Method and equipment for determining reaction activity of material molecules based on quantum calculation

Abstract

The invention discloses a method and equipment for determining the reaction activity of material molecules based on quantum computing, and relates to the technical field of material performance analysis based on quantum computation.The method comprises the steps that the geometric structure of molecules of a target material and initial asymmetry configuration are obtained, and the initial asymmetry configuration comprises a plurality of excitation operators; determining an Arbel point group corresponding to the molecules of the target material based on the geometric structure of the molecules of the target material; determining an irreducible representation of each spin orbit of the molecules of the target material, and determining an irreducible representation direct product table of the Arbel point groups; obtaining the final symmetry simulation of the molecules of the target material according with the point group symmetry; constructing a quantum circuit based on the final symmetric configuration; based on the quantum circuit, the reactivity of the molecules of the target material is determined. According to the method, the reliability and the efficiency of constructing the symmetric configuration are improved, so that a feasible and excellent technical basis is provided for efficiently and accurately determining the reaction activity of molecules of a target material.

Description

Technical Field

[0001] This invention relates to the field of quantum computing-based material property analysis technology, and in particular to a method and apparatus for determining the reactivity of material molecules based on quantum computing. Background Technology

[0002] The precise determination of molecular energy levels is a core technological foundation supporting breakthroughs in key fields such as drug design, materials development, and energy conservation. In drug development, it helps elucidate the binding mechanism between drug molecules and target proteins, thereby enabling the optimized design of drug-active molecular structures. In materials development, energy level analysis technology allows for precise control of the optical response and electrical properties of materials. Furthermore, in energy conservation, it serves as a crucial theoretical basis for developing efficient catalysts and optimizing energy conversion pathways. However, traditional classical computational algorithms encounter significant computational limitations when dealing with molecular energy level determination. Because molecular systems are essentially quantum systems, the computational complexity of classical algorithms for simulating their energy levels increases exponentially with the number of atoms in the molecule. When the molecular scale expands to medium or higher levels, even classical computers utilizing massive computing resources struggle to complete the task within a reasonable timeframe. This severely restricts the progress and efficiency improvement of related research fields.

[0003] The rise of quantum computing technology has provided a novel solution to this dilemma, with the Variational Quantum Eigensolver (VQE) showing particularly impressive performance. As a quantum computing algorithm specifically designed for solving molecular energy levels, VQE's computational resource requirements only exhibit a polynomial growth characteristic with molecular scale, achieving exponential computational speedup compared to traditional classical methods. This advantage makes VQE a promising solution for the energy level problem of large and complex molecules. In VQE algorithms, the Unitary Coupled Cluster with Single and Double excitations (UCCSD) hypothesis is a widely used quantum state hypothesis. It constructs quantum states that can well describe the electronic structure of molecules by exponentially combining single-electron and double-electron excitation operators. However, as the scale of the molecular system increases, the number of excitation operators increases dramatically. This phenomenon significantly increases the depth of the quantum circuit, thus affecting its practical application on current medium-scale noisy quantum computing hardware.

[0004] To reduce the quantum circuit depth, a symmetric unitary coupled cluster single-double excitation scheme (SymUCCSD) has been proposed. The core innovation of this method lies in fully utilizing the spatial symmetries of molecules (such as point group symmetries like C2v and D2h) and, based on the orthogonality principle of irreducible representations in group theory, retaining only excitation terms that belong to the same irreducible representation as the reference state (usually a Hartley-Fock state). In practice, the point group affiliation of the target molecule must first be determined, and an irreducible representation assigned to each spin orbital. Then, the irreducible representation corresponding to each excitation determinant is determined using the product table of irreducible representations of the molecular point group. All excitation operators in the UCCSD scheme are iterated and screened. If the excitation determinant obtained after the action of a certain excitation operator has an irreducible representation consistent with the irreducible representation of the reference state, it is retained; otherwise, it is discarded. This scheme significantly reduces the number of excitation operators and lowers the quantum circuit depth while maintaining the original computational accuracy. However, the strategy of constructing SymUCCSD described above requires calculating the irreducible representation of the corresponding excitation determinant when determining whether the excitation operator conforms to the molecular point group symmetry. This requires considering all the electrons contained in the molecule, which is computationally expensive and prone to errors for large molecules.

[0005] Therefore, in order to overcome the shortcomings of existing symmetry fitting construction methods, such as large computational load and easy error, reduce the design cost of the fitting circuit used in the variable quantum eigenvalue solution algorithm, and promote its application in applications such as determining the molecular reactivity of materials, there is an urgent need for a new point group symmetry fitting construction method that is more convenient, reliable and easy to automate. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the shortcomings of existing technologies, specifically by providing a method and apparatus for determining the reactivity of material molecules based on quantum computing, as detailed below: 1) In a first aspect, the present invention provides a method for determining the reactivity of material molecules based on quantum computing, the specific technical solution of which is as follows: The molecular geometry of the target material and the initial asymmetry simulation are obtained. The initial asymmetry simulation includes multiple excitation operators. Based on the molecular geometry of the target material, the Abelian point group corresponding to the molecules of the target material is determined; Determine the irreducible representation of each spin orbital of the target material molecule, and determine the direct product table of irreducible representations of the Abelian point group; Initialize an empty symmetry fitting, and based on the irreducible representation and the product table of irreducible representations of each spin orbital, traverse each excitation operator in the initial asymmetry fitting, calculate the first product of the irreducible representations of the spin orbitals acted by all the generation operators in the currently traversed excitation operator, and calculate the second product of the irreducible representations of the spin orbitals acted by all the annihilation operators in the currently traversed excitation operator. If the first product equals the second product, add the currently traversed excitation operator to the initialized symmetry fitting; otherwise, do not add it. After completing the traversal of all excitation operators in the initial asymmetry fitting, the final symmetry fitting of the molecular coincidence point group symmetry of the target material is obtained. Based on the final symmetry assumption, a quantum circuit is constructed. Based on quantum circuits, the reactivity of molecules in the target material is determined.

[0007] The beneficial effects of the method for determining the reactivity of material molecules based on quantum computing provided by this invention are as follows: Symmetry is determined by directly comparing the irreducible direct product of the spin orbitals acted upon by the generating and annihilating operators in the excitation operator, avoiding the complex process of calculating the irreducible representation of the excitation determinant involving all molecular electrons in existing techniques. This method only needs to handle a small number of spin orbitals directly associated with the excitation operator; for single-excitation and double-excitation operators, only 2 and 4 orbitals need to be considered, respectively, significantly reducing the computational load, making it particularly suitable for large molecular systems. This criterion is based on the representation theory of Abelian point groups, with rigorous logic and clear steps, making it easy to automate through programming, reducing the possibility of human error, and improving the reliability and efficiency of constructing the symmetry simulation. Finally, the final symmetry simulation obtained based on this method can effectively reduce the number of parameters and the depth of the quantum circuit, maintaining the computational accuracy of the variational quantum eigenvalue solving algorithm while making it more adaptable to the hardware limitations of current noisy quantum computing devices, thus providing a feasible and superior technical foundation for efficiently and accurately determining the molecular reactivity of target materials.

[0008] Based on the above scheme, the method for determining the reactivity of material molecules based on quantum computing of the present invention can be further improved as follows.

[0009] Furthermore, it also includes: when the point group corresponding to the molecules of the target material is a non-Abelian point group, the Abelian subgroup with the highest order of the non-Abelian point group is selected as the Abelian point group.

[0010] The beneficial effect of adopting the above-mentioned further scheme is that by explicitly stipulating that when the molecular point group is not an Abelian point group, its highest-order Abelian subgroup is used as the basis for calculation, the universal applicability of this method to all molecular point groups is ensured. This approach utilizes the commutative and one-dimensional representation of symmetry operations on Abelian subgroups, making the subsequent rules for irreducible direct product operations simple and clear, and providing a unified mathematical foundation and reliable premise for the entire symmetry simulation and construction process.

[0011] Furthermore, based on quantum circuits, the reactivity of the target material molecules is determined, including: determining the energy level distribution of the target material molecules based on quantum circuits; and determining the reactivity of the target material molecules based on the energy level distribution of the target material molecules.

[0012] The advantages of adopting the above-mentioned further approach are: it clearly divides the process of determining reactivity into two logical steps: first, solving for the molecular energy level distribution, and then analyzing the reactivity based on the energy level information. This division makes the method structure clear; the first step focuses on obtaining accurate electronic structure data using quantum computing, and the second step focuses on predicting properties using physicochemical principles. This enhances the systematicity and interpretability of the method and facilitates flexible expansion for different reactivity indices.

[0013] Furthermore, it also includes: when the target material is a fluorescent material, determining the luminescence characteristics of the target material based on the energy level distribution of the target material's molecules, and determining whether the target material is to be used for fluorescent labeling based on the luminescence characteristics of the target material; when the target material is a photocatalyst, determining the photocatalytic activity of the target material based on the energy level distribution of the target material's molecules, and determining whether the target material is to be used for visible light-driven chemical reactions based on the photocatalytic activity of the target material.

