Method and apparatus for determining reactivity of material molecules based on quantum computing

Abstract

The application discloses a kind of based on quantum computing's material molecule's reactive activity determination method and equipment, it is related to based on quantum computing's material performance analysis technical field, method includes: by iteratively constructing symmetrization quantum ansatz to estimate molecular ground state energy.First, construct excitation operator pool and complete hamiltonian, and initialize reference state.In iteration, based on each operator is locally optimized on tentative state, select the largest norm of optimized parameter operator to join ansatz, then update the ansatz after global optimization to update all parameters.Cycle until meeting termination condition, finally calculate ground state energy using optimized ansatz and parameter, and then evaluate molecular reactivity.The application can reduce the overall consumption of quantum computing resources under the premise of obtaining high-precision molecular ground state energy estimate, improve the calculation efficiency and feasibility of determining the material molecule reactivity process.

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] In many key areas of modern scientific research, the accurate determination of molecular energy levels occupies a central and indispensable position. Whether it's analyzing the inherent physicochemical properties of matter, predicting its evolution in different environments, efficiently developing new materials, precisely designing targeted drugs, or overcoming technological bottlenecks in environmental protection fields such as improving energy conversion efficiency and efficiently degrading pollutants, all rely on the accurate acquisition of molecular energy levels. The accuracy and efficiency of molecular energy level determination directly determine the rate of progress and the quality of results in related research, and are key factors restricting the development of the field. In particular, to determine the reactivity of material molecules, it is necessary to accurately calculate the ground state energy of the molecule and the energy of the transition states along the reaction pathway, thereby obtaining the activation energy and predicting the reaction rate. However, traditional classical algorithms have fundamental limitations in the process of molecular energy level determination, and these limitations become increasingly significant as the molecular size increases. As the number of atoms in a molecule increases, the complexity of its electronic structure and interactions grows exponentially, directly leading to an exponential increase in the computational resource requirements of classical algorithms. This "exponential dilemma" means that classical algorithms can only achieve efficient and accurate solutions for small molecular systems. For large and medium-sized molecules containing tens to hundreds of atoms, classical algorithms often fail to complete the solution task due to exhaustion of computing resources, making it difficult to meet the urgent needs of materials science, drug development and other fields for the study of the reactivity of complex molecular systems.

[0003] The rise of quantum computing technology has provided a new research approach to overcome the aforementioned difficulties. Among them, the variable quantum eigenvalue algorithm, as an important application of quantum computing in the field of chemistry, has shown advantages that are distinctly different from classical algorithms. The core breakthrough of the variable quantum eigenvalue algorithm lies in the fact that its computational resource consumption follows a polynomial growth law, that is, as the molecular size increases, the computational resource requirement only increases polynomially with the molecular scale. This key characteristic fundamentally overcomes the "exponential dilemma" of classical algorithms, making the variable quantum eigenvalue algorithm potential for solving the energy level problem of large and medium-sized molecules, a difficult problem for classical algorithms. The standard variable quantum eigenvalue algorithm is based on a quantum-classical hybrid computing architecture, which approximates the molecular ground state energy through iterative optimization. In the initial stage of the process, a test state needs to be constructed based on a quantum simulation circuit with adjustable parameters. The simulation circuit design needs to combine molecular symmetry and electron distribution characteristics to evolve the easily prepared initial quantum state into a test state that approximates the target ground state. After the test state is constructed, a quantum measurement is performed on the total Hamiltonian describing the molecular interaction, and the expected energy value is extracted through multiple measurements. In practical applications of variational quantum eigenvalue solving algorithms, the choice of quantum simulation is crucial. The unitary coupled cluster single-double excitation simulation, due to its accurate description of molecular electronic excited states, has become one of the most widely used simulations. However, the unitary coupled cluster single-double excitation simulation has a significant drawback: its corresponding quantum circuit depth is large. Current quantum computers, limited by technical bottlenecks such as qubit coherence time and gate operation errors, can only effectively execute a limited circuit depth, making it impossible to support a complete unitary coupled cluster single-double excitation simulation, severely restricting the practical application efficiency of variational quantum eigenvalue solving algorithms. To address the problem of excessive circuit depth in the unitary coupled cluster single-double excitation simulation, Grimsley et al. proposed the ADAPT-VQE algorithm, whose core innovation lies in employing a dynamically constructed simulation approach. This algorithm first extracts all single and double excitation operators in the unitary coupled cluster single-double excitation simulation, constructs a complete pool of excitation operators, and selects the Hartree-Fock state as the initial test state. Subsequently, the absolute values ​​of the gradients of all operators in the excitation operator pool when the parameters are 0 are calculated. The excitation operator with the largest gradient norm is included in the current hypothesis, and all parameters in the hypothesis are optimized until convergence. The above "operator selection-parameter optimization" process is iterated repeatedly until the gradient norms of all remaining operators in the excitation operator pool when the parameters are 0 are less than a preset threshold, at which point the iteration process terminates. At this point, the expected value of the Hamiltonian measured in the current trial state is the calculated result of the ground state energy of the target molecule.

[0004] Compared to conventional variational quantum eigenvalue solving algorithms, ADAPT-VQE, by dynamically selecting key operators, can construct quantum simulations with shallower circuit depth, effectively adapting to the performance constraints of current quantum computers. However, this method still has two major problems: First, the excitation operator selection mechanism relies entirely on the gradient norm when the parameters are zero. Although empirically, the larger the absolute value of the gradient, the more significant the operator's contribution to energy, this rule is not absolute. In practical applications, this strategy often selects redundant operators with weak energy contributions, leading to deep redundancy in the final simulation, increasing the difficulty and cost of the final experiment. Second, to reduce the number of parameter updates in a single iteration, ADAPT-VQE introduces a warm-start strategy. Specifically, during parameter optimization, only the initial parameters of newly added excitation operators are set to 0, while the remaining optimized parameters use the optimization results from the previous iteration. Compared to the traditional approach of initializing all parameters to 0, this strategy makes the initial point of parameter optimization closer to the global optimum, reducing the number of parameter update steps in the optimization process, but the overall measurement cost remains high. Therefore, in applications that determine the molecular reactivity of materials based on quantum computing, the hypothesis constructed by the ADAPT-VQE algorithm may contain redundant operators, which leads to an unnecessary increase in the depth of the quantum circuit. At the same time, the parameter optimization process requires a large number of measurements, resulting in low computational efficiency and increased resource consumption.

[0005] Developing novel excitation operator selection strategies and parameter optimization schemes to achieve the dual goals of simplifying the design depth and reducing overall measurement costs is a key breakthrough direction for promoting the transformation of variable quantum eigenvalue solving algorithms from theoretical research to practical application, especially for efficiently and accurately determining the molecular reactivity of materials. 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: S1. Obtain the unitary coupling cluster single / double excitation hypothesis of the target material's molecules; extract single and double excitation operators from the unitary coupling cluster single / double excitation hypothesis to form an excitation operator pool; construct the complete Hamiltonian of the molecule based on the same set of spin orbitals as the one used to construct the excitation operator pool; for each excitation operator in the excitation operator pool, select excitation terms from the complete Hamiltonian that overlap with the spin orbital index of the excitation operator, and construct the corresponding sub-Hamiltonian; initialize the reference state and initialize the symmetric quantum hypothesis to a unit operator, wherein the symmetric quantum hypothesis follows the constraints of particle number conservation and spin symmetry; set an iteration termination condition including a parameter norm threshold and a maximum number of iterations, and initialize the number of iterations; S2. Determine whether the number of iterations exceeds the maximum number of iterations; if it does, proceed to S6; otherwise, prepare the current trial state based on the reference state and the current symmetric quantum assumption; for each excitation operator in the excitation operator pool, take the sub-Hamiltonian corresponding to the excitation operator as the target, and perform local variable quantum eigenvalue optimization involving only the excitation operator to obtain the convergence value corresponding to the excitation operator; S3. Determine whether the maximum norm of all the converged values ​​is less than the parameter norm threshold; if yes, proceed to S6; if no, proceed to S4. S4. Select the excitation operator with the largest convergence norm from the excitation operator pool, add the unitary operator corresponding to the excitation operator to the current symmetric quantum hypothesis, and add the convergence value to the current parameter set; S5. Taking the symmetric quantum fitting containing the newly added excitation operator and all parameters in the current parameter set as the object, and the complete Hamiltonian as the target, perform global variable quantum eigenvalue optimization, update all parameters until convergence; increment the number of iterations, and return to execute S2. S6. Based on the reference state, the final symmetric quantum design and the optimized parameter set, prepare the final test state, calculate the expected value of the complete Hamiltonian in the final test state, and obtain the ground state energy estimate of the molecule; S7. Determine the reactivity of the target material molecules based on the estimated ground-state energy of the molecules.

[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: In determining the molecular reactivity of materials using quantum computing, a new rule employing the parameter norm after local optimization as the selection criterion for excitation operators allows for more accurate screening of excitation operators that significantly contribute to energy reduction. This effectively avoids including redundant operators in the symmetric quantum fitting, directly reducing the depth and complexity of the final symmetric quantum fitting. Simultaneously, the scheme introduces a hot-start strategy, using the optimal parameters obtained from local variable quantum eigenvalue optimization as the initial values ​​for the operator in subsequent global variable quantum eigenvalue optimization. This makes the starting point of global optimization closer to the optimal solution, significantly reducing the number of iterations and gradient measurements required for global variable quantum eigenvalue optimization to converge. These two improvements work synergistically to significantly reduce the overall consumption of quantum computing resources while ensuring high-precision estimates of the molecular ground state energy, thereby improving the computational efficiency and feasibility of determining the molecular reactivity of 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, the optimization of local variable quantum eigenvalues ​​in S2 and the optimization of global variable quantum eigenvalues ​​in S5 both include: calculating the gradient using parameter offset rules and completing parameter optimization using the BFGS optimizer.

[0010] The advantages of adopting the above-mentioned further scheme are as follows: Using parameter offset rules to calculate gradients in the local and global variational quantum eigenvalue optimization can obtain accurate analytical gradient values, avoiding the approximation errors and numerical instabilities caused by the finite difference method, thereby improving the accuracy and reliability of parameter optimization. Combined with the BFGS optimizer for iteration, gradient information can be used to efficiently approximate the minimum value of the energy expectation function, accelerating the optimization convergence process. This combined optimization scheme reduces the number of quantum measurements required to reach convergence, saving quantum computing resources and providing an efficient and robust numerical optimization foundation for the entire process of determining reaction activity.

[0011] Furthermore, the reference state is the Hartree-Fock state of the molecule, the initialization iteration number is specifically set to 1, and the parameter norm threshold is a positive number greater than 0.

