding to the target molecule, wherein the first target quantized Hamiltonian is a second quantized Hamiltonian of the target molecule; The Pauli term set and the normalized weight coefficient are determined according to the first target quantized Hamiltonian.

3. The method according to claim 2, characterized in that The determining, based on the target molecule, a first target quantized Hamiltonian corresponding to the target molecule includes: Determining the geometric structure and basis set of the target molecule based on the acquired input parameters, wherein the input parameters include elemental composition, atomic coordinates, and basis set type of the target molecule; According to the target molecule, the geometric structure, and the basis set, a one-electron integral and a two-electron integral of the target molecule are calculated, wherein the one-electron integral is used to describe the energy integral of the motion of a single electron in the target molecule in the nuclear potential field, and the two-electron integral is used to describe the energy integral of the Coulomb repulsion energy between two electrons in the target molecule; The first target quantized Hamiltonian is constructed according to the one-electron integral and the two-electron integral.

4. The method according to claim 2, characterized in that The determining, according to the first target quantized Hamiltonian, the Pauli term set and the normalized weight coefficient includes: Performing a transformation on the fermion operator in the first target quantized Hamiltonian to obtain a second target quantized Hamiltonian; The Pauli term set and the normalized weight coefficient are determined according to the second target quantized Hamiltonian.

5. The method according to claim 4, characterized in that The fermion operator includes a generation operator and an annihilation operator, and the transforming process of the fermion operator in the first target quantized Hamiltonian to obtain the second target quantized Hamiltonian includes: Based on a first preset transformation rule, transforming the generation operator into a Pauli term form to generate a first tensor product; Based on a second preset transformation rule, transforming the annihilation operator into a Pauli term form to generate a second tensor product; The second target quantized Hamiltonian is determined according to the first tensor product and the second tensor product.

6. The method according to claim 4, characterized in that The determining, according to the second target quantized Hamiltonian, the Pauli term set and the normalized weight coefficient includes: processing the second target quantized Hamiltonian based on a linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine a third target quantized Hamiltonian; performing a Pauli term extraction process on the third target quantized Hamiltonian to determine the Pauli term set and a weight coefficient corresponding to each Pauli term in the Pauli term set; The weight coefficient is normalized to determine the normalized weight coefficient.

7. The method according to claim 6, characterized in that The processing of the second target quantized Hamiltonian based on the linear relationship of the first temporary Pauli term in the second target quantized Hamiltonian to determine the third target quantized Hamiltonian includes: Simplifying the second target quantized Hamiltonian according to the commutation relation of the first temporary Pauli term to determine a fourth target quantized Hamiltonian; The second temporary Pauli terms in the fourth target quantized Hamiltonian are merged to determine the third target quantized Hamiltonian.

8. The method according to claim 1, characterized in that The performing local compatibility grouping on the Pauli term set according to the local compatibility rule and the normalized weight coefficient to determine the target group includes: Performing descending processing on the normalized weight coefficients to determine a target weight coefficient of a preset proportion and a target Pauli term corresponding to the target weight coefficient, wherein the Pauli term set includes the target Pauli term; According to the local compatibility rule, the target Pauli items are grouped according to local compatibility to determine the target group.

9. The method according to claim 1, characterized in that The step of achieving quantum compatibility optimization of the molecular Hamiltonian measurement according to the target grouping includes: Determining a quantum compatibility relationship between Pauli terms in the target group based on a preset quantum compatibility rule; Grouping the Pauli terms of the target group according to the quantum compatibility relationship and the obtained measurement requirements to determine a target measurement group; The target measurement group is measured in parallel to achieve quantum compatibility optimization of the molecular Hamiltonian measurement.

10. The method according to claim 9, characterized in that The step of grouping the Pauli terms of the target group according to the quantum compatibility relationship and the acquired measurement requirements to determine the target measurement group includes: Constructing a compatibility graph model corresponding to the target group according to the quantum compatibility relationship and the target group; The Pauli items in the target group are grouped according to the measurement requirement and the compatibility graph model to determine the target measurement group.

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