[0014] The beneficial effects of adopting the above-mentioned further approach are: it provides specific pathways for determining the reactivity of two important material classes, fluorescent materials and photocatalysts. This enables the method to not only provide general energy level data, but also directly output qualitative or quantitative judgments closely related to material applications, such as whether the luminescence characteristics match the labeling requirements, or whether the photocatalytic activity meets the reaction driving force conditions, thereby enhancing the practical value and guiding significance of the method in the targeted design and screening of materials.

[0015] 2) In a second aspect, the present invention also provides a system for determining the reactivity of material molecules based on quantum computing, the specific technical solution of which is as follows: It includes a structure operator acquisition module, a first determination module, a second determination module, a final symmetry simulation acquisition module, a quantum circuit construction module, and a reaction activity determination module; The structure operator acquisition module is used to: acquire the molecular geometry of the target material and the initial asymmetry simulation, which includes multiple excitation operators; The first determining module is used to: determine the Abelian point group corresponding to the molecules of the target material based on the geometric structure of the molecules of the target material; The second determining module is used to: determine the irreducible representation of each spin orbital of the target material's molecules, and determine the direct product table of irreducible representations of the Abelian point group; The final symmetry fitting module is used to: initialize an empty symmetry fitting, and based on the irreducible representation and irreducible representation direct product table of each spin orbital, traverse each excitation operator in the initial asymmetry fitting, calculate the first direct product of the irreducible representations of the spin orbitals acted by all the generation operators in the currently traversed excitation operator, and calculate the second direct product of the irreducible representations of the spin orbitals acted by all the annihilation operators in the currently traversed excitation operator. If the first direct product is equal to the second direct product, the currently traversed excitation operator is added to the initialized symmetry fitting; otherwise, it is not added. After completing the traversal of all excitation operators in the initial asymmetry fitting, the final symmetry fitting of the target material's molecular coincidence point group symmetry is obtained. The quantum circuit construction module is used to construct quantum circuits based on the final symmetry assumption. The reactivity determination module is used to determine the reactivity of molecules in a target material based on quantum circuits.

[0016] Based on the above scheme, the system for determining the reactivity of material molecules based on quantum computing of the present invention can be further improved as follows.

[0017] Furthermore, the first determining module is also used to: when the point group corresponding to the molecules of the determined target material is a non-Abelian point group, select the Abelian subgroup with the highest order of the non-Abelian point group as the Abelian point group.

[0018] Furthermore, the reaction activity determination module is specifically used for: Based on quantum circuits, the energy level distribution of molecules in the target material is determined; The reactivity of the target material molecules is determined based on the energy level distribution of the target material molecules.

[0019] Furthermore, it also includes a materials application module, which is used for: When the target material is a fluorescent material, the luminescence properties of the target material are determined based on the energy level distribution of the molecules of the target material, and the target material is then used for fluorescent labeling based on the luminescence properties. When the target material is a photocatalyst, the photocatalytic activity of the target material is determined based on the energy level distribution of its molecules; and based on the photocatalytic activity of the target material, it is determined whether the target material can be used for visible light-driven chemical reactions.

[0020] 3) In a third aspect, the present invention also provides an electronic device, the electronic device including a processor coupled to a memory, the memory storing at least one computer program, the at least one computer program being loaded and executed by the processor, so as to enable the electronic device to realize any of the above-mentioned methods for determining the reactivity of material molecules based on quantum computing.

[0021] 4) In a fourth aspect, the present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements any of the above-mentioned methods for determining the reactivity of material molecules based on quantum computing.

[0022] It should be noted that the beneficial effects of the technical solutions of the second to fourth aspects of the present invention and their corresponding possible implementations can be found in the above description of the technical effects of the first aspect and its corresponding possible implementations, and will not be repeated here. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below: Figure 1 This is a flowchart illustrating a method for determining the reactivity of material molecules based on quantum computing, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of a system for determining the reactivity of material molecules based on quantum computing, according to an embodiment of the present invention. Detailed Implementation

[0024] The principles and features of the present invention are described below. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0025] The technical solution of the present invention and how the technical solution of the present invention solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0026] like Figure 1 As shown in the figure, a method for determining the reactivity of material molecules based on quantum computing according to an embodiment of the present invention includes the following steps: S1. Obtain the molecular geometry of the target material and the initial asymmetry simulation. The initial asymmetry simulation includes multiple excitation operators, and the specific implementation process is as follows: S10. The molecular geometry of the target material refers to the specific arrangement of all atoms constituting the molecule in three-dimensional space, including structural parameters such as bond lengths, bond angles, and dihedral angles. This information is the fundamental physical input for all subsequent quantum chemical calculations. In practical implementation, it can be obtained through various means. For known stable molecules, their coordinate files can be directly queried and exported from standard computational chemistry databases or crystal structure databases. For newly designed molecules or those without precise experimental structures, computational chemistry software is needed for structural optimization. Specifically, quantum chemistry computational software packages such as Gaussian, ORCA, or PySCF are used to perform energy minimization calculations on the molecular configuration based on density functional theory or other electronic structure methods. After the calculation converges, the output file will contain the element type of each atom and its precise coordinates in the Cartesian coordinate system; for example, the coordinates of atom A are... The coordinates of atom B are This allows for the complete definition of the molecular geometry of the target material.

[0027] S11. After obtaining the precise geometric structure, further calculations of its electronic structure are needed to prepare for constructing the initial asymmetric hypothesis. This process is typically accomplished by performing Hartree-Fock self-consistent field calculations. The atomic coordinates, atom types, and selected basis sets obtained in the previous step are submitted to the quantum chemistry calculation program as input. The program solves the Hartree-Fock equations, outputting a series of molecular orbitals and their corresponding energy eigenvalues. These molecular orbitals are ordered from low to high energy, with lower-energy orbitals occupied by electrons and called occupied orbitals; higher-energy orbitals are not occupied by electrons and are called virtual orbitals. Each molecular orbital can be further distinguished into α-spin orbitals and β-spin orbitals, together forming a complete set of spin orbitals. The output of this step is the wavefunction information and energy of all spin orbitals, which are the direct basis for defining the excitation operator.

[0028] S12, the initial asymmetric hypothesis, is a set of excitation operators that describe various possible modes of electron transition from occupied orbits to virtual orbits. These operators are used to construct trial wave functions in variational quantum eigenfunction algorithms. The excitation operators are combinations of operators in a second-order quantized form, and their general form consists of a production operator and an annihilation operator. The production operator... Indicates in spin orbit An electron is produced on the annihilation operator. Indicates from spin orbit An electron is annihilated. A typical initial asymmetric simulation usually chooses a unitary coupled cluster single- and two-electron excitation simulation, which systematically includes all possible single-electron and two-electron excitations. The specific construction method is based on the occupied spin orbital list and the virtual spin orbital list obtained from S11. For a single excitation, all occupied spin orbitals are traversed. and all virtual spin orbits Generate a form like The excitation operator, where These are the variational parameters to be optimized. For dual excitation, iterate through all pairwise distinct occupied spin orbitals. And all the different virtual spin orbits Generate a form like The excitation operators are then used. Combining all the generated single and double excitation operators constitutes the initial asymmetric hypothesis. This hypothesis does not yet consider the point group symmetry constraints of the molecule itself, and therefore includes all possible excitation modes in all forms.

[0029] The molecular geometry of a target material is a physical quantity describing the spatial relative positions of all atomic nuclei within that molecule. It includes information about the distances, angles, and orientations between atoms, which determine the molecule's shape, size, and potential chemical properties. Geometric structure is an absolute prerequisite for any first-principles electronic structure calculations because the system's Hamiltonian depends on the coordinates of the atomic nuclei. Obtaining an accurate geometric structure is crucial for the accuracy of the final calculations of molecular energy levels and reactivity.

[0030] In this context, the excitation operator is a mathematical object used within the framework of second-order quantization to describe changes in electronic configuration. It consists of the multiplication of a production operator and an annihilation operator in a specific order, acting on a quantum state and capable of transferring an electron from one set of specified spin orbitals to another. For example, a single excitation operator... This means moving an electron from its spin orbital Excited to spin orbit ; Bi-excitation operator This means simultaneously releasing two electrons from their spin orbitals. and Excited to spin orbit and In the initial asymmetric hypothesis, excitation operators are the cornerstone of constructing parameterized quantum circuits, with each operator corresponding to a sub-circuit module and an optimizable parameter.

[0031] S2. Based on the molecular geometry of the target material, determine the Abelian point group corresponding to the molecules of the target material. It should be noted that when the determined point group corresponding to the molecules of the target material is a non-Abelian point group, the Abelian subgroup with the highest order of the non-Abelian point group is selected as the Abelian point group. The specific implementation process is as follows: S20. Input the molecular geometry of the target material. The input is the molecular geometry information obtained in the previous step, typically presented as a file containing the coordinates of all atoms. The file format can be the common XYZ format, Gaussian input format, or a PySCF-recognizable internal data structure. This file precisely records the element symbol of each atom in the molecule and its position coordinates in a three-dimensional Cartesian coordinate system. subscript This involves traversing all atoms in the molecule. This precise spatial coordinate data is the sole physical basis for subsequent symmetry analysis.