[0012] The advantages of adopting the above-mentioned further scheme are as follows: Clearly defining the reference state as the Hartree-Fock state of the molecule provides a reliable initial state with clear physical meaning and easy preparation by a quantum computer for constructing a symmetric quantum hypothesis. Initializing the number of iterations to 1 ensures that the algorithm starts execution from the correct logical starting point. Setting the parameter norm threshold to a positive number greater than 0 provides a reasonable and flexible criterion for terminating the iteration. This effectively identifies excitation operators that substantially contribute to the energy, avoiding the omission of key components, while preventing the algorithm from introducing unnecessary redundant operators or performing excessive iterations due to overly strict thresholds, thus achieving a balance between computational efficiency and result accuracy.

[0013] Further, based on the ground-state energy estimate of the molecule, the reactivity of the target material molecule is determined, including: obtaining the ground-state energy estimate of the transition state molecule related to the target material molecule; calculating the difference between the ground-state energy estimate of the transition state molecule and the target material molecule to obtain the activation energy; substituting the activation energy into a preset relationship model between activation energy and reaction rate constant to calculate the reaction rate constant of the target material molecule; and using the reaction rate constant as a quantitative characterization of the reactivity of the target material molecule.

[0014] The beneficial effects of adopting the above-mentioned further approach are as follows: by calculating the difference between the estimated ground-state energies of the target material molecules and the transition-state molecules, the activation energy of the reaction is obtained, directly converting the microscopic energy information output by quantum computing into key chemical reaction energy barrier parameters. Subsequently, by substituting the activation energy into the pre-defined quantitative relationship model of the Eileen formula, the reaction rate constant can be calculated. This rate constant, as a quantitative characterization of reactivity, enables the molecular energy results based on quantum computing to directly serve the prediction of chemical reaction trends and rates, providing a clear and quantifiable theoretical basis for practical applications such as material design and catalyst screening.

[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 an initialization module, a first judgment module, a second judgment module, a selection and addition module, an update module, a calculation module, and a determination module; The initialization module is used for: obtaining the unitary coupling cluster single and double excitation hypothesis of the target material's molecules; extracting single and double excitation operators from the unitary coupling cluster single and double excitation hypothesis to form an excitation operator pool; constructing the complete Hamiltonian of the molecule based on the same set of spin orbitals used to construct the excitation operator pool; for each excitation operator in the excitation operator pool, selecting excitation terms from the complete Hamiltonian that overlap with the spin orbital index of the excitation operator, and constructing the corresponding sub-Hamiltonian; initializing the reference state and initializing the symmetric quantum hypothesis to a unit operator, wherein the symmetric quantum hypothesis obeys the particle number conservation and spin symmetry constraints; setting an iteration termination condition including a parameter norm threshold and a maximum number of iterations, and initializing the number of iterations. The first judgment module is used to: determine whether the number of iterations exceeds the maximum number of iterations; if it exceeds, call the calculation module; otherwise, prepare the current trial state based on the reference state and the current symmetric quantum assumption; for each excitation operator in the excitation operator pool, take the sub-Hamiltonian corresponding to the excitation operator as the target, perform local variable quantum eigenvalue optimization involving only the excitation operator, and obtain the convergence value corresponding to the excitation operator; The second judgment module is used to: determine whether the maximum norm of all the converged values ​​is less than the parameter norm threshold; if yes, then call the calculation module; if no, then call the selection and addition module. The selection and addition module is used to: select the excitation operator with the largest convergence norm from the excitation operator pool, add the unitary operator corresponding to the excitation operator to the current symmetric quantum hypothesis, and add the convergence value to the current parameter set; The update module is used to: take the symmetric quantum fitting object containing the newly added excitation operator and all parameters in the current parameter set as the object, take the complete Hamiltonian as the target, perform global variable quantum eigenvalue optimization, update all parameters until convergence; increment the number of iterations, and return to call the first judgment module; The calculation module is used to: prepare a final trial state based on the reference state, the final symmetric quantum assumption and the optimized parameter set, calculate the expected value of the complete Hamiltonian in the final trial state, and obtain the ground state energy estimate of the molecule; The determining module is used to: determine the reactivity of the target material molecules based on the estimated ground-state energy of the molecules.

[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 local variable quantum eigenvalue optimization performed by the first judgment module and the global variable quantum eigenvalue optimization performed by the update module both include: calculating the gradient using parameter offset rules and completing parameter optimization using the BFGS optimizer.

[0018] Furthermore, the reference state is the Hartree-Fock state of the molecule, the initialization iteration number is specifically set to 1, and the parameter norm threshold is a positive number greater than 0.

[0019] Furthermore, the determining module is specifically used to: obtain the ground state energy estimate of the transition state molecule related to the target material molecule, calculate the difference between the ground state energy estimate of the transition state molecule and the target material molecule to obtain the reaction activation energy; substitute the reaction activation energy into a preset relationship model between activation energy and reaction rate constant to calculate the reaction rate constant of the target material molecule, and use the reaction rate constant as a quantitative characterization of the reactivity of the target material molecule.

[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 unitary coupling cluster single / double excitation hypothesis of the target material's molecules; extract single and double excitation operators from the unitary coupling cluster single / double excitation hypothesis to form an excitation operator pool; construct the complete Hamiltonian of the molecule based on the same set of spin orbitals as the one used to construct the excitation operator pool; for each excitation operator in the excitation operator pool, select excitation terms from the complete Hamiltonian that overlap with the spin orbital index of the excitation operator, and construct the corresponding sub-Hamiltonian; initialize the reference state and initialize the symmetric quantum hypothesis to a unit operator, wherein the symmetric quantum hypothesis follows the constraints of particle number conservation and spin symmetry; set an iteration termination condition including a parameter norm threshold and a maximum number of iterations, and initialize the number of iterations; Wherein, the reference state is the Hartree-Fock state of the molecule, the number of initialization iterations is specifically set to 1, and the parameter norm threshold is a positive number greater than 0, such as 0.0001 or 0.001, which can be set according to the actual situation.

[0027] The unitary coupled cluster single-double excitation hypothesis is a parameterized quantum circuit form used in quantum computational chemistry to describe the electronic structure of molecules. It consists of a series of unitary exponential operators derived from the single and double excitation operators of fermions. This hypothesis aims to prepare quantum trial states that can approximate the true ground state and low-excitation states of molecules with high precision. Mathematically, a unitary coupled cluster single-double excitation hypothesis containing multiple excitation operators can be represented as a product of multiple exponential operators.

[0028] The reference state is the initial quantum state at the start of the algorithm, typically chosen as the ground state of the molecule under the mean-field approximation, i.e., the Hartree-Fock state. This state is a standard starting point in computational chemistry, and its wavefunction is the Slater determinant of all occupied spin orbitals. In quantum computing, the Hartree-Fock state usually corresponds to a specific computational basis state for a set of qubits. For example, for a closed-shell molecule, its Hartree-Fock state corresponds to the first N qubits being in the |1> state and the remaining qubits being in the |0> state, where N is the number of electrons.

[0029] The symmetric quantum hypothesis is a quantum circuit composed of a series of parameterized quantum gate operations. Its function is to evolve the reference state into a trial state that is closer to the eigenstate of the target molecule. The "symmetry" of this hypothesis is reflected in the fact that its construction process requires the generated quantum state to maintain certain physical conservation quantities, and its circuit structure is determined by the selected excitation operator and its parameters.

[0030] The identity operator is an operator that does not alter a quantum state. In quantum mechanics, the identity operator, when acting on any quantum state, yields that quantum state itself. In the initialization step, setting the symmetric quantum hypothesis as the identity operator means that the initial quantum circuit does not contain any parameterized gate operations, and the trial state is equal to the reference state.

[0031] The symmetric quantum hypothesis, which adheres to the constraints of particle number conservation and spin symmetry, means that the expected values ​​of the total number of electrons and the total spin quantum number of the quantum trial state constructed by this hypothesis are consistent with those of the reference state. This is achieved by using only those excitation operators (such as single excitation operators) that do not change the total number of particles and the total spin z-component in the second quantization form. and double-excitation operator These operators are constructed to meet the corresponding symmetry requirements and are naturally realized.

[0032] The specific implementation process of S1 is as follows: S10. Obtain the unitary coupled cluster single and double excitation hypothesis of the target material's molecule. This process is accomplished by calling a mature classical quantum chemistry computational software package. The user inputs the geometric structure and basis set information of the target molecule. The software package generates a complete list of all single and double excitation operators for the molecule under the selected basis set by solving the Hartree-Fock equation and performing subsequent coupled cluster theoretical calculations. These operators constitute the components of the theoretical unitary coupled cluster single and double excitation hypothesis. For a given molecule with... Molecules with 10 spin orbitals, this list contains Single-trigger operator and Double-excitation operator , where index Indicates occupied track, index Indicates a virtual orbit.

[0033] S11. Extract single-excitation operators and double-excitation operators from the obtained unitary coupling cluster single- and double-excitation scheme to form an excitation operator pool. Specifically, directly read the excitation operator list output by the classic software in S10, and extract all single-excitation operators from this list. With double-excitation operator Stored in a data structure, this data set is called the trigger operator pool, denoted as... The activation operator pool is a candidate set for selecting key operators in subsequent iterative algorithms.

[0034] S12. Based on the same set of spin orbitals as the one used to construct the excitation operator pool, construct the complete Hamiltonian of the molecule. The set of spin orbitals is determined by the basis set in S10, and the total number is... The electronic Hamiltonian of a molecule, expressed in second-order quantization, is: in, and These are the single-electron integral and the two-electron integral, respectively, and these scalar coefficients are also calculated using classical quantum chemistry software. and It is an excitation term composed of combinations of fermion generation and annihilation operators. (Symbol) Traverse all Index of spin orbitals. Complete Hamiltonian. It contains all possible excitation terms that describe all electronic interactions in a molecule.

[0035] S13. For each excitation operator in the excitation operator pool, select excitation terms from the complete Hamiltonian that overlap with the spin-orbit index acted upon by that excitation operator, and construct the corresponding sub-Hamiltonian. For a given excitation operator, such as a single excitation operator... The set of track indices it functions on is Traversing the complete Hamiltonian Each item in, for example, item Check the set of spin orbit indexes involved in this item. Whether or not There is overlap. If the following conditions are met... Then this activation term Added to the sub-Hamiltonian constructed for this excitation operator In the middle. For all excitation operators in the pool This process is repeated to generate a smaller sub-Hamilton for each operator. For biexcitation operators... Its track index set is The filtering rules are the same.