[0032] S21. After obtaining molecular geometric structure data, specialized computational chemistry software packages are needed to automatically identify the point group to which the molecule belongs. This operation can be accomplished by writing scripts to call the symmetry analysis modules embedded in packages such as PySCF or OpenMolcas. Taking PySCF as an example, the atomic coordinates and element types of the molecule are used as input, and its relevant symmetry detection functions such as symm.D2h or symm.Oh are called. This function module compares the input geometry with a series of predefined point group symmetry operations (such as identity operations, rotation operations, reflection operations, inversion operations, etc.), and determines the precise point group to which the molecule belongs by calculating whether the molecular skeleton coincides with the original configuration under various symmetry operations. The program will output a standard point group symbol, for example... , or This step achieves the classification from geometric coordinates to abstract symmetry groups.

[0033] S22. The point group output in the previous step may be an abelian point group or a non-abelian point group. Therefore, logical judgment code needs to be written. If the point group symbol output by the program belongs to a known list of abelian point groups (such as...), the logic will be applied. If the output point group is a non-Abelian point group (e.g., ...), then that point group is directly determined as the final Abelian point group to be used. , , If the subgroup is an abelian point group (e.g., ...), then additional processing is required. The processing involves selecting subgroups that are themselves abelian point groups from all subgroups of the non-abelian point group. Next, the "orders" of these abelian subgroups are compared. The order of a point group refers to the total number of independent symmetry operations contained in the group. The abelian subgroup with the largest order is calculated and selected as the "highest-order abelian subgroup of the non-abelian point group," and will be used as the abelian point group in all subsequent steps. For example, for... The highest-order Abelian subgroup of a point group is usually Point group. The entire judgment and mapping relationship can be implemented in the code through a pre-established lookup table.

[0034] S23. After the judgment and selection in step S22, the system obtains a uniquely determined Abelian point group symbol. This point group symbol, along with its complete set of symmetry operations, will be output and stored, providing the necessary symmetry framework for determining the irreducible representation of each orbital in the next step. The entire process is now complete, successfully transforming the geometric characteristics of the molecule into a commutative symmetry group description for simplifying the construction of quantum hypotheses.

[0035] Abelian point groups, also known as commutative point groups, are a special class of molecular symmetry groups. In these point groups, the final effect of any two consecutive symmetry operations is independent of the order in which they are performed; that is, the commutative law of multiplication applies between symmetry operations. All irreducible representations of an abelian point group are one-dimensional, and their characteristic labels (i.e., the traces of the matrix) are all real numbers of +1 or -1. This property makes calculating the direct product of irreducible orbital representations extremely simple in abelian point groups, and the result can be obtained directly through multiplication. This is the mathematical basis for the method in this patent to conveniently determine the symmetry of the excitation operator.

[0036] The highest-order abelian subgroup of a non-Abelian point group is a concept derived from it. A "subgroup" of a point group is a set of symmetry operations from the original group that also satisfies the four fundamental axioms of a group. A non-Abelian point group has multiple subgroups of varying sizes. Those subgroups whose structure is an abelian point group are called abelian subgroups of that non-Abelian point group. The "highest-order" abelian subgroup is the one containing the most symmetry operations among all these abelian subgroups. Choosing the highest-order abelian subgroup aims to satisfy the commutativity requirement of symmetry operations in subsequent algorithms while preserving as much of the original molecular symmetry as possible, thus achieving a balance between computational simplicity and symmetry utilization efficiency.

[0037] S3. Determine the irreducible representation of each spin orbital of the target material molecule, and determine the direct product table of the irreducible representations of the Abelian point group. The specific implementation process is as follows: S30. Obtain the molecular orbital wavefunctions and distinguish spin orbitals. The input for this step is a series of molecular orbitals and their wavefunctions obtained previously using Hartree-Fock calculations. Each molecular orbital... It is a spatial function that describes the electron in spatial coordinates. The probability amplitude at a given location. To fully describe the electronic state, the spin degree of freedom needs to be introduced. Therefore, for each spatial molecular orbital... Construct two spin orbitals: one corresponding to the α spin, denoted as α. or Its spin part is The other corresponds to the β spin, denoted as... or Its spin part is .here It is a spin variable. Thus, a variable containing... A system of space orbits will have Each spin orbital forms an ordered list. This prepares for the subsequent assignment of symmetrical labels one by one.

[0038] S31, based on the previously determined Abel point group (e.g. This group contains a finite set of symmetry operations. ,in It is the order of the point group. For a given spatial molecular orbital wavefunction... and a symmetric operation (For example, rotating 180 degrees around the z-axis), calculate the new function after this operation. In terms of computational implementation, the transformation properties of each molecular orbital under each symmetry operation can be directly obtained through the application programming interface of quantum chemistry software packages (such as PySCF). For spin orbitals, since the symmetry operations of the Abelian point group generally do not act on the spin part, the transformation properties of each spin orbital under each symmetry operation can be obtained directly. The transformation properties are entirely determined by its corresponding spatial orbit. Decide.

[0039] S32. For the Abelian point group, all its irreducible representations are one-dimensional. This means that any molecular orbital under a certain symmetry operation... Below, the transformed track With the original orbit They can only differ by one complex factor. That is, satisfying the relation .factor This is the characteristic index of the orbit under this symmetry operation. Since the characteristic index of the Abelian point group can only be +1 or -1, representing whether the orbit is symmetric or antisymmetric under this operation, the software can automatically determine and output this factor through the transformation calculation of S31. For example, for For a point group's orbit, the program may output a list of features. This corresponds to the transformation result of each operation in the group.

[0040] S33. Each irreducible representation of an Abelian point group has a unique set of characteristic labels. The resulting representation, specific to a given spatial orbit... Feature sequence This is compared with the characteristic label table of all known irreducible representations of the point group. The characteristic label table is a predefined mathematical table that lists every irreducible representation of the point group (e.g., ...). (etc.) Feature labels (+1 or -1) under all symmetry operations. Through exact matching, find the row that perfectly matches the orbital feature label sequence, and the irreducible representation label corresponding to that row (e.g., This space orbit was then assigned. Because spin orbits inherit the symmetry of their corresponding space orbits, they are similar to... Two related spin orbitals and They are also given the same irreducible representation.

[0041] S34. The direct product table of irreducible representations describes the result of performing a "direct product" operation on any two irreducible representations. For an abelian point group, the direct product operation is equivalent to multiplying the feature labels of the two irreducible representations under each symmetric operation, resulting in a new sequence of feature labels. This new sequence necessarily corresponds to another irreducible representation of the point group. Technically, no manual calculation is required. It can be generated automatically by calling group theory software libraries (such as `symm.irrep_name` and product-related functions in PySCF) or based on the mathematical rules of the point group feature label table. For example, for... A point group, a portion of its irreducible direct product table, is shown below: In this table, This represents a direct product operation. The intersection of a row and a column gives the result of the direct product of two corresponding irreducible representations. For example, , This complete table will be stored for use in subsequent steps to quickly compute the direct product of the irreducible representations of multiple orbitals.

[0042] In this context, the spin orbital is a mathematical object used to describe the complete quantum state of a single electron in a molecule. It consists of a spatial wavefunction and a spin wavefunction. The spatial wavefunction describes the probability distribution of the electron in three-dimensional space and is usually calculated from molecular orbitals; the spin wavefunction describes the projection of the electron's intrinsic angular momentum, taking values ​​of either α-spin or β-spin. Therefore, the spin orbital simultaneously encodes both the spatial position and spin orientation information of the electron. Within the framework of second-order quantization, each spin orbital corresponds to a generation operator and an annihilation operator, serving as the fundamental unit for constructing excitation operators and describing electron occupancy.

[0043] S4. Initialize an empty symmetry fitting, and based on the irreducible representation and the direct product table of irreducible representations of each spin orbital, traverse each excitation operator in the initial asymmetry fitting. Calculate the first direct product of the irreducible representations of the spin orbitals acted by all production operators in the currently traversed excitation operator, and calculate the second direct product of the irreducible representations of the spin orbitals acted by all annihilation operators in the currently traversed excitation operator. If the first direct product equals the second direct product, add the currently traversed excitation operator to the initialized symmetry fitting; otherwise, do not add it. After completing the traversal of all excitation operators in the initial asymmetry fitting, the final symmetry fitting of the target material's molecular compliance with the point group symmetry is obtained. The specific implementation process is as follows: S40. Create an empty data structure to store the excitation operators that satisfy the point group symmetry selected in subsequent steps. This data structure is usually an empty list, which can be represented as symmetric_ansatz=[] in Python code. This list does not contain any elements initially and will be gradually filled in during subsequent traversal and judgment.

[0044] S41. Read the input data and prepare for the traversal loop. The input data includes three parts: first, the list or dictionary obtained in the previous steps that records all spin orbitals and their corresponding irreducible representations, for example, irrep_dict={0: ,1: ,2: ,3: The initial asymmetric hypothesis list consists of three parts: 1) a list of spin-orbit indices and 2) a list of irreducible representation labels; 3) a list of irreducible representation direct products of the abelian point group, typically stored as a two-dimensional dictionary or matrix, used for quickly querying the result of the direct product of any two irreducible representations; and 4) an initial asymmetric hypothesis, which is a list containing multiple excitation operator objects, e.g., initial_ansatz=[op1,op2,op3,…]. The program will use a loop to process each excitation operator in the initial asymmetric hypothesis list sequentially.

[0045] S42. For the excitation operator currently being processed in the loop, the program needs to parse its mathematical form to identify all the production and annihilation operators it contains, and extract the spin orbital indices of these operators. For an excitation operator, its general form can be written as... ,in, These are variational parameters. It generates operators. It is an annihilation operator, subscript and It is a spin orbital index. The program logic needs to be able to extract the set that generates the operator index from the representation of this operator. The set of annihilation operator indices .

[0046] S43. Based on the set of spin orbital indices extracted in S42 for the actions of the generating operators, retrieve the irreducible representation label corresponding to each index from the dictionary storing irreducible representations of spin orbitals. Then, using the direct product table of irreducible representations of the abelian point group, perform direct product operations on these irreducible representations sequentially. The order of the direct product operations does not affect the final result because the direct product of the abelian point group satisfies the commutative law. The calculation process is as follows: take the irreducible representation of the orbital corresponding to the first generating operator. The irreducible representation of the orbit corresponding to the second generating operator. Looking up a table and performing a direct product yields an intermediate irreducible representation. Then, perform a direct product between this intermediate result and the irreducible representation of the orbital corresponding to the next generating operator. This process is iterated until all orbitals corresponding to generating operators have participated in the operation. The final result is called the first direct product, denoted as […]. If there is only one generating operator, then its orbital irreducibility representation is itself the first straight product.

[0047] S44. Based on the set of spin-orbit indices of the annihilation operator extracted in S42, retrieve the irreducible representation label corresponding to each index from the dictionary. Similarly, using the irreducible representation direct product table, perform direct product operations on these irreducible representations sequentially. The final result is called the second direct product, denoted as... If there is only one annihilation operator, then its orbital irreducibility representation is itself a second direct product.

[0048] S45. Compare the first direct product calculated in S43. The second direct product calculated by S44 In the program implementation, this is a check to determine whether two strings (irreducible label representations) are completely identical. If the check is true, then... This means that the currently traversed excitation operator satisfies the point group symmetry requirement. The program will process this complete excitation operator object (including its variational parameters). (and operator structures) are added to the end of the initialized empty symmetric hypothesis list symmetric_ansatz. If the evaluation result is false, i.e. Not equal to If so, the program will not perform any operation on the symmetric hypothetical list and will directly ignore the currently triggered operator.

[0049] S46. Return to the loop start point of S41 and continue processing the next excitation operator in the initial asymmetric fitting list, repeating S42 to S45. The loop ends when all excitation operators in the initial asymmetric fitting list have been processed. At this point, the symmetric fitting list `symmetric_ansatz` contains all the selected excitation operators that meet the point group symmetry requirement. This list is the final symmetric fitting of the target material's molecules, conforming to the point group symmetry requirement. It is output for subsequent quantum circuit construction.

[0050] Taking the hydrogen molecule as an example, let's assume the initial asymmetry is set as follows: Given that the dictionary of irreducible spin orbitals is {0:} ,1: ,2: ,3: The irreducible direct product rule is: , , , specifically, Initialize symmetric_ansatz=[]. The first excitation operator is The set of operator indices is {2}, and the set of annihilation operator indices is {0}. Calculate the first right product: Only one operator is generated, and the irreducible representation of orbital 2 is... Therefore ; Calculate the second direct product: There is only one annihilation operator, and the irreducible representation of orbital 0 is: Therefore . Not equal to Therefore, it is not added. At this point, symmetric_ansatz remains []. The second excitation operator is This generates an operator index set of {3} and an annihilation operator index set of {1}. The first direct product is calculated: the irreducible representation of orbital 3 is... Therefore Calculate the second direct product: the irreducible representation of orbital 1 is... Therefore . Not equal to Therefore, it is not added. symmetric_ansatz remains []. The third excitation operator is The set of operator indices is {3,2}, and the set of annihilation operator indices is {1,0}. Calculate the first right product: first check the irreducible representations of orbitals 3 and 2. Look up the direct product table. Therefore Calculate the second direct product: First, check the irreducible representations of orbitals 1 and 0, both of which are... Look up the direct product table. Therefore . equal Therefore, this operator Add to symmetric_ansatz. After the traversal, the final symmetric approximation is set to... .

[0051] Point group symmetry refers to the property that, after a series of specific geometric transformations (symmetry operations) in three-dimensional space, the overall configuration of a molecule can perfectly coincide with the original configuration. These symmetry operations constitute a mathematical "point group." Point group symmetry is an inherent physical property of molecules, profoundly influencing their electronic wavefunctions, orbital energy levels, and spectral properties. In quantum chemical calculations, point group symmetry can be used to simplify calculations, such as by partitioning the Hamiltonian into block diagonalizations, or, as in this method, by screening excitation operators that preserve the system's symmetry, thereby effectively reducing the complexity of computational parameters and quantum circuits.

[0052] S5. Based on the final symmetry assumption, construct a quantum circuit, specifically: S50, Based on the total number of spin orbitals of the target material's molecules The appropriate number of qubits are allocated. Each qubit corresponds to a spin orbital, and its state... Indicates that the orbit is empty and occupied, state This indicates that the orbital is occupied by an electron. The initial state of a quantum circuit is typically prepared as a Hartley-Fock reference state. The preparation method involves applying a qubit to the corresponding spin orbital that is occupied by an electron in the Hartley-Fock state. A gate (Pauli-X gate) that changes the state from Flip to For the qubits corresponding to the virtual orbitals, the behavior remains unchanged. For example, in a system with four spin orbitals, where orbitals 0 and 1 are occupied, actions need to be performed on qubits Q0 and Q1 respectively. This allows for the preparation of the initial quantum state. .

[0053] S51. Iterate through each excitation operator in the final symmetry-proposed list. Each excitation operator needs to be transformed into a sub-circuit composed of basic quantum gates. There are well-established templated quantum circuit construction schemes for this transformation. For a single excitation operator, its corresponding sub-circuit typically revolves around the target qubit and the controlled qubit, using two CNOT gates and several parameterized single-qubit rotation gates (such as...). or It is constructed using gates. Parameters This is encoded into the rotation angle of these rotating gates. For dual-excitation operators, the sub-circuit structure is more complex, requiring the operation of four qubits. Typically, about 13 CNOT gates and several single-qubit rotating gates are needed to accurately implement its exponential form. These construction templates are known and can be directly called through function libraries, with input parameters... and the spin orbit index involved This will generate the corresponding quantum gate sequence.

[0054] S52. Following the order of the excitation operators in the final symmetry simulation list, connect each parameterized quantum circuit generated in S51 sequentially to the Hartley-Focke state circuit prepared in S51. Assume the final symmetry simulation is... ,in, It is the total number of operators that are activated after filtering. Indicates the first The gate sequence mapped by each activation operator These are its variational parameters. Therefore, the evolution operator of the constructed total quantum circuit is approximately: in, Indicates the first Each excitation operator corresponds to a fermion operator. It is a gate operation for preparing the Hartley-Fock reference state. This is the variational parameter vector to be optimized. The depth of the circuit and the number of gates depend on... And the complexity of each sub-line.

[0055] S53. After completing the connection of all sub-circuits, a complete, parameterized quantum circuit is obtained. This circuit uses a set of variational parameters. As input, output a final quantum state. In terms of program implementation, this circuit is defined as a circuit object that can be executed on a quantum simulator or real quantum hardware. Typically, it is necessary to record each parameter. The position of the quantum circuit within the circuit allows each parameter to be independently adjusted and gradients calculated during subsequent optimization loops of the variable quantum eigenvalue solving algorithm. Ultimately, this constructed quantum circuit object is output as the core component for executing the variable quantum eigenvalue solving algorithm to calculate molecular energy levels.

[0056] S6. Based on quantum circuits, determine the molecular reactivity of the target material, specifically including: S60. Based on quantum circuits, the energy level distribution of the target material's molecules is determined. The specific implementation process is as follows: S600 maps the electronic structure of molecules to qubit space. Based on the same basis set and geometry used previously, the second quantized form of the molecule, the Hamiltonian, is obtained through classical quantum chemical calculations (such as PySCF). in, and They are single-electron and two-electron integrals, respectively. and These are the production and annihilation operators, respectively. Subsequently, using transformations such as Jordan-Wigner or Bravyi-Kitaev, the fermion Hamiltonian is mapped to a Pauli operator (…). The Hamiltonian of a qubit is represented by the sum of () : in, It is the Pauli operator tensor product acting on multiple qubits (e.g. ), These are the corresponding real coefficients. It is the operator basis for calculating the expected value of energy.