[0036] S14. Initialize the reference state and initialize the symmetric quantum hypothesis to the unit operator. Initialize the reference state to the Hartree-Fock state of the target molecule. On a quantum computer, this corresponds to representing A spin orbit Each qubit is prepared into a specific computational basis state, such as the previous one. Each quantum bit is set to The rest are set to The symmetric quantum hypothesis is initialized to the identity operator. At the quantum circuit level, this represents an empty circuit that does not contain any parameterized quantum gates. Therefore, the initial trial state... .

[0037] S15. Set an iteration termination condition that includes a parameter norm threshold and a maximum number of iterations, and initialize the number of iterations. The parameter norm threshold is a small positive real number. This is used to determine whether the parameter of the triggering operator is small enough to be ignored; its value is typically in the range of... to The range is selected based on the accuracy requirements; for example, it can be set to... Maximum number of iterations It is a positive integer used to prevent the algorithm from looping infinitely; for example, it can be set to... Number of iterations Initialize to This indicates that the first iteration is about to begin.

[0038] S2. Determine whether the number of iterations exceeds the maximum number of iterations; if it does, proceed to S6; otherwise, prepare the current trial state based on the reference state and the current symmetric quantum assumption; for each excitation operator in the excitation operator pool, take the sub-Hamiltonian corresponding to the excitation operator as the target, and perform local variable quantum eigenvalue optimization involving only the excitation operator to obtain the convergence value corresponding to the excitation operator; The optimization of local variational quantum eigenvalues ​​in S2 includes: calculating the gradient using the parameter offset rule and performing parameter optimization using the BFGS optimizer.

[0039] Here, the current symmetric quantum hypothesis refers to the parameterized quantum circuit that has been constructed in the current iteration of the algorithm. It consists of the sequential product of the unitary exponent operators corresponding to all the excitation operators selected and added to the hypothesis from the beginning of the algorithm to the current iteration. This hypothesis indicates that the set of variational parameters of the quantum operation sequence constructed by the algorithm so far for evolving the reference state to a better trial state has also been optimized in previous iterations.

[0040] The current trial state is a quantum state prepared by applying the current symmetric quantum assumption to the initial reference state. Mathematically, if the current iteration index is... The current symmetric quantum hypothesis is set as ,in It was after the previous Given the set of parameters obtained after round-robin global optimization, the current trial state is represented as: This state serves as the starting point for evaluating the contributions of candidate excitation operators and executing a new round of optimization.

[0041] Among these, the optimization of local variational quantum eigenvalues ​​involving only the excitation operator is a special type of parameter optimization process. In this process, the optimization objective is not the complete molecular Hamiltonian, but rather the sub-Hamiltonian associated with the excitation operator; simultaneously, there is only one variational parameter, namely the parameter inherent to the excitation operator itself. The optimization goal is to find the optimal value of this single parameter, while keeping the current trial state and all other operator parameters fixed, so that the expected value of the sub-Hamiltonian under that parameter is minimized.

[0042] The parameter offset rule is a protocol for accurately calculating the derivative of the expected value of a parameterized quantum circuit with respect to its parameters. This rule applies to parameterized quantum gates composed of generators satisfying specific commutation relations. For forms of... The door, among which It is to satisfy Generator, target Hamiltonian Expected value The derivative can be obtained by calculating the expected value at two offset points and taking the difference, as shown in the formula: This avoids the approximation errors and numerical instabilities associated with the finite difference method, and is one of the standard techniques for obtaining gradients in variational quantum algorithms.

[0043] The BFGS optimizer is a classic quasi-Newton numerical optimization algorithm. This optimizer iteratively searches for the minimum point of a multivariable function. In each iteration, it uses the function value and gradient information at the current point to update an approximate matrix with respect to the Hessian matrix inverse of the objective function, thus determining the next search direction and step size. Due to its superlinear convergence speed and avoidance of direct calculation of the second derivative, the BFGS optimizer is widely used in variational quantum eigenvalue optimization—parameter update processes driven by classical computers and based on quantum measurement feedback.

[0044] The specific implementation process of S2 is as follows: S20. The algorithm maintains an iteration counter. Its value is initialized to in step S1. At the beginning of each iteration, it is necessary to compare the current iteration number. With the preset maximum number of iterations If conditions If the condition is met, it means the algorithm has reached the preset iteration limit. At this point, the iteration loop should be terminated, and the process should jump directly to step S6 to output the final result. If the condition is not met, i.e. If the algorithm fails, it will continue to execute the subsequent operations of this round.

[0045] S21. Based on the reference state and the current symmetric quantum assumption, prepare the current test state, reference state The state has been initialized to Hartree-Fock in step S1. Current symmetric quantum hypothesis. and its corresponding optimized parameters This is generated from step S5 of the previous iteration. For the first iteration, since there is no previous iteration, Defined as the unit operator Parameter set It is an empty set. Prepare the current trial state. The operation is performed on the quantum processor: first, the qubits are prepared into a reference state. Then run the representation The quantum circuit. Once the circuit is running, the quantum state in the quantum processor corresponds to the current trial state. .

[0046] S22. Traverse each activation operator in the activation operator pool, and the activation operator pool... The process has been completed in step S1. The algorithm creates a loop to process the pool sequentially. Each of the activation operators in For each operator The algorithm will then perform subsequent local optimization processes. (Symbol) Here, it serves as a general index for the activation operator, representing a single activation operator. It can also represent a double-excitation operator. .

[0047] S23. For the currently traversed trigger operator Define and perform local variational quantum eigenvalue optimization involving only a single parameter of the excitation operator. The objective function of this process is the sub-Hamiltonian. The expected value of the sub-Hamiltonian has been specifically constructed for this operator in step S1. The optimization involves only one variational parameter. It is applied to the operator The rotation angle on. The optimization problem is formally defined as finding the parameters. This minimizes the following energy expectation: In this formula, This indicates that only for the current trial state Apply by operator and parameters Unitary operation Subsequently, the quantum state of the obtained sub-Hamiltonian The expected value. yes The Hermitian conjugate. The optimization objective is to adjust... To minimize .

[0048] S24. Using parameter offset rules to calculate the objective function in local variational quantum eigenvalue optimization. Regarding parameters gradient The parameter offset rule is a scheme for accurately calculating the derivative of the expected value of a parameterized quantum circuit. For many common quantum gate parameterizations, including unitary operations generated by excitation operators, their gradients can be obtained by measuring the expected value at two different parameter points and taking the difference. Specifically, for the current parameter value... The gradient calculation formula is: This means that in order to calculate in The gradient at a given point needs to be prepared on the quantum processor, corresponding to the parameters. and quantum state and And measure the sub-Hamiltonian multiple times in each state. To obtain the expected value and The estimated value is then substituted into the above formula to calculate the gradient.

[0049] S25. The parameter optimization is performed using the BFGS optimizer, a classic quasi-Newton numerical optimizer. The algorithm runs the BFGS optimization program on a classical computer, which calls an algorithm to calculate the objective function value. and its gradient The subroutine. Whenever the BFGS optimizer needs to evaluate function values ​​or gradients, it sends the corresponding circuit task to the subprocessor and obtains the measurement results. The BFGS optimizer uses this information to iteratively update the parameters. The estimated value is obtained, and an inverse matrix approximating the Hessian matrix is ​​maintained internally to determine the search direction. The optimization process continues until the convergence criteria built into BFGS are met, such as the gradient norm being less than a certain tolerance or the function value change being less than a certain threshold. The parameter value obtained at this point is recorded as the convergent value. .

[0050] S26, When targeting the triggering operator After the local variational quantum eigenvalues ​​are optimized, the algorithm obtains the convergence parameter values. Save it and associate it with the operator. Complete the activation operator pool. After iterating through all operators in the pool, the algorithm will obtain a complete set containing every firing operator in the pool. Convergence value of independently optimized parameters These values ​​will be used for the judgment in step S3 and the selection in step S4.

[0051] S3. Determine whether the maximum norm of all converged values ​​is less than the parameter norm threshold; if yes, proceed to S6; if no, proceed to S4. The specific implementation process is as follows: S30. Collect and organize all convergence values ​​of the local variational quantum eigenvalues ​​from step S2. After completing the loop in step S2, the algorithm stores a data set in the memory of a classical computer. Each element in this set corresponds to the pool of excitation operators. One of the excitation operators And associated with a real number This real number This is the convergent value obtained after performing local variational quantum eigenvalue optimization on the operator involving only a single parameter. Assume an excitation operator pool. The CCP If there are 1 triggering operator, then the set of convergent values ​​can be represented as: .

[0052] S31. Calculate the absolute value of each convergent value, i.e., its norm, for each convergent value in the set. The algorithm performs a mathematical operation that takes the absolute value. In the real number field, the norm of a number is usually taken as its absolute value. Therefore, for each Calculate its norm .if If it is a positive number or zero, then ;if If it is a negative number, then The computation is performed on a classical processor, resulting in a new set of norms. .

[0053] S32. The obtained norm set Perform a single traversal search operation. Initialize a variable. Set its value to a very small number, such as 0. Then check each element in the set in turn. If the current check Greater than The value stored in will be Update the value to the current After the iteration is complete, the variable... The value stored in the table is the maximum norm of all convergent values. This operation is implemented on a classic computer using a simple sequence of comparison and assignment instructions.

[0054] S33. Compare the found maximum norm with a preset parameter norm threshold. Parameter norm threshold It is a positive real number, which is preset in step S1, for example... The algorithm performs a numerical comparison operation on a classical computer: determining... Does this logical condition hold true? This is a precise floating-point comparison.

[0055] S34 determines the execution branch of the algorithm based on the comparison result. This decision logic is implemented through conditional statements on a classic computer. Specifically, if the comparison result in S33 is "yes", that is, if the condition is met, then the branch is executed. If the condition is met, it means that in the current trial state, even after independent local optimization, the magnitude of the optimal parameter of any excitation operator in the excitation operator pool is less than the set threshold. This is interpreted as the potential contribution of all candidate operators to further energy reduction being negligible, and the algorithm has converged to a sufficiently good trial state. Therefore, the algorithm execution flow jumps, no longer performing subsequent operator addition and global optimization, but directly proceeding to step S6 to calculate and output the final energy estimate. If the comparison result in S33 is "no", i.e., condition... Not true (equivalent to) If the threshold is met, it means that there exists at least one excitation operator whose norm of the local optimal convergence value is greater than or equal to the threshold. This indicates that adding this operator to the current symmetric quantum hypothesis could significantly improve the trial state. Therefore, the algorithm continues to execute the process, proceeding to step S4, to select the excitation operator from the pool that is most likely to bring improvement and incorporate it into the hypothesis.