[0057] S601 is the code in the quantum circuit. Variational parameters Assign initial values. There are two main strategies: one is zero initialization, which initializes all values. Setting it to 0, the output state of the quantum circuit is the Hartley-Fock reference state; the second is classical approximate initialization, using the excitation amplitude calculated by the classical coupled cluster single-double excitation method as the corresponding excitation operator parameter. The initial values. The initialized parameter vector. The input will be fed into the optimization loop.

[0058] S602, Enter the parameter optimization loop, which is an iterative process. In the... In this iteration, the following sub-steps are executed: 1) Set the current parameter value Load the data into the constructed quantum circuit. Run the circuit on a quantum processor or simulator to evolve the quantum register and prepare parameterized quantum states. .

[0059] 2) Calculate the molecular Hamiltonian in this quantum state. Expected value .because It is a linear combination of Pauli operators, and its expected value can be decomposed into the values ​​of each Pauli term. Weighted sum of expected values: Each item The acquisition of this requires the preparation of the state. exist Multiple projection measurements are performed under the corresponding measurement basis, and the expected value is estimated by statistically analyzing the measurement results (0 or 1) of the qubits. The calculation of the entire expected value requires combining the measurement results of all Pauli terms.

[0060] 3) Calculate the expected energy value And the energy gradient calculated using methods such as parameter shift rules. This information is passed to a classical optimizer (such as BFGS, ADAM, or SLSQP). Based on this information, the optimizer determines a new set of parameter values ​​using its internal algorithm (such as a quasi-Newton method). The aim is to reduce the expected energy level.

[0061] S603. After each iteration, check the convergence criterion. A commonly used criterion is the energy difference between two consecutive iterations. Less than the preset threshold (For example Hartree), and the norm of the energy gradient. Less than the threshold (e.g., 10) -4 If the convergence condition is met, the optimization loop exits. At this point, the final parameters... Corresponding energy expectation value This refers to the ground-state energy level of the target material's molecules, obtained from the variable quantum eigenvalue solving algorithm. This energy level is the lowest in the molecular energy level distribution and is the core input for subsequent reactivity analysis.

[0062] S604. To obtain a higher excited-state energy level distribution, an extended algorithm can be used based on the obtained ground state. For example, a constrained variable quantum eigenvalue solution algorithm or a subspace expansion method can be employed. The constrained variable quantum eigenvalue solution algorithm requires that the trial state be orthogonal to the obtained ground state during optimization. The first excited-state energy level is obtained by solving the constrained optimization problem, and so on. The subspace expansion method utilizes a set of low-energy wavefunctions prepared by quantum circuits at different points in the parameter space to construct and diagonalize a small effective Hamiltonian, thereby estimating several low-excited-state energy levels at once. Through these methods, the low-energy excited-state energy levels of the target material's molecules can be systematically determined, thus constructing a more complete molecular energy level distribution map.

[0063] S61. Based on the energy level distribution of the target material's molecules, determine the reactivity of the target material's molecules. The specific implementation process is as follows: S610. Based on the intended use of the target material's molecules, determine the specific metrics to be calculated to characterize the reactivity. For elementary reactions involving bond breaking and formation, the core metric is the reaction rate constant, which requires calculating the energy barrier between the reactants and the transition state. For photophysical or photochemical processes, such as fluorescence emission or photocatalysis, the core metrics may involve excited state energy levels, excited state lifetimes, redox potentials, or the energies of specific electronic transitions. This step guides all subsequent quantitative calculations.

[0064] S611. Based on the scenario defined in S610, calculate the ground-state energy levels of all necessary molecular systems. For example, to calculate the chemical reaction rate, it is necessary to calculate the ground-state electron energies of the reactant molecule (R) and the transition state molecule (TS) separately. and To evaluate the redox capabilities of photocatalysts, it may be necessary to calculate the ground-state energies of the catalyst molecules in their ground state and in each ionic state after gaining or losing electrons. These energy calculations require repeatedly executing the aforementioned complete "quantum circuit-based determination of molecular energy level distribution" process, independently performing variational quantum eigenvalue calculations for each relevant molecular system to obtain highly accurate ground-state energy levels. .

[0065] S612. Substitute the series of ground state energy levels obtained in S611 into the physical model corresponding to the scenario selected in S610, and calculate the intermediate energy parameters. Specifically, ① for chemical reaction rate: calculate the activation energy of the reaction. Under the adiabatic approximation, the activation energy is the energy difference between the transition state and the ground state electrons of the reactants, i.e. ② For redox processes: Calculate the ionization energy, electron affinity, or corresponding redox potential of the molecule. For example, ionization energy... ,in and These represent the ground state energy levels of cations and neutral molecules, respectively. ③ For photophysical processes: If the excited state energy level distribution of molecules has been obtained through the extended algorithm... Then the lowest excited state energy can be obtained directly. or These are used to estimate fluorescence emission wavelengths or determine the likelihood of energy transfer.

[0066] S613. Input the energy parameters calculated in S612 into classical physicochemical formulas to obtain activity indicators that can be experimentally observed or directly used for engineering judgment. Specifically, ① calculate the chemical reaction rate constant: use the Irene formula of transition state theory. The activation energy... As activation free energy The main contributions (often approximated as) Alternatively, by adding zero-point energy correction and enthalpy correction, the temperature can be calculated using the formula. rate constant at the following : in, It is Boltzmann's constant. It is Planck's constant. (Calculated) The value directly characterizes the reaction rate, i.e., the reaction activity. ② Determining the driving force of the photocatalyst: The calculated ground-state oxidation potential of the catalyst... With reduction potential The potential is compared with the standard potential of the target reactant (such as the oxidation of water or the reduction of carbon dioxide). If the conditions are met... More negative than the oxidation potential of the reactants (or If the catalyst has a more positive reduction potential than the reactants, then it is thermodynamically determined that the catalyst is active in driving the reaction. ③ Predict the emission characteristics of fluorescent materials: using the formula Estimate its fluorescence emission wavelength ,in, The speed of light. The suitability of a material for fluorescent labeling in a specific wavelength range can be determined based on the wavelength range.

[0067] S614. Conduct a comprehensive analysis of the various indicators calculated in S613. For example, compare the reaction rate constants calculated for different molecular structures. The higher the value, the higher the reactivity; or it can be used to determine whether the redox potential of the photocatalyst meets the thermodynamic requirements of a specific reaction. Ultimately, it outputs a qualitative conclusion or quantitative prediction report on the reactivity of the target material molecule, such as "the predicted rate constant for reaction A at 298 K is..." "The lowest excited state energy of this material corresponds to visible blue light emission, making it suitable for fluorescent labeling in bioimaging." "The catalyst's conduction band bottom potential is lower than the standard potential for CO2 reduction to CO, theoretically indicating catalytic activity." These results provide direct theoretical basis and predictions for the application of the target material in drug design, catalyst screening, and functional material development.

[0068] In another feasible approach, the reactivity of the target material molecules is determined based on their energy level distribution. The specific implementation process is as follows: 1) Based on the ground state and low-excited state energy level data of the target material's molecules obtained by the variational quantum eigenvalue solution algorithm, the vertical transition energies between each electronic state and the corresponding Frank-Condon factors are calculated. These factors are obtained by overlapping integrals of different electronic potential energy surfaces under the harmonic oscillator model, and are used to quantify the intensity and probability of electronic transitions between different energy levels. Specifically: Vertical transition energy Directly composed of two electronic states and The energy difference at the potential energy surface minimum is given, i.e. ,in and They are states Harmony The electron energy under the equilibrium geometry. Then, under the harmonic oscillator approximation, each electron potential energy surface is determined by a set of simple harmonic frequencies. and the corresponding equilibrium coordinates Description. Frank-Condon factor. Quantitative characterization from the initial state vibrational energy level To the final state vibrational energy level The transition intensity is determined by the degree of mismatch between the two electronic potential energy surfaces, with the core being the calculation of the overlap integral of different vibrational wave functions. For the multimode case, the total Frank-Condon factor is the product of the contributions of each vibrational mode. By solving for the electronic potential energy surfaces and vibrational wave functions, the vertical transition energies between all relevant electronic state pairs and a complete set of Frank-Condon factors can be systematically calculated, providing initial excitation weights and transition probabilities for subsequent dynamical simulations.

[0069] 2) Based on the vertical transition energy and Frank-Condon factor obtained in the previous step, construct a non-adiabatic coupling matrix. This matrix describes the interaction strength between different electronic potential energy surfaces, and the matrix elements... From electronic state and The inner product of the wave function derivative and the nuclear kinetic energy operator jointly determine the specific: Non-adiabatic coupled matrix element Nuclear coordinates The function characterizing electronic states and The coupling strength between them. Its calculation formula is as follows: In this formula, It is the reduced Planck constant, summation index Traverse all kernel degrees of freedom. First-order non-adiabatic coupled vector. It is the electron wave function The inner product of the derivatives with respect to the kernel coordinates exhibits a singularity near the potential energy surface intersection region in the adiabatic representation. Scalar coupling terms. Typically small. In practical calculations, these matrix elements can be numerically solved and fitted to analytical functions using quantum chemical calculation programs in key nuclear configuration regions (such as near the minimum energy crossover point), ultimately constructing a complete, non-adiabatic coupled matrix related to the nuclear coordinates. .

[0070] 3) Using a non-adiabatic coupling matrix, the time-dependent Schrödinger equation is solved to simulate the non-adiabatic dynamic evolution of molecules in the target material under photoexcitation or thermal perturbation. The trajectory of wave packets on various electronic potential energy surfaces is tracked numerically, and the probability of them crossing specific potential energy surface intersection regions and reaching specific product regions is statistically analyzed. Specifically: Time-dependent wave function of the system Under an adiabatic base, it unfolds as follows ,in It is the first Nuclear wave packets in adiabatic electronic states. Substituting these into the time-dependent Schrödinger equation, we obtain the coupled nuclear motion equations: here It is a nuclear kinetic energy operator. It is the identity matrix. It is a diagonal matrix whose elements are the various adiabatic potential energy surfaces. Initial wave packet Determined by the Frank-Condon factor, the nuclear wave packet is typically placed on the ground potential energy surface and given a certain initial momentum or placed in a specific vibrational state. Numerical methods (such as the time-dependent Hartree method for multiple configurations or trajectory-based surface transition methods) are used to solve this system of equations, allowing the tracking of the nuclear wave packet's trajectory across multiple coupled potential energy surfaces and real-time recording of its transitions between different electronic states. Through statistical analysis of a large number of trajectories, the probability of the wave packet traversing a specific potential energy surface intersection region and ultimately reaching different product regions (defined by the coordinate range of the product configuration) can be calculated. .

[0071] 4) Analyze the kinetic simulation results from the previous step to extract the key reaction pathways and their branching ratios of the target material molecules. Correlate the final state probability of reaching different product regions with the reaction timescale to quantitatively assess the photochemical or thermal reactivity of the target material molecules, and predict its main reaction pathways and product distribution. Specifically: Based on the geometric configuration of the final stable distribution of nuclear wave packets, different reaction product channels were identified. The branching ratio of each channel... The value is given by the proportion of the number of trajectories or probability densities belonging to that channel at the end of the evolution. Secondly, the average time of wave packet arrival at each product region is analyzed. Alternatively, the reaction half-life can be used to obtain information on the reaction timescale. Finally, the branching ratio is correlated with the reaction timescale to achieve a quantitative assessment of the reaction activity. For photochemical reaction activity, a high product branching ratio and a short reaction time together characterize high reaction efficiency and selectivity. For thermal reaction activity, the reaction rate constant obtained based on trajectory statistics at a specific temperature can be calculated. This allows for quantitative description. By combining these analytical results, we can clearly reveal the dominant and secondary reaction pathways of the target material's molecules, as well as the efficiency and rate of each pathway. This enables a comprehensive prediction of its photochemical or thermal reactivity and provides clear guidance for material design.

[0072] Optionally, the above technical solution also includes: 1) When the target material is a fluorescent material, the luminescence properties of the target material are determined based on the energy level distribution of its molecules. Based on these luminescence properties, it is then determined whether the target material is suitable for fluorescent labeling. Specifically: By analyzing the energy level distribution of the target material's molecules using the VQE algorithm, the focus is on the energy difference between the excited and ground states, i.e., the excitation energy, and the characteristics of key excited states (usually the first excited state) directly related to the fluorescence emission process are extracted. Determining the luminescence properties depends on calculating the transition probabilities between energy levels, which is achieved by calculating the transition dipole moments between relevant electronic states. This physical quantity directly determines the magnitude of the radiative transition rate and is a core parameter for evaluating fluorescence intensity (i.e., quantum yield). A strong transition dipole moment implies a high radiative transition rate and strong fluorescence emission intensity. Simultaneously, the competition for non-radiative transition channels (such as internal conversion and intersystem crossing) needs to be evaluated. This can be indirectly inferred by analyzing the band gap between different electronic states; a larger band gap can suppress non-radiative transitions, thus favoring fluorescence emission. The fluorescence quantum yield of the fluorescent material can be theoretically estimated by combining the ratio of the radiative to the non-radiative transition rates. Finally, the suitability for fluorescent labeling is determined based on the identified luminescent properties (including excitation wavelength, emission wavelength, Stokes shift, fluorescence intensity, and quantum yield); materials used for fluorescent labeling must meet the following quantification threshold conditions: The calculated fluorescence quantum yield must be no less than 0.8 to ensure a sufficiently bright signal; the calculated excitation wavelength must be strictly within the visible light range of 400 nm to 700 nm to match the light source of conventional optical instruments, while the calculated emission wavelength should also be within the effective response range of the detector of 400 nm to 800 nm; the calculated Stokes shift must be greater than 50 nm to ensure that the excitation light and emission light can be effectively separated.

[0073] If the calculated luminescence characteristic parameters simultaneously meet all the above threshold conditions, the target material can be determined to be suitable for fluorescent labeling; otherwise, if any condition is not met, the target material can be determined to be unsuitable for fluorescent labeling.

[0074] 2) When the target material is a photocatalyst, its photocatalytic activity is determined based on the energy level distribution of its molecules; based on this activity, it is determined whether the target material can be used for visible light-driven chemical reactions. Specifically: First, based on the energy level distribution of the target material molecules accurately calculated using the VQE algorithm, the focus is on analyzing the energy difference between its highest occupied molecular orbital (HOMO) level and its lowest unoccupied molecular orbital (LUMO) level, i.e., the band gap. This band gap energy must be less than the maximum energy of a visible light photon; this is a prerequisite for determining whether the material can be excited by visible light to generate electron-hole pairs, and is the foundation for its visible light photocatalytic activity. Determining photocatalytic activity further relies on comparing the aforementioned molecular orbital energy level positions with the energy level benchmark of the standard redox potential. Specifically, the material's conduction band or LUMO level must be more negative than the potential of the target reduction reaction to ensure sufficient reduction driving force for photogenerated electrons; simultaneously, its valence band or HOMO level must be more positive than the potential of the target oxidation reaction to ensure sufficient oxidation driving force for photogenerated holes. Furthermore, the recombination probability of photogenerated carriers (electrons and holes) needs to be indirectly evaluated from the energy level structure. A well-separated energy level distribution facilitates the effective separation and migration of carriers, thereby improving photocatalytic efficiency. By considering the band gap energy, the matching degree between energy level positions and redox potentials, and the potential carrier separation efficiency, the photocatalytic activity of the target material can be theoretically determined. Finally, the determined photocatalytic activity is used to determine whether it is suitable for visible light-driven chemical reactions.

[0075] If the calculated bandgap value of the target material is within the visible light absorption range of 1.6 eV to 3.2 eV, and its LUMO energy level is below -4.44 eV (relative to the vacuum energy level, to meet the requirements) (Reduction potential requirement), while its HOMO energy level is higher than -5.67 eV (relative to the vacuum energy level, to meet the requirement). If the oxidation potential requirement is met, the photocatalyst can be determined to be suitable for visible light-driven chemical reactions (such as photocatalytic water splitting to produce hydrogen, photocatalytic degradation of pollutants, etc.); conversely, if any of the above threshold conditions are not met, the photocatalyst can be determined to be unsuitable for visible light-driven chemical reactions.

[0076] Continuing with the construction of a hydrogen molecule for solving for a bond length of 0.87 angstroms The process of assuming the symmetry of energy levels is described below as a specific example: 1) Obtain the molecular geometry and initial asymmetry simulation of the target material. In this embodiment, the target material is a hydrogen molecule. Its molecular geometry consists of two hydrogen atoms with an interatomic bond length of 0.87 Å. Based on this geometry, molecular orbitals can be obtained through classical quantum chemical calculations, and then spin orbitals can be defined. The hydrogen molecule has four spin orbitals under the selected basis set. The initial asymmetry simulation is a simplified subset of the commonly used unitary coupled cluster single-double excitation simulation, specifically represented as a list containing multiple excitation operators: .in, These are the variational parameters to be optimized; Indicates the generation of an operator. Indicates the annihilation operator; subscript number It is the index of the spin orbital.

[0077] 2) Based on the molecular geometry of the target material, determine the Abelian point group corresponding to the target material's molecules. For a hydrogen molecule with a bond length of 0.87 Å... Its complete spatial symmetry belongs to Point cluster. Identified using symmetry analysis software. The point group is a non-Abelian point group. According to the method of this invention, when the determined point group is a non-Abelian point group, the highest-order Abelian subgroup of this non-Abelian point group needs to be selected as the Abelian point group used for subsequent calculations. For The highest-order Abelian subgroup of a point group is Point group. Therefore, in this embodiment, the Abel point group ultimately determined to be used is... .