[0056] S4. Select the excitation operator with the largest convergence norm from the excitation operator pool, add the unitary operator corresponding to the excitation operator to the current symmetric quantum hypothesis, and add the convergence value to the current parameter set.

[0057] The current parameter set is a collection of optimized variational parameters that correspond one-to-one with the excitation operators in the current symmetric quantum hypothesis during algorithm execution. In the current iteration, this set contains the optimal parameter values ​​for all excitation operators selected and added to the hypothesis from the start of the algorithm up to this iteration. The order of elements in the parameter set is consistent with the order of operators in the symmetric quantum hypothesis, together defining the specific form of the hypothesis.

[0058] The specific implementation process of S4 is as follows: S40. Identify and locate the excitation operator with the largest convergence norm. This operation depends on the calculation results of step S3. In step S3, the algorithm has already calculated the pool of excitation operators. Each triggering operator The corresponding local optimization convergence value And from this, the maximum norm was found. At this point, the algorithm needs to process the stored data on a classical computer. The data pairs are retrieved to find the one that satisfies the criteria. excitation operator Since multiple operators may have the same maximum norm, the algorithm typically selects the first operator found as the selected operator, denoted as . At the same time, record the convergence value corresponding to this operator. .

[0059] S41, Each triggering operator (whether it is single excitation) or dual stimulation Each of these defines a parameterized unitary operator. The mathematical form of this unitary operator is an exponential mapping. ,in This is the convergence value obtained for the operator just from the local optimization in step S2. This exponential operator represents a parameterized quantum gate module implemented on the quantum circuit, whose parameters... It has been fixed to the optimized value.

[0060] S42. Let the current iteration index be... The current (i.e., the first) The symmetric quantum fitting after round iterations is The algorithm's rule is to append the new unitary operator to the left of the existing set. This update operation is mathematically defined as a reassignment of the set: The left side of the equals sign Indicates the updated version used for the first A new symmetric quantum hypothesis for round-based global optimization. The symbol " " indicates an assignment operation, " "" represents operator multiplication (i.e., the cascading of quantum circuits). At the physics and circuit level, this means that it will represent The quantum gate module is spliced ​​into the representation The right end of the existing quantum circuit (observed from the initial reference state as the input starting point) is used to form a deeper new quantum circuit.

[0061] S43, Let the first The current parameter set after round of iterations is It is a collection A sequence of optimization parameters. The algorithm needs to create a new parameter sequence. To correspond with the updated proposed design Since the new unitary operator is added to the far left of the proposed configuration, according to the principle of parameter-operator order correspondence, its parameters... The parameter set should be the first element of the new parameter set, followed by the original parameter sequence. Therefore, the parameter set update operation is defined as: . The concatenation operation represents the joining of sequences, i.e., joining individual elements. spliced ​​into sequence The front. New parameter set. Includes These parameters will serve as the initial values ​​for the global variable quantum eigenvalue optimization in the next step (step S5).

[0062] S5. Taking the symmetric quantum fitting containing the newly added excitation operator and all parameters in the current parameter set as the object, and the complete Hamiltonian as the target, perform global variable quantum eigenvalue optimization, update all parameters until convergence; increment the number of iterations, and return to execute S2. The global variational quantum eigenvalue optimization in S5 includes: calculating the gradient using the parameter offset rule and performing parameter optimization using the BFGS optimizer.

[0063] Here, the newly added excitation operator refers to the excitation operator with the largest convergence norm selected from the excitation operator pool in step S4 during the current iteration. This operator is the only new component selected to be added to the symmetric quantum hypothesis in this iteration, and its corresponding unitary operator... It has already been constructed in the previous step.

[0064] The specific implementation process of S5 is as follows: S50, the optimization goal is the complete Hamiltonian. The expected value. The object of optimization is the symmetric quantum hypothesis updated in step S4. and the complete set of parameters in the current parameter set. Parameter set It is a collection A vector of variational parameters, denoted as These parameters will serve as independent variables for optimization.

[0065] S51, Global optimization with an initial parameter vector To begin. According to the rules of the invention, this initial value is directly taken from the set of parameters determined at the end of step S4. In other words, This means that the parameters of the newly added excitation operator are initialized to their local optimization convergence values. The parameters of the original triggering operators in the proposed scheme are initialized to the optimal values ​​after the previous round of global optimization. This initialization strategy is called "warm start".

[0066] S52. The objective function is the expected value of the complete Hamiltonian in the trial state prepared from the current assumptions and parameters. The mathematical expression is: ,in, It is a symmetric quantum hypothesis that includes newly added excitation operators. It is a Hartree-Fock reference state. yes Hermitian conjugate. The task of global variational quantum eigenvalue optimization is to find an optimal parameter vector. This makes the expected value To reach the minimum.

[0067] S53. In order to optimize the objective function It is necessary to calculate it with respect to each variational parameter. ( partial derivatives of ) For a hypothesis consisting of exponential forms of the excitation operator, the parameter offset rule applies to each parameter. Calculate specific parameters. When calculating the gradient, all other parameters need to be kept constant. According to the rule, the gradient is given by the following formula: here, This indicates that only the parameter vector will be used. The first in Each component increases The remaining components remain unchanged, and then the new expected value is calculated; Similarly, each gradient calculation requires preparing the corresponding quantum state and measuring the complete Hamiltonian on the quantum processor. The expected value.

[0068] S54. The BFGS optimizer program on the classic computer is started to minimize the objective function. The optimizer's workflow is as follows: it starts from the initial point... Initially, a subroutine is repeatedly requested to retrieve the function value at the current parameter point. and gradient vector Whenever a request is received, process S53 is executed, acquiring the necessary data through quantum measurement and returning it to the BFGS optimizer. The BFGS optimizer uses this information to update its internal approximate Hessian inverse matrix and calculates a new parameter vector proposal point with a lower objective function value. This process iterates continuously.

[0069] The S55 and BFGS optimizers typically have built-in convergence criteria. These criteria include: the L2 norm of the gradient vector is less than a certain tolerance. ,Right now Or, the change in function value between two consecutive iterations is less than a certain tolerance. ,Right now When any convergence criterion is met, the BFGS optimizer stops iterating and outputs the current optimal parameter vector, denoted as . .

[0070] S56. Convert the convergence parameter vector output by the BFGS optimizer. Save this as the final result of this round of global variable quantum eigenvalue optimization. This will be used as the parameter corresponding to the "current symmetric quantum hypothesis" in the next iteration (i.e., step S2).

[0071] S57. After completing global optimization, the algorithm needs to update the iteration counter. This involves updating the variable representing the iteration round. The value is increased by 1, which means the operation is performed. This operation is performed on a classic computer. The algorithm then returns to the beginning of step S2, using the updated number of iterations. The updated symmetric quantum hypothesis (At this point, its parameters have been updated to) (and the corresponding parameter set) to start a new round of iteration.

[0072] S6. Based on the reference state, the final symmetric quantum design and the optimized parameter set, prepare the final test state, calculate the expected value of the complete Hamiltonian in the final test state, and obtain the ground state energy estimate of the molecule; The final symmetric quantum hypothesis is the parameterized quantum circuit constructed when the algorithm terminates its iterations. It is composed of the sequential product of the unitary exponent operators corresponding to all the excitation operators selected and added to the hypothesis throughout the entire process from initialization to termination of the algorithm. This hypothesis represents the final sequence of quantum operations found by the algorithm that can evolve the initial reference state to the closest approximation of the target molecule's ground state, and its circuit structure remains unchanged after the iterations terminate.

[0073] The optimized parameter set is a set of variational parameter values ​​that strictly correspond to each excitation operator in the final symmetric quantum hypothesis and are obtained after optimization through the last round of global variational quantum eigenvalue solving in step S5. The parameter values ​​in this set are numerical solutions that make the expected value of the complete Hamiltonian reach a local or global minimum under the final hypothesis, and they collectively determine the specific form of the final trial state.

[0074] The ground-state energy of a molecule refers to the energy value possessed by the target molecule when it is in its stable state with the lowest electronic energy. In quantum chemistry, it is the smallest eigenvalue of the molecular electronic Hamiltonian. The ground-state energy estimate obtained through the variational quantum eigenvalue solving algorithm is the expected value of the complete Hamiltonian in the final trial state, which is the best approximation of the true ground-state wavefunction found by the variational method.

[0075] The specific implementation process of S6 is as follows: S60. The process terminates in step S3 if the convergence condition is met (the norm of the local optimization parameters of all candidate operators is less than the threshold) or if the maximum number of iterations is reached in step S2. Let the iteration index at termination be... At this point, two key objects are output from the algorithm's memory: one is the final symmetric quantum hypothesis. The other is the corresponding optimized parameter set. .symbol Indicates the final iteration index, It is a collection A vector of optimization parameters.

[0076] S61, Reference State This is the initial Hartree-Fock state, as defined in step S1. The preparation process is performed on the quantum processor: first, the qubits are reset and initialized to the reference state. Next, the operation represents the final symmetric quantum hypothesis. The quantum circuit, and the optimized parameter set The specific values ​​are loaded into the corresponding variational parameter positions of the circuit. After the circuit has finished running, the quantum state in the quantum processor is the final test state. This state is strictly defined by the formula: ,in, This represents the final trial state, that is, the quantum state that approximates the molecular ground state obtained after the algorithm iterations are completed; The final symmetric quantum hypothesis is a parameter vector-dependent one. The unitary operator is used to evolve the reference state into the final trial state; Represents the optimized parameter set, which is a real number vector containing all parameter values ​​that converge after global optimization; This represents the reference state, typically taken as the Hartree-Fock state. .

[0077] S62, Complete Hamiltonian The general form of the structure constructed in step S1 is as follows: ,in, It represents the complete Hamiltonian of a molecule and describes all electronic interactions within the molecule; This represents the spin orbital index, with a value range of 100. ,in It is the total number of spin orbitals; This represents the single-electron integral coefficient, indicating the rate of a single electron's movement from its orbital orbit. Jump to orbit Energy contribution; This represents the integral coefficient of the two electrons, indicating the distances from the orbital to the electron's orbital. Jump to orbit Energy contribution; The operator represents a single excitation term, which in second-order quantization indicates the generation of an orbital excitation term. The electron annihilates one in orbit. electrons; The double-excitation operator indicates the simultaneous production of two electrons (in orbitals). And annihilate two electrons (in orbit) ).