[0078] 3) Determine the irreducible representation of each spin orbital of the target material molecule, and determine the direct product table of the irreducible representations of the Abelian point group. For the hydrogen molecule, in In the point group, its four spin orbitals need to be assigned irreducible representations. Orbitals with spin orbital indices 0 and 1 are occupied orbitals, while those with indices 2 and 3 are dummy orbitals. This is achieved by analyzing the wavefunction of each orbital in... The transformation characteristics under various symmetric operations of the point group can determine their corresponding irreducible representations as follows: the orbital with index 0 is... Track 1 is Track 2 is Index 3 track is At the same time, it is necessary to determine The direct product table of irreducible representations of a point group defines the rules for performing a direct product operation on any two irreducible representations. Some of the direct product relationships involved in this embodiment are as follows: In this table, This represents the direct product operation. For example, , .

[0079] 4) Initialize an empty symmetry simulation and, based on the irreducible representation of each spin orbital and the direct product table of irreducible representations, traverse each excitation operator in the initial asymmetry simulation and perform filtering. First, initialize an empty symmetry simulation, represented as an empty list in the computer program. Then, begin traversing each excitation operator in the initial asymmetry simulation list. Specifically, ① for the first excitation operator... Calculate the first direct product of the irreducible representations of the spin orbitals acted upon by all the production operators: there is only one production operator among the excitation operators. Its spin orbital index is 2, and the corresponding irreducible representation is: Therefore, the first straight product Calculate the second direct product of the irreducible representations of the spin orbitals acted upon by all annihilation operators: this excitation operator contains only one annihilation operator. Its spin orbital index is 0, and the corresponding irreducible representation is: Therefore, the second direct product Compare the first product. With the second direct product .because Not equal to Therefore, this excitation operator does not meet the point group symmetry requirement and is not added to the symmetry hypothesis. ② For the second excitation operator... Calculate the first direct product: generate the operator The spin orbital index of the action is 3, and the irreducible representation is: Therefore Calculate the second direct product: annihilation operator The spin orbital index of the action is 1, and the irreducible representation is: Therefore .because Not equal to Therefore, this excitation operator does not meet the point group symmetry requirement and is ignored. ③ For the third excitation operator Calculate the first direct product: This operator contains two generating operators. and The spin orbital indices of the action are 3 and 2, respectively, and their corresponding irreducible representations are both 3 and 2. Calculate the first direct product based on the irreducible direct product table. Calculate the second direct product: This operator contains two annihilation operators. and The spin-orbit indices of the action are 1 and 0, respectively, and the corresponding irreducible representations are both 1 and 0. Calculate the second direct product based on the irreducible direct product table. The first product is obtained by comparison. Equal to the second direct product (All are) This indicates that the excitation operator satisfies the point group symmetry requirement. Therefore, it is added to the previously initialized symmetry hypothesis list. After traversing all excitation operators, the final symmetry hypothesis satisfying the point group symmetry requirement for the target material hydrogen molecule is obtained as follows: .

[0080] 4) After outputting the final symmetry simulation, a quantum circuit can be constructed based on this simulation, and the variable quantum eigenvalue solving algorithm can be further executed to finally solve for the ground state energy level of the hydrogen molecule. This specific embodiment fully demonstrates every step of the process from molecular structure to obtaining the symmetry simulation, verifying the systematic nature and convenience of the method of this invention.

[0081] 5) After obtaining the final symmetry hypothesis, the quantum computing implementation stage begins. This stage includes three main parts: quantum circuit construction, parameter optimization, and energy level calculation. Specifically: ① Based on the final symmetry simulation, construct quantum circuits. Specifically, design a corresponding parameterized quantum circuit for each excitation operator in the symmetry simulation list. For a single excitation operator... Its quantum circuit can consist of two CNOT gates combined with several parameterized single-qubit rotation gates (such as...). or (Gate) construction. For bi-excitation operators Its quantum circuitry is more complex, typically requiring 13 CNOT gates and corresponding single-qubit gates. In the program implementation, these construction templates can be encapsulated as functions. Then, following the logical order in the final symmetry simulation list, the quantum circuitry corresponding to each excitation operator is sequentially connected in series and connected after the initial circuitry used to prepare the Hartley-Fock reference state, thus completing the construction of the entire quantum circuitry for the quantum state simulation.

[0082] ② The variational parameter initialization strategy directly affects convergence efficiency and computational accuracy. Mainstream strategies fall into two categories: one is zero-value initialization, which initializes all variational parameters... The first method sets the initial value to 0, which is simple to operate and has no additional computational cost, making it suitable for small molecule systems. The second method initializes the system with classical approximation results, using classical quantum chemical methods such as the coupled cluster single-double excitation method to pre-calculate the electronic transition coefficients, which are then used as the variational parameters of the corresponding excitation operators. The initial value is determined by the coupled cluster single-double excitation method. Because the results obtained using this method are highly accurate and the excitation amplitude has a clear physical correspondence with the variational parameters, this initialization method allows the initial value to be closer to the minimum region of the optimization, effectively reducing the number of iterations. This method is suitable for medium to large molecules or complex structures. The parameter optimization process is completed using a classical optimizer, with the BFGS algorithm being the mainstream choice. The BFGS algorithm is a quasi-Newton method that does not require direct calculation of the complex Hessian matrix. It updates the approximate Hessian inverse matrix using gradient information during the iteration process, thereby determining the optimal search direction. In the variational quantum eigenvalue solution algorithm, the objective function is the expected value of the molecular Hamiltonian. This value is derived from the probability distribution of quantum states obtained through repeated operation and measurement of the quantum circuit, combined with the matrix elements of the Hamiltonian. The objective function with respect to the parameters... The gradient is obtained through an efficient parameter offset rule, which has the advantage of low noise.

[0083] ③ The convergence criterion used in the optimization process is usually the energy difference obtained from two consecutive iterations. Less than Hartree, and the L2 norm of the energy gradient vector is less than Once the optimization process of the variable quantum eigenvalue solving algorithm reaches the preset convergence criterion, the expected value of the Hamiltonian corresponding to the output state of the quantum circuit is the ground state energy level of the target material's molecules obtained by the algorithm. The accuracy of this calculation result needs to be verified in a reliable manner. There are two main verification methods: one is to compare it with the results of classical high-precision calculation methods, such as comparing it with the results of the fully configured interaction method; the other is to compare it with experimental measurement data. On near-term noisy quantum computing devices, the ground state energy level results obtained through the variable quantum eigenvalue solving algorithm can usually meet the chemical accuracy requirements, i.e., an energy error of less than 1 kcal per mole.

[0084] ④ The precise ground-state energy level data of different molecular systems obtained based on the variable quantum eigenvalue solving algorithm can be further used to predict macroscopic properties through physicochemical theory. For example, the Irene formula can be used to predict the chemical reaction rate between two materials. As the core expression of transition state theory, the Irene formula directly establishes the relationship between the chemical reaction rate constant and the activation energy of the reaction. Its expression is: in, It is the chemical reaction rate constant. It is Boltzmann's constant. It is thermodynamic temperature. It is Planck's constant. This is the activation free energy of the reaction. The core contributor to the activation free energy is the energy difference between the ground state energy levels of the reactant molecules and the transition state molecules. Therefore, after obtaining the precise ground state energy levels of the reactant and transition state molecules using a variable quantum eigenvalue solution algorithm, the activation energy can be calculated. Substituting this into the Eileen formula, the reaction rate constant can then be calculated. This theoretical predictive capability provides crucial theoretical support for practical applications such as material synthesis process optimization and catalytic reaction system design.

[0085] The beneficial effects provided by the technical solution of this invention are mainly reflected in three aspects. First, in the process of constructing the symmetry simulation, only the spin orbitals directly associated with the excitation operator need to be examined, without calculating the irreducible representation of the excitation determinant involving all molecular electrons. For single-excitation operators and double-excitation operators, only the irreducible representation information of 2 and 4 spin orbitals need to be processed, respectively, fundamentally reducing the computational load, making it applicable to large molecular systems, and significantly reducing the possibility of introducing errors due to processing a large number of electrons. Second, the method is systematic and robust. By uniformly reducing non-Abelian point groups to their highest-order Abelian subgroups, the universal applicability of the method to all molecular point groups is ensured, while maintaining the simplicity of the direct product operation of irreducible representations. The logic of each step is clear and the rules are well-defined, making it easy to automate the entire process and improving the reliability and efficiency of constructing the symmetry simulation. Third, the final constructed quantum circuit has significant advantages. The final symmetry simulation obtained based on the above method contains fewer excitation operators, effectively reducing the parameter scale and circuit depth of the quantum circuit, making it more suitable for the hardware limitations of current noisy quantum computing devices. While maintaining the computational accuracy of the variable quantum intrinsic solution algorithm, this method provides a superior technical foundation for efficiently and accurately determining the reactivity of target material molecules, and strongly supports the development of related fields of materials research and development.