[0078] Calculate the expected value Need to estimate .because It is a linear combination of multiple observables, whose expected value is equal to the linear combination of the expected values ​​of each observation. The specific operation is: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Each term (or a new set of observations obtained by reducing the number of measurements through linear combination) is used as a measurement operator. For each term, in the prepared final trial state... Multiple projection measurements are performed, and the frequency of the measurement results is statistically analyzed to estimate the expected value of each term. The weighted sum of the expected values ​​of all terms is the total expected value of the complete Hamiltonian. ,in, This represents the estimated ground-state energy of the molecule, i.e., the expected value of the complete Hamiltonian in the final trial state; Indicates the operator In state Quantum expectation value calculation.

[0079] S63, a classical processor, collects all data obtained from quantum measurements and completes the... Numerical calculation of this scalar value. This is the algorithm's final estimate of the ground-state energy of the target molecule. The algorithm outputs this value to the user as the core result of this quantum computational chemical simulation. This result can be further used to compare different molecular structures, verify the algorithm's accuracy, or serve as input for the reactivity analysis in step S7.

[0080] S7. Determine the reactivity of the target material molecules based on the estimated ground-state energy of the molecules.

[0081] Optionally, in the above technical solution, determining the reactivity of the target material molecules based on the estimated ground-state energy of the molecules includes: S70. Obtain the ground state energy estimate of the transition state molecule related to the target material molecule, calculate the difference between the ground state energy estimate of the transition state molecule and the target material molecule, and obtain the activation energy of the reaction; The transition state molecule associated with the target material molecule refers to the highest-energy and unstable intermediate configuration molecule in the chemical reaction pathway in which the target material molecule participates and transforms into a specific product. From a quantum chemical perspective, it corresponds to a first-order saddle point on the potential energy surface between the reactants and products. Its geometry, electronic configuration, and unique imaginary frequency vibrational mode are different from those of the reactants and products. Determining the structure and properties of this transition state molecule is a crucial prerequisite for calculating the reaction rate using transition state theory. Taking the addition reaction of hydrogen molecules with ethylene as an example, the target material molecule is ethylene. The associated transition state molecule can be described as follows: In the pathway where the carbon-carbon double bond of ethylene reacts with hydrogen molecules to form ethane, there exists a highest-energy unstable configuration, in which the HH bond of the hydrogen molecule is breaking, and two hydrogen atoms simultaneously begin to bond with two carbon atoms of ethylene, forming a cyclic [CH2-CH2-HH]⁺ four-membered ring structure. This is the transition state molecule of the reaction. The ground state energy estimates of the ethylene molecule and this transition state molecule are obtained through quantum calculations, and the difference is the activation energy of the reaction.

[0082] The specific implementation process of S70 is as follows: S700. Identify the target chemical reaction and locate the transition state molecular structure. Specifically, clarify the specific chemical reaction in which the target material molecule participates. Using classical computational chemistry methods, such as density functional theory or ab initio methods, combined with transition state search algorithms (such as the synchronous transition method, quasi-Newton method, or micro-motion elastic band method), optimize and determine the precise three-dimensional geometric configuration of the transition state molecule along this chemical reaction pathway on a classical computer. This configuration includes the spatial coordinates of all atoms and is the basis for calculating its electronic structure. Let the target material molecule be R, and its transition state molecule be TS.

[0083] S701: Based on the geometry of the transition state molecule TS obtained from S700, the same basis set as that used in calculating the target material molecule is selected to maintain computational consistency. Key physical quantities such as the total number of electrons and spin multiplicity of the transition state molecule under the selected basis set are determined. These parameters will serve as inputs for constructing the fermionic Hamiltonian of the transition state molecule.

[0084] S702. Perform a complete quantum computation process on the transition state molecule to obtain its ground state energy estimate. This process completely repeats the entire algorithm described in steps S1 to S6 of the technical solution, but the input molecule is replaced by the transition state molecule TS instead of the target material molecule R. Specifically, using the geometry of the transition state molecule TS and the selected basis set as input, the following steps are performed: obtain the unitary coupled cluster single and double excitation simulation of the transition state molecule and construct its excitation operator pool; construct the complete Hamiltonian of the transition state molecule; construct the sub-Hamiltonian for each excitation operator in the pool; initialize the reference state (the Hartree-Fock state of the transition state molecule); set the iteration termination condition and run the Param-ADAPT-VQE algorithm for simulation construction and parameter optimization; finally, prepare the final trial state of the transition state molecule and calculate the expected value of its complete Hamiltonian. The output of this expected value is the ground state energy estimate of the transition state molecule, denoted as . .symbol This represents the ground state energy of the transition state molecule obtained through quantum algorithms.

[0085] S703, ground state energy estimate of target material molecule R The value has already been obtained and output through quantum computing in step S6. In this step, the value is read directly from storage. .

[0086] S704. According to transition state theory, under the adiabatic potential energy surface approximation, the energy barrier of a reaction, i.e., the activation energy, can be approximated as the energy difference between the ground-state electrons of the transition state molecule and the reactant molecule. Therefore, the activation energy... Calculated using the following formula: ,in, It is the calculated ground-state energy estimate of the transition state molecule. It is the estimated value of the ground state energy of the target material molecules. The unit is usually Hartley. This calculation is performed on a classical computer and is a simple scalar subtraction operation. The result is... The value is the activation energy of the reaction, which quantitatively characterizes the energy barrier that the chemical reaction needs to overcome.

[0087] S71. Substitute the activation energy of the reaction into a preset model relating activation energy and reaction rate constant, calculate the reaction rate constant of the target material molecule, and use the reaction rate constant as a quantitative characterization of the reactivity of the target material molecule.

[0088] The pre-defined model relating activation energy to reaction rate constant is a mathematical formula based on chemical kinetics theory that links the macroscopically observable chemical reaction rate constant to the microscopic molecular energy barrier (i.e., activation energy or activation free energy). In this invention, this model specifically refers to the Eileen formula, which is the core expression of transition state theory and establishes a quantitative relationship between the reaction rate constant and the Gibbs free energy difference between reactants and transition states.

[0089] The specific implementation process of S71 is as follows: S710. Select and confirm the specific form of the preset model relating activation energy and reaction rate constant. Specifically, the Irene formula can be used as the model for calculating the reaction rate constant. in, Represents the rate constant of the chemical reaction to be calculated; It is the Boltzmann constant; It is the thermodynamic temperature at which the reaction takes place; It is Planck's constant; It is the activation free energy of the reaction. The Eileen formula is the standard model in chemical kinetics, and its inherent property is reflected in the direct encoding of this formula into a fixed calculation module during algorithm implementation.

[0090] S711. Prepare the input parameters required for the relational model calculation. The data required for the calculation includes: ① Activation energy of the reaction. This value is obtained from the previous step, and is the difference between the estimated ground-state energy of the transition state molecule and the target material molecule. This energy difference is usually expressed in Hartley units. ② Reaction temperature ③ Physical constant: Boltzmann constant and Planck's constant These are recognized physical constants that can be directly accessed from the constant library.

[0091] A key conversion step is to change the electron energy difference. Approximate or converted into activation free energy In simple calculations, contributions such as entropy change and zero-point energy are often neglected, and the activation enthalpy is... Approximately And further hypothesize Therefore, directly use Substitute into the formula For more accurate calculations, additional frequency analysis is required to determine the vibrational partition functions of the transition state and reactants, thereby obtaining... This step is typically performed in classical quantum chemistry calculations. Let's assume an approximation is used here. .

[0092] S712. Substitute the input parameters into the Eileen formula and perform the calculation. Write or call a calculation function on a classical computer to implement the Eileen formula. The calculation process follows the following mathematical order: ① Calculate the pre-exponential factors: ② Calculate the parameters of the exponential term: Here use Approximate substitution. ③ Calculate the exponential term: ④ Calculate the reaction rate constant: It should be noted that in the calculation, [the following will be used] Convert Hartley to Joules / moles or with The units are consistent to ensure that the exponent is a dimensionless number. The entire calculation process is a deterministic numerical operation, performed by a classical computer.

[0093] S713, Calculated numerical values That is, the target material molecules at a specific temperature Below, the reaction rate constant is the chemical reaction proceeding along the studied reaction pathway. Reaction rate constant The magnitude of the reaction directly reflects the ease and speed of the chemical reaction: A higher value indicates a faster reaction rate under the same conditions, and higher reactivity of the target material molecules; conversely, a lower value indicates a lower reactivity. The smaller the value, the lower the reactivity. Therefore, the algorithm ultimately determines the reaction rate constant. The system outputs quantitative and comparable indicators of the reactivity of target material molecules to users, completing the entire process from quantum microscopic calculations to macroscopic chemical property predictions.

[0094] Optionally, the above technical solution also includes: S80. Based on the final symmetric quantum hypothesis, construct a quantum circuit; The final symmetric quantum hypothesis is the parameterized quantum operation sequence obtained after the algorithm iteration terminates. Its mathematical form is the product of multiple unitary exponent operators, for example... Each of them This indicates a selected single-excitation or double-excitation operator. These are the corresponding optimized parameters. The purpose of constructing the corresponding quantum circuit is to realize this hypothesis on a physical quantum processor, thereby preparing the final test state.

[0095] The specific implementation process of S80 includes: S800, Output Final Symmetric Quantum Simulation and its corresponding list of excitation operators and parameter list Each triggering operator It has a definite form under the fermion representation, such as a single-excitation operator. or double-excitation operator The spin orbit index of its effect is known.

[0096] S801. For fermion excitation operators, a specific quantum circuit compilation scheme is required. For single excitation operators... Its exponential form can be realized using a fixed subcircuit consisting of two CNOT gates and several single-qubit rotation gates. For bi-excitation operators It can be implemented using a fixed sub-circuit consisting of 13 CNOT gates and several single-qubit rotation gates. The design of these sub-circuits ensures that, under qubit encoding, the effect of this quantum gate sequence is equivalent to the target fermion unitary operator under the desired mapping. Parameters It is encoded into the angle of the corresponding single-qubit rotation gate.

[0097] S802, according to the final symmetrization quantum hypothesis The order in which the excitation operators appear is either from right to left (corresponding to the first operator applied from the initial reference state) or from left to right (corresponding to the timing of line execution), and the sub-lines corresponding to each excitation operator are connected sequentially. Specifically, if it is intended to be set as Furthermore, since the input of the quantum circuit is on the left and the output is on the right, then... The sub-line is executed first, placed on the far left of the line; then... The sub-lines, and so on, until... The sub-circuit is placed on the far right. This connection method constitutes a multi-layered quantum circuit, the total depth of which depends on the sum of the depths of all sub-circuits.

[0098] S803 verifies whether the constructed quantum circuit can correctly prepare the expected quantum state through classical simulation or test runs on a quantum processor. Furthermore, the circuit can be further compiled and optimized based on the native gate set and connectivity of the specific quantum hardware, such as merging adjacent single-qubit gates or mapping CNOT gates onto the actual qubit topology to reduce circuit depth and error rate.

[0099] S81. Based on the quantum circuit and combined with the Eileen formula, the reactivity of the target material molecules is determined. The specific implementation process is as follows: S810. Utilize quantum circuits to obtain ground-state energy estimates for the target material molecule and its transition state. For the target material molecule, run the quantum circuit corresponding to its final symmetry quantum simulation. On the quantum processor, prepare the qubits to the reference state. For example, a Hartree-Fock state is used, and then the constructed quantum circuit is executed. Multiple measurements are performed on the circuit's output state to estimate the complete Hamiltonian. Expected value This is the estimated ground-state energy of the target material molecules. For the transition state molecule associated with this reaction, the entire algorithm process is repeated independently: construct its own final symmetric quantum hypothesis, compile it into a quantum circuit, run and measure it to obtain its ground state energy estimate. .

[0100] S811, Activation Energy of Reaction Approximating the energy difference between the ground-state electrons of the transition state molecule and the target material molecule, the calculation formula is: . It is an estimate of the ground state energy of the transition state molecule. This is an estimate of the ground-state energy of the target material molecules. This calculation is performed on a classical computer. For use in the Irene formula, it is often necessary to convert the electron energy difference into activation free energy. In the simplified model, it can be approximated as... We can ignore entropy change and zero-point energy correction. For more accurate calculations, the free energy correction term needs to be obtained through classical frequency analysis.

[0101] S812. Calculate the reaction rate constant using the Irene formula. The expression for the Irene formula is: In the formula, It is the chemical reaction rate constant to be determined; It is the Boltzmann constant, and its value is approximately ; It is the thermodynamic temperature at which the reaction takes place, measured in Kelvin, and is provided by the user based on the actual chemical environment. It is Planck's constant, and its value is approximately ; It is the activation free energy of the reaction, and its unit is equal to that of the reaction. Consistent, typically converted to joules per mole. The calculation process is performed on a classical computer: first, the pre-exponential factor is calculated. Then calculate the exponential term parameter. Next, calculate the exponent term. Finally, multiplying the two results gives the reaction rate constant. .

[0102] S813. The reaction rate constant is output as a quantitative characterization of reaction activity. Calculated... The value directly reflects the molecular properties of the target material at a specified temperature. The rate at which a chemical reaction proceeds along a specific reaction pathway. A higher value indicates a faster reaction and higher molecular reactivity; conversely, a lower value indicates a lower reactivity. The smaller the value, the lower the reactivity. This value provides a quantitative theoretical basis for material design, catalyst screening, or reaction condition optimization, completing the entire process from quantum computing to macroscopic chemical property prediction.

[0103] This invention can reduce the measurement costs of the proposed depth and training process. The technical solution includes the following: In the variational quantum eigenvalue solving algorithm, the complete Hamiltonian of the target material molecule is expressed in second-order quantization as: Among them, symbols It is the index of the spin orbital, traversing from arrive All integers, This represents the total number of spin orbitals in the molecular computational model. and These are the single-electron and two-electron integrals, respectively; these are scalar coefficients that can be solved using quantum chemistry programs on classical computers. Single excitation term. This indicates that a single electron will be moved from index 1. The spin orbital excitation to index is Spin orbital; dual excitation term This means that two electrons will be simultaneously drawn from index 1. and index as The spin orbital excitation to index is and index as The spin orbit. For a spin orbit with A molecule with a number of spin orbitals contains a total of [number] Hamiltonians. Single excitation term and There are 1 double-excitation term, and the overall complexity is O(n). .

[0104] The single-excitation operator and double-excitation operator proposed for the unitary coupled cluster can be denoted as follows: and Single-excitation operator Achieving a single electron at index 0 The spin orbitals and indices are Transitions between spin orbitals; dual-excitation operator Achieving simultaneous two electrons at index 0 and index as The two spin orbitals and their indices are and index as The transition between two spin orbitals. For single-excitation operators and double-excitation operators, quantum circuits consisting of 2 and 13 CNOT gates and several single-qubit gates can be used, respectively. For those with A molecule with a spin orbital, a unitary coupled cluster, single and double excitations are proposed to contain... Single-excitation operator and A double-excitation operator.

[0105] The present invention specifically includes the following steps: S101. Obtain the unitary coupled cluster single and double excitation simulation of the target material molecules, and extract single and double excitation operators from the unitary coupled cluster single and double excitation simulation to form an excitation operator pool. Based on the same set of spin orbitals used to construct the excitation operator pool, the complete Hamiltonian of the molecule is constructed. For each firing operator in the firing operator pool By screening complete Hamiltonians Zhongyu The excitation terms that overlap with the applied spin orbital index are used to construct the corresponding sub-Hamiltonian. Set the iteration termination condition: parameter norm threshold. and maximum number of iterations Choose a suitable reference state. For example, Hartree-Fock state The symmetric quantum hypothesis is initialized as the identity operator. The symmetric quantum hypothesis follows the constraints of particle number conservation and spin symmetry. Initialize the iteration index. .

[0106] S102, Determine the iteration index Has the maximum number of iterations been exceeded? If the energy exceeds the limit, proceed to the final energy calculation step, i.e., S6 in the technical solution. Otherwise, perform the following steps to begin the next step. Round iteration. Based on reference state. Compared with the current symmetric quantum hypothesis Preparation of the current trial state ,in Indicates the first The optimized parameters for the next iteration. It should be noted that in this algorithm, the superscript * indicates the optimized result, not the complex conjugate operation. For each excitation operator in the excitation operator pool... The sub-Hamiltonians corresponding to the excitation operator are respectively used. For the target, the execution involves only a single parameter of the triggering operator. The optimization of the local variational quantum eigenvalues ​​is performed to minimize the energy expectation of the sub-Hamiltonian until convergence, thus obtaining the convergence value corresponding to the parameter. The local variational quantum eigenvalue optimization is defined as follows: That is, optimizing parameters This makes the sub-Hamiltonian Minimize the expected value.

[0107] S103. Determine all convergence values. Is the maximum norm less than the parameter norm threshold? That is, the judgment condition Is the condition met? If yes, terminate the iteration process and proceed to the final energy calculation step, i.e., S6 in the technical solution. If no, continue to execute S104.

[0108] S104, from the trigger operator pool Selecting the convergent norm Largest excitation operator The unitary operator corresponding to the excitation operator. Add to the left side of the current symmetric quantum hypothesis, and the update operation is: At the same time, this convergence value Add to the current parameter set, the update operation is: .

[0109] S105, A symmetric quantum hypothesis that includes the newly added excitation operator and all parameters in the current parameter set. As the object, with the complete Hamiltonian To achieve the objective, perform global variational quantum eigenvalue optimization. This involves optimizing all the proposed variational parameters after the update. Perform global optimization until convergence: Obtain the optimized variational parameters After completing this round of global optimization, the iteration index will be incremented. Return to S102 to begin the next iteration.

[0110] S106, Based on reference state Final symmetric quantum hypothesis With the optimized parameter set Preparation of the final test state Calculate the complete Hamiltonian. The expected value in the final trial state, i.e. This value is then output as an estimate of the molecular ground-state energy. This energy estimate will be used to subsequently determine the reactivity of the target material molecules.

[0111] To further explain the method proposed in this invention, a specific embodiment is proposed using the construction of an H2 molecule with a bond length of 1.23 Å, demonstrating the specific operational flow of the method, which includes the following steps: The S201 and H2 molecules contain a total of four spin orbitals under the STO-3G basis set. A unitary coupled cluster single-double excitation hypothesis for this molecule was obtained. This hypothesis includes three excitation operators, namely single excitation operators. , and double-excitation operator These operators are extracted from the single-double excitation hypothesis of the unitary coupled cluster to form an excitation operator pool. Based on the same set of four spin orbitals, the complete Hamiltonian of this molecule is constructed. This complete Hamiltonian contains 14 excitation terms: These excitation terms and coefficients can be obtained from existing development packages, such as MindQuantum. For each excitation operator in the excitation operator pool, the complete Hamiltonian is filtered. For excitation terms that overlap with the spin-orbit index acted upon by the excitation operator, construct the corresponding sub-Hamiltonians. These sub-Hamiltonians are constructed as follows: For the excitation operator... Its function is the orbital index. Hamiltonian Depend on All index sets in Intersecting terms constitute: For the excitation operator Its function is the orbital index. Hamiltonian Depend on All index sets in Intersecting terms constitute: For the excitation operator Its function is the orbital index. Hamiltonian Depend on All index sets and The intersecting terms constitute the sub-Hamiltonian, which is identical to the complete Hamiltonian here, since the set contains all orbitals: in, and The size of the quantity is compressed compared to the full Hamiltonian, while Since all spin orbitals are included, compression is not achieved here. In the more general case, all sub-Hamiltons can be effectively compressed. The iteration termination condition is set as a parameter norm threshold. and maximum number of iterations Select Hartree-Fock state as a reference state The symmetric quantum hypothesis is initialized as the identity operator. and set the iteration index. .

[0112] S202, Determine the iteration index Has the maximum number of iterations been exceeded? .condition The condition is met, but the iteration termination condition is not met. Therefore, the following steps are performed to begin the first iteration. Based on the reference state. Compared with the current symmetric quantum hypothesis Preparation of the current trial state For activating the operator pool Each triggering operator in The sub-Hamiltonians corresponding to the excitation operator are respectively used. For the target, the execution involves only a single parameter of the triggering operator. The local variational quantum eigenvalues ​​are optimized to minimize the energy expectation of the sub-Hamiltonian until convergence, yielding the convergence value corresponding to the parameter. After this step, we can obtain: for the operator... convergence value For operators convergence value For operators convergence value .

[0113] S203. Determine whether the maximum norm of all convergent values ​​is less than the parameter norm threshold. The maximum norm of all parameters is calculated to be... This value is greater than the threshold. Therefore, the iteration process continues, executing S204.

[0114] S204, from the trigger operator pool The activation operator with the largest convergence norm is selected. The norms of the three convergence values ​​are compared. The maximum value is chosen, therefore the excitation operator is selected. The unitary operator corresponding to the excitation operator. Add to the left side of the current symmetric quantum hypothesis, and the update operation is: At the same time, this convergence value Add to the current parameter set, the update operation is: .