[0086] In the above embodiments, although the steps are numbered S1, S2, etc., they are only specific embodiments given by the present invention. Those skilled in the art can adjust the execution order of S1, S2, etc. according to the actual situation. The scheme after adjusting the order is also within the protection scope of the present invention. It can be understood that in some embodiments, some or all of the above embodiments may be included.

[0087] like Figure 2As shown, an embodiment of the present invention provides a system 200 for determining the reactivity of material molecules based on quantum computing, comprising a structure operator acquisition module 201, a first determination module 202, a second determination module 203, a final symmetry simulation acquisition module 204, a quantum circuit construction module 205, and a reactivity determination module 206. The structure operator acquisition module 201 is used to: acquire the molecular geometry of the target material and the initial asymmetry simulation, the initial asymmetry simulation including multiple excitation operators; The first determining module 202 is used to: determine the Abelian point group corresponding to the molecules of the target material based on the geometric structure of the molecules of the target material; The second determining module 203 is used to: determine the irreducible representation of each spin orbital of the target material molecule, and determine the direct product table of irreducible representations of the Abelian point group; The final symmetry fitting module 204 is used to: initialize an empty symmetry fitting, and based on the irreducible representation of each spin orbital and the product table of irreducible representations, traverse each excitation operator in the initial asymmetry fitting, calculate the first product of the irreducible representations of the spin orbitals acted by all the generating operators in the currently traversed excitation operator, and calculate the second product of the irreducible representations of the spin orbitals acted by all the annihilation operators in the currently traversed excitation operator. If the first product equals the second product, the currently traversed excitation operator is added to the initialized symmetry fitting; otherwise, it is not added. After completing the traversal of all excitation operators in the initial asymmetry fitting, the final symmetry fitting of the target material's molecular coincidence point group symmetry is obtained. The quantum circuit construction module 205 is used to: construct quantum circuits based on the final symmetry design; The reactivity determination module 206 is used to: determine the reactivity of the target material molecules based on quantum circuits.

[0088] Optionally, in the above technical solution, the first determining module 202 is further configured to: when the point group corresponding to the molecule of the determined target material is a non-Abelian point group, select the Abelian subgroup with the highest order of the non-Abelian point group as the Abelian point group.

[0089] Optionally, in the above technical solution, the reactivity determination module 206 is specifically used to: determine the energy level distribution of the target material's molecules based on quantum circuits; and determine the reactivity of the target material's molecules based on the energy level distribution of the target material's molecules.

[0090] Optionally, the above technical solution also includes a material application module, which is used to: when the target material is a fluorescent material, determine the luminescence characteristics of the target material based on the energy level distribution of the molecules of the target material, and determine whether the target material is used for fluorescent labeling based on the luminescence characteristics of the target material; when the target material is a photocatalyst, determine the photocatalytic activity of the target material based on the energy level distribution of the molecules of the target material; and determine whether the target material is used for visible light-driven chemical reactions based on the photocatalytic activity of the target material.

[0091] It should be noted that the beneficial effects of the quantum computing-based material molecule reactivity determination system 200 provided in the above embodiments are the same as those of the quantum computing-based material molecule reactivity determination method described above, and will not be repeated here. Furthermore, the system provided in the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the system can be divided into different functional modules according to the actual situation to complete all or part of the functions described above. In addition, the system and method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, and will not be repeated here.

[0092] An electronic device according to an embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the above-mentioned methods for determining the reactivity of material molecules based on quantum computing.

[0093] An embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the above-mentioned methods for determining the reactivity of material molecules based on quantum computing.

[0094] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this invention is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-disclosed concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this invention.

[0095] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for determining the reactivity of material molecules based on quantum computing, characterized in that, include: The molecular geometry of the target material and the initial asymmetry simulation are obtained, wherein the initial asymmetry simulation includes multiple excitation operators; Based on the molecular geometry of the target material, the Abelian point group corresponding to the molecules of the target material is determined; Determine the irreducible representation of each spin orbital of the molecules of the target material, and determine the direct product table of the irreducible representations of the Abelian point group; An empty symmetry fitting is initialized, and based on the irreducible representation of each spin orbital and the direct product table of the irreducible representations, each excitation operator in the initial asymmetry fitting is traversed. The first direct product of the irreducible representations of the spin orbitals acted by all the generating operators in the currently traversed excitation operator is calculated, and the second direct product of the irreducible representations of the spin orbitals acted by all the annihilation operators in the currently traversed excitation operator is calculated. If the first direct product is equal to the second direct product, the currently traversed excitation operator is added to the initialized symmetry fitting; otherwise, it is not added. After completing the traversal of all excitation operators in the initial asymmetry fitting, the final symmetry fitting of the target material's molecular point group symmetry is obtained. Based on the proposed final symmetry, a quantum circuit is constructed. Based on the quantum circuit, the reactivity of the target material molecules is determined.

2. The method for determining the reactivity of material molecules based on quantum computing according to claim 1, characterized in that, Also includes: When the point group corresponding to the molecules of the target material is determined to be a non-Abelian point group, the Abelian subgroup with the highest order of the non-Abelian point group is selected as the Abelian point group.

3. The method for determining the reactivity of material molecules based on quantum computing according to claim 1 or 2, characterized in that, Based on the quantum circuit, the reactivity of the target material molecules is determined, including: Based on the quantum circuit, the energy level distribution of the molecules of the target material is determined; The reactivity of the target material molecules is determined based on the energy level distribution of the target material molecules.

4. The method for determining the reactivity of material molecules based on quantum computing according to claim 3, characterized in that, Also includes: When the target material is a fluorescent material, the luminescence characteristics of the target material are determined based on the energy level distribution of the molecules of the target material, and whether the target material is to be used for fluorescent labeling is determined based on the luminescence characteristics of the target material. When the target material is a photocatalyst, the photocatalytic activity of the target material is determined based on the energy level distribution of its molecules; and the target material is then used to determine whether it is suitable for visible light-driven chemical reactions based on its photocatalytic activity.

5. A system for determining the reactivity of material molecules based on quantum computing, characterized in that, It includes a structure operator acquisition module, a first determination module, a second determination module, a final symmetry simulation acquisition module, a quantum circuit construction module, and a reaction activity determination module; The structure operator acquisition module is used to: acquire the molecular geometry of the target material and the initial asymmetry simulation, wherein the initial asymmetry simulation includes multiple excitation operators; The first determining module is used to: determine the Abelian point group corresponding to the molecules of the target material based on the geometric structure of the molecules of the target material; The second determining module is used to: determine the irreducible representation of each spin orbital of the molecules of the target material, and determine the irreducible direct product table of the Abelian point group; The final symmetry fitting module is used to: initialize an empty symmetry fitting, and based on the irreducible representation of each spin orbital and the direct product table of irreducible representations, traverse each excitation operator in the initial asymmetry fitting, calculate the first direct product of the irreducible representations of the spin orbitals acted by all the generating operators in the currently traversed excitation operator, and calculate the second direct product of the irreducible representations of the spin orbitals acted by all the annihilation operators in the currently traversed excitation operator. If the first direct product is equal to the second direct product, then the currently traversed excitation operator is added to the initialized symmetry fitting; otherwise, it is not added. After completing the traversal of all excitation operators in the initial asymmetry fitting, the final symmetry fitting of the target material's molecular compliance with the point group symmetry is obtained. The quantum circuit construction module is used to: construct quantum circuits based on the final symmetry design; The reactivity determination module is used to: determine the reactivity of the target material molecules based on the quantum circuit.

6. The system for determining the reactivity of material molecules based on quantum computing according to claim 5, characterized in that, The first determining module is further configured to: when the point group corresponding to the molecule of the target material is determined to be a non-Abelian point group, select the Abelian subgroup with the highest order of the non-Abelian point group as the Abelian point group.

7. A system for determining the reactivity of material molecules based on quantum computing according to claim 5 or 6, characterized in that, The reaction activity determination module is specifically used for: Based on the quantum circuit, the energy level distribution of the molecules of the target material is determined; The reactivity of the target material molecules is determined based on the energy level distribution of the target material molecules.

8. The system for determining the reactivity of material molecules based on quantum computing according to claim 7, characterized in that, It also includes a materials application module, which is used for: When the target material is a fluorescent material, the luminescence characteristics of the target material are determined based on the energy level distribution of the molecules of the target material, and whether the target material is to be used for fluorescent labeling is determined based on the luminescence characteristics of the target material. When the target material is a photocatalyst, the photocatalytic activity of the target material is determined based on the energy level distribution of its molecules; and the target material is then used to determine whether it is suitable for visible light-driven chemical reactions based on its photocatalytic activity.

9. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for determining the reactivity of material molecules based on quantum computing as described in any one of claims 1 to 4.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method for determining the reactivity of material molecules based on quantum computing as described in any one of claims 1 to 4.

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