[0115] S205, including the newly added excitation operator and all parameters in the current parameter set Symmetric quantum hypothesis As the object, with the complete Hamiltonian To achieve the objective, perform global variational quantum eigenvalue optimization. Re-optimize all the proposed variational parameters after the update until convergence, obtaining the optimized set of variational parameters. Increment the iteration index. Return to S202. Execute S202 again, specifically, determine the iteration index. Has the maximum number of iterations been exceeded? .condition The condition is met, but the iteration termination condition is not met, so the second iteration begins. (Based on the reference state) Compared with the current symmetric quantum hypothesis Preparation of the current trial state For activating the operator pool Each triggering operator in Then, perform local variational quantum eigenvalue optimization again, each involving only a single parameter, to obtain new convergence values. After this step, we can obtain: , , Then execute S203 again, specifically, determining whether the maximum norm of all newly converged values ​​is less than the parameter norm threshold. At this point, the maximum norm of all parameters is This value is less than the threshold. Therefore, the iteration process is terminated, and the process proceeds to S206.

[0116] S206, Based on reference state Final symmetric quantum hypothesis With the optimized parameter set Preparation of the final test state Calculate the complete Hamiltonian. The expected value in the final trial state, i.e. This value is the calculated ground-state energy estimate of the target H2 molecule.

[0117] The unitary coupled cluster single-double excitation hypothesis contains three excitation operators, while the symmetric quantum hypothesis constructed using the above steps of this invention contains only one excitation operator. This allows for a reduction in the target depth, and for larger-scale molecules, it can further demonstrate a reduction in measurement costs during the training process.

[0118] Optionally, after obtaining the final symmetric quantum hypothesis, it needs to be converted into a quantum circuit that can be executed on a quantum processor. For each single-excitation operator and double-excitation operator, corresponding sub-circuits can be constructed using 2 and 13 CNOT gates and several single-qubit gates, respectively. By sequentially connecting the sub-circuits of all excitation operators in the hypothesis, the quantum circuit of the entire symmetric quantum hypothesis can be obtained. This process directly constructs the quantum circuit of the excitation operator.

[0119] After the quantum circuit is constructed, the core optimization stage of the variational quantum eigenvalue solving algorithm begins. The rationality of parameter initialization directly affects the optimization convergence speed and final accuracy. There are generally two mainstream initialization strategies: one is zero-value initialization, which initializes all variational parameters in the quantum circuit to 0. This method is simple to operate and suitable for small molecule systems with few excitation modes and simple simulated structures. The other is classical approximation result initialization, which uses electronic transition coefficients calculated by mature classical quantum chemical methods such as coupled-cluster single-double excitation as the initial values ​​of the variational parameters of the quantum circuit. The coupled-cluster single-double excitation method can provide a high-precision approximation of the molecular ground state energy on a classical computer. The calculated excitation amplitude has a clear physical correspondence with the variational parameters in the quantum simulation. Using this strategy can ensure that the initial parameter values ​​are near the local minimum of the optimization objective, shortening the number of optimization iterations. This strategy is suitable for simulations of medium to large molecular systems or systems with a high proportion of excited states.

[0120] The parameter optimization process employs classical optimizers, with the BFGS algorithm being the mainstream choice due to its convergence performance. This algorithm belongs to the quasi-Newton method, eliminating the need to calculate the second derivative of the objective function. It determines the optimal search direction by updating the inverse of the approximate Hessian matrix using gradient information from each iteration. In the optimization of variable quantum eigenvalues, the objective function is the expected value of the molecular Hamiltonian, whose gradient is calculated using the measurement results of the quantum circuit. This is achieved by performing multiple measurements on the output state of the quantum circuit, statistically analyzing the measurement probabilities under different basis vectors, and combining this with the matrix elements of the Hamiltonian to solve for the expected value. Gradient calculation typically employs the parameter offset rule, efficiently obtaining gradient information by applying small offsets near the parameter values ​​and repeating measurements. A reasonable convergence criterion needs to be set during the optimization process, typically requiring the difference between the expected values ​​of the Hamiltonian in two consecutive iterations to be less than [a certain value]. Hartree, and the L2 norm of the gradient is less than This serves as a convergence indicator.

[0121] Once the optimization of the quantum eigenvalue solution for the variable converges, the expected value of the Hamiltonian corresponding to the output state of the quantum circuit is the molecular ground state energy level calculated by the algorithm. The accuracy of this result can be verified by comparing it with the calculation results of classical high-precision methods (such as the fully configured interaction method) or experimental measurements. On medium-scale quantum devices with noise, it can usually achieve chemical accuracy (error less than 1 kcal / mol).

[0122] Based on the ground state energy level data of different molecules, the chemical reaction rate can be predicted using the Irene formula. As the core expression of transition state theory, the Irene formula directly correlates the chemical reaction rate constant with the activation energy of the reaction. Its expression is: in , , , , These are the chemical reaction rate constant, Boltzmann constant, thermodynamic temperature, Planck constant, and activation free energy, respectively. The core contributor to the activation free energy is the energy difference between the reactant and the ground state energy levels of the transition state. After obtaining the precise ground state energy levels of the reactant and transition state molecules using a variable quantum eigenvalue solution algorithm, the reaction rate constant can be calculated by substituting these values ​​into the formula. This provides crucial theoretical prediction basis for fields such as materials synthesis and catalytic reaction design.

[0123] This invention proposes a novel rule for selecting excitation operators and training the quantum simulation within the framework of the adaptive quantum variational algorithm ADAPT-VQE. When selecting excitation operators to construct the quantum simulation, firstly, for each excitation operator in the pool, local variational quantum eigenvalue optimization is performed under the current simulation state until convergence. Then, the excitation operator with the largest parameter norm is selected and included in the symmetric quantum simulation. When performing local variational quantum eigenvalue optimization for a single excitation operator, the corresponding sub-Hamiltonian is used to complete the optimization process. This sub-Hamiltonian is constructed by extracting all excitation terms from the full Hamiltonian that overlap with the spin-orbit indices acted upon by the excitation operator. After including the excitation operator in the symmetric quantum simulation, its parameters directly adopt the optimal values ​​obtained from the local optimization. The original excitation operators in the symmetric quantum simulation retain their previously optimized parameter values, and global variational quantum eigenvalue optimization under the full Hamiltonian is performed starting from these parameter combinations. The above strategy can effectively reduce the proportion of redundant excitation operators in the constructed symmetric quantum simulation, thereby reducing the quantum simulation depth and significantly decreasing the measurement cost during algorithm execution. The key points and precautionary provisions of this invention address the following characteristics of the ADAPT-VQE algorithm during the training process: First, when adding a new excitation operator, the excitation operator with the largest parameter norm after optimization using independent local variable quantum eigenvalue solving is selected and included in the symmetricized quantum hypothesis. Second, when performing independent local variable quantum eigenvalue solving optimization on the new excitation operator, excitation terms that overlap with the spin-orbit index acted upon by the excitation operator are extracted from the full Hamiltonian to construct a sub-Hamiltonian, and the local variable quantum eigenvalue solving optimization of the parameters is completed based on this sub-Hamiltonian. Third, the selected excitation operators and their locally optimized parameters are simultaneously added to the symmetricized quantum hypothesis and parameter set, and the global variable quantum eigenvalue solving optimization under the full Hamiltonian is performed using the optimized parameters as the initial point. The comparison results with existing technologies are as follows: 1) Unlike the traditional ADAPT-VQE which uses gradients as the criterion for selecting new excitation operators, this patented method uses the parameters of the individually optimized new excitation operators as the criterion. We name this patented method Param-ADAPT-VQE. In a new iteration, Param-ADAPT-VQE will select each candidate excitation operator in the operator pool... Assign parameters The optimized parameters are obtained by optimizing the parameters until convergence, i.e., by solving the local variational quantum eigenvalues. This allows for independent testing of each candidate excitation operator in the current trial state; subsequently, the parameter norm is selected. The largest operator is incorporated into the symmetric quantum hypothesis. It should be noted that although this strategy adds more optimization steps than the gradient-based ADAPT-VQE algorithm, it does not significantly increase experimental costs and may even reduce them.

[0124] 2) An important conclusion can be drawn in the fermionic context: In the symmetric quantum hypothesis, the newly introduced operator... When optimizing parameters independently, only the gradient of that parameter needs to be calculated; there is no need to solve for the complete Hamiltonian. The energy value. Here, "complete" means that the Hamiltonian contains all non-zero excitation terms and has a size of... In this optimization process, only the complete Hamiltonian is used. Neutral and excitation operators Excitation terms with overlapping spin orbitals will contribute, i.e., satisfying... (The two sets are Hamiltonian excitation terms and excitation operators, respectively) (Index of the spin orbital being acted upon). Therefore, it is only necessary to obtain the complete Hamiltonian. Extract these related terms and construct a new sub-Hamiltonian. And based on this sub-Hamiltonian, the excitation operator is calculated. The gradient is sufficient. For a single-excitation operator, its sub-Hamiltonian... The scale is The sub-Hamiltonian size corresponding to the double-excitation operator is also [size missing]. .here, Represents the number of combinations. It represents the total number of spin orbitals.

[0125] 3) Employing the parameter offset rule, the gradient of the variational parameters can be obtained by solving for the difference in the expected value of the objective Hamiltonian through several quantum circuits after parameter offset. Using the BFGS optimizer, for conditions containing... Symmetric quantum fitting of variational parameters When performing optimization, it is usually necessary to The gradient evaluation of the local variational quantum eigenvalue solver is as follows. Since the local variational quantum eigenvalue solver optimization involves only a single variational parameter, the number of gradient evaluations required for convergence is... Given that the sub-Hamiltonian has a scale of... The size of the operator pool is Therefore, the total measurement cost required to solve for the convergence parameter values ​​of all firing operators in the operator pool is... This aligns with the operator selection cost of the gradient-based ADAPT-VQE algorithm. However, compared to ADAPT-VQE, Param-ADAPT-VQE, by employing new parameter values ​​obtained through local optimization, allows the initial point of the global variable quantum eigenvalue optimization in step S5 to be closer to the global optimum. This improvement significantly reduces the number of iterations in global optimization, thereby lowering the overall measurement cost. The ADAPT-VQE algorithm sets the initial value of the new parameters to 0 for global variable quantum eigenvalue optimization; this strategy is called warm start. Our approach uses the parameters optimized through local variable quantum eigenvalue optimization as the starting point for global variable quantum eigenvalue optimization, which we call hot start. For strongly correlated molecules with larger system scales, their symmetry quantum fitting typically includes more excitation operators and variational parameters. In such scenarios, hot start offers a more significant advantage in measurement cost compared to warm start.

[0126] 4) It should be noted that compared with the ADAPT-VQE algorithm, Param-ADAPT-VQE only improves the selection rules and training methods of the excitation operators, while retaining the core framework of ADAPT-VQE. Therefore, this algorithm is still compatible with a variety of ADAPT-VQE derivatives, thus inheriting its advantages, such as adding multiple excitation operators in parallel in one iteration to reduce the quantum circuit depth and adopting more advanced quantum implementation schemes for excitation operators.

[0127] 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.

[0128] like Figure 2 As shown, an embodiment of the present invention provides a quantum computing-based system for determining the reactivity of material molecules, comprising an initialization module 201, a first judgment module 202, a second judgment module 203, a selection and addition module 204, an update module 205, a calculation module 206, and a determination module 207. The initialization module 201 is used for: obtaining the unitary coupling cluster single and double excitation hypothesis of the target material molecule; extracting single excitation operators and double excitation operators from the unitary coupling cluster single and double excitation hypothesis to form an excitation operator pool; constructing the complete Hamiltonian of the molecule based on the same set of spin orbitals as the one used to construct the excitation operator pool; for each excitation operator in the excitation operator pool, selecting excitation terms from the complete Hamiltonian that overlap with the spin orbital index of the excitation operator, and constructing the corresponding sub-Hamiltonian; initializing the reference state and initializing the symmetric quantum hypothesis to a unit operator, wherein the symmetric quantum hypothesis follows the constraints of particle number conservation and spin symmetry; setting an iteration termination condition including a parameter norm threshold and a maximum number of iterations, and initializing the number of iterations. The first judgment module 202 is used to: determine whether the number of iterations exceeds the maximum number of iterations; if it exceeds, call the calculation module; otherwise, prepare the current trial state based on the reference state and the current symmetric quantum assumption; for each excitation operator in the excitation operator pool, take the sub-Hamiltonian corresponding to the excitation operator as the target, perform local variable quantum eigenvalue optimization involving only the excitation operator, and obtain the convergence value corresponding to the excitation operator; The second judgment module 203 is used to: determine whether the maximum norm of all the converged values ​​is less than the parameter norm threshold; if yes, then call the calculation module; if no, then call the selection and addition module. The selection and addition module 204 is used to: select the excitation operator with the largest convergence norm from the excitation operator pool, add the unitary operator corresponding to the excitation operator to the current symmetric quantum hypothesis, and add the convergence value to the current parameter set; The update module 205 is used to: take the symmetric quantum fitting object containing the newly added excitation operator and all parameters in the current parameter set as the object, take the complete Hamiltonian as the target, perform global variable quantum eigenvalue optimization, update all parameters until convergence; increment the number of iterations, and return to call the first judgment module 202 and the second judgment module 203; The calculation module 206 is used to: prepare a final trial state based on the reference state, the final symmetric quantum hypothesis and the optimized parameter set, calculate the expected value of the complete Hamiltonian in the final trial state, and obtain the ground state energy estimate of the molecule; The determining module 207 is used to: determine the reactivity of the target material molecules based on the estimated ground state energy of the molecules.

[0129] Optionally, in the above technical solution, the local variable quantum eigenvalue optimization performed by the first judgment module 202 and the global variable quantum eigenvalue optimization performed by the update module 205 both include: calculating the gradient using parameter offset rules and completing parameter optimization using the BFGS optimizer.

[0130] Optionally, in the above technical solution, the reference state is the Hartree-Fock state of the molecule, the initialization iteration number is specifically set to 1, and the parameter norm threshold is a positive number greater than 0.

[0131] Optionally, in the above technical solution, the determining module 207 is specifically used for: Obtain the ground state energy estimate of the transition state molecule associated with the target material molecule, calculate the difference between the ground state energy estimate of the transition state molecule and the target material molecule, and obtain the activation energy of the reaction; The reaction activation energy is substituted into a preset model relating activation energy and reaction rate constant to calculate the reaction rate constant of the target material molecule, which is then used as a quantitative characterization of the reactivity of the target material molecule.

[0132] 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.

[0133] 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.

[0134] 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.

[0135] 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.

[0136] 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: S1. Obtain the unitary coupling cluster single and double excitation simulation of the target material's molecules, and extract single excitation operators and double excitation operators from the unitary coupling cluster single and double excitation simulation to form an excitation operator pool. Based on the same set of spin orbitals used to construct the excitation operator pool, the complete Hamiltonian of the molecule is constructed. For each excitation operator in the excitation operator pool, excitation terms that overlap with the spin orbital indices acted upon by the excitation operator are selected from the complete Hamiltonian, and corresponding sub-Hamiltonians are constructed. The reference state is initialized, and the symmetry quantum hypothesis is initialized to the unit operator, wherein the symmetry quantum hypothesis obeys the particle number conservation and spin symmetry constraints. An iteration termination condition including a parameter norm threshold and a maximum number of iterations is set, and the number of iterations is initialized. S2. Determine whether the number of iterations exceeds the maximum number of iterations; if it does, proceed to S6; otherwise, prepare the current trial state based on the reference state and the current symmetric quantum assumption; for each excitation operator in the excitation operator pool, take the sub-Hamiltonian corresponding to the excitation operator as the target, and perform local variable quantum eigenvalue optimization involving only the excitation operator to obtain the convergence value corresponding to the excitation operator; S3. Determine whether the maximum norm of all converged values ​​is less than the parameter norm threshold; if yes, proceed to S6; if no, proceed to S4. S4. Select the excitation operator with the largest convergence norm from the excitation operator pool, add the unitary operator corresponding to the excitation operator to the current symmetric quantum hypothesis, and add the convergence value to the current parameter set; S5. Taking the symmetric quantum fitting containing the newly added excitation operator and all parameters in the current parameter set as the object, and the complete Hamiltonian as the target, perform global variable quantum eigenvalue optimization, update all parameters until convergence; increment the number of iterations, and return to execute S2. S6. Based on the reference state, the final symmetric quantum design and the optimized parameter set, prepare the final test state, calculate the expected value of the complete Hamiltonian in the final test state, and obtain the ground state energy estimate of the molecule; S7. Determine the reactivity of the target material molecules based on the estimated ground-state energy of the molecules.

2. The method for determining the reactivity of material molecules based on quantum computing according to claim 1, characterized in that, The optimization of local variable quantum eigenvalues ​​in S2 and the optimization of global variable quantum eigenvalues ​​in S5 both include: calculating the gradient using parameter offset rules and completing parameter optimization using the BFGS optimizer.

3. The method for determining the reactivity of material molecules based on quantum computing according to claim 1, characterized in that, The reference state is the Hartree-Fock state of the molecule, the initialization iteration number is specifically set to 1, and the parameter norm threshold is a positive number greater than 0.

4. A method for determining the reactivity of material molecules based on quantum computing according to any one of claims 1 to 3, characterized in that, Determining the reactivity of the target material molecules based on the estimated ground-state energy of the molecules includes: Obtain the ground state energy estimate of the transition state molecule associated with the target material molecule, calculate the difference between the ground state energy estimate of the transition state molecule and the target material molecule, and obtain the activation energy of the reaction; The reaction activation energy is substituted into a preset model relating activation energy and reaction rate constant to calculate the reaction rate constant of the target material molecule, which is then used as a quantitative characterization of the reactivity of the target material molecule.

5. A system for determining the reactivity of material molecules based on quantum computing, characterized in that, It includes an initialization module, a first judgment module, a second judgment module, a selection and addition module, an update module, a calculation module, and a determination module; The initialization module is used to: obtain the unitary coupling cluster single and double excitation simulation of the molecules of the target material, and extract single excitation operators and double excitation operators from the unitary coupling cluster single and double excitation simulation to form an excitation operator pool; Based on the same set of spin orbitals used to construct the excitation operator pool, the complete Hamiltonian of the molecule is constructed. For each excitation operator in the excitation operator pool, excitation terms that overlap with the spin orbital indices acted upon by the excitation operator are selected from the complete Hamiltonian, and corresponding sub-Hamiltonians are constructed. The reference state is initialized, and the symmetry quantum hypothesis is initialized to the unit operator, wherein the symmetry quantum hypothesis obeys the particle number conservation and spin symmetry constraints. An iteration termination condition including a parameter norm threshold and a maximum number of iterations is set, and the number of iterations is initialized. The first determination module is used to: determine whether the number of iterations exceeds the maximum number of iterations; If the limit is exceeded, the computation module is invoked; otherwise, the current trial state is prepared based on the reference state and the current symmetric quantum assumption; for each excitation operator in the excitation operator pool, the local variable quantum eigenvalue optimization involving only the excitation operator is performed with the sub-Hamiltonian corresponding to the excitation operator as the target, and the convergence value corresponding to the excitation operator is obtained. The second judgment module is used to: determine whether the maximum norm of all the converged values ​​is less than the parameter norm threshold; if yes, then call the calculation module; if no, then call the selection and addition module. The selection and addition module is used to: select the excitation operator with the largest convergence norm from the excitation operator pool, add the unitary operator corresponding to the excitation operator to the current symmetric quantum hypothesis, and add the convergence value to the current parameter set; The update module is used to: take the symmetric quantum fitting object containing the newly added excitation operator and all parameters in the current parameter set as the object, take the complete Hamiltonian as the target, perform global variable quantum eigenvalue optimization, update all parameters until convergence; increment the number of iterations, and return to call the first judgment module; The calculation module is used to: prepare a final trial state based on the reference state, the final symmetric quantum assumption and the optimized parameter set, calculate the expected value of the complete Hamiltonian in the final trial state, and obtain the ground state energy estimate of the molecule; The determining module is used to: determine the reactivity of the target material molecules based on the estimated ground-state energy of the molecules.

6. The system for determining the reactivity of material molecules based on quantum computing according to claim 5, characterized in that, The local variable quantum eigenvalue optimization performed by the first judgment module and the global variable quantum eigenvalue optimization performed by the update module both include: calculating the gradient using parameter offset rules and completing parameter optimization using the BFGS optimizer.

7. The system for determining the reactivity of material molecules based on quantum computing according to claim 5, characterized in that, The reference state is the Hartree-Fock state of the molecule, the initialization iteration number is specifically set to 1, and the parameter norm threshold is a positive number greater than 0.

8. A system for determining the reactivity of material molecules based on quantum computing according to any one of claims 5 to 7, characterized in that, The determining module is specifically used for: Obtain the ground state energy estimate of the transition state molecule associated with the target material molecule, calculate the difference between the ground state energy estimate of the transition state molecule and the target material molecule, and obtain the activation energy of the reaction; The reaction activation energy is substituted into a preset model relating activation energy and reaction rate constant to calculate the reaction rate constant of the target material molecule, which is then used as a quantitative characterization of the reactivity of the target material molecule.

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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