Fast searching method for low-energy state of many-body field based on topological charge constraint and constraint optimization

Abstract

The application discloses a kind of based on topological charge constraint and constraint optimization's many-body field low-energy state fast search method and system, belong to quantum simulation and computational physics technical field.The application maps many-body system configuration as the coordinate point sequence on prime spectrum manifold, with total topological charge zero condition as global constraint guide search process, by alternately executing gradient descent and constraint projection, quickly locate the low-energy state configuration satisfying finite energy boundary condition.The application can avoid local minimum value trap, accelerate convergence times, applicable to high-dimensional energy landscape search, protein folding simulation, quantum many-body system ground state search and so on scene.

Description

Technical Field

[0001] This invention belongs to the field of quantum simulation and computational physics, and is particularly applicable to low-energy state search of quantum many-body systems, phase transition analysis in condensed matter physics, molecular configuration optimization in quantum chemistry, and energy minimum search in protein folding simulation. Specifically, it relates to a system and method that uses the zero-return condition of the topological charge of the prime spectrum manifold as a global constraint to guide the rapid convergence of a many-body field to a low-energy state. Background Technology

[0002] Existing low-energy state search methods (such as simulated annealing, genetic algorithms, gradient descent, Bayesian optimization, and particle swarm optimization) have the following inherent limitations: Easily trapped in local minima: Gradient descent and local search methods are prone to getting trapped in local minima in high-dimensional energy landscapes and cannot guarantee finding a global low-energy state. Global search methods are computationally intensive: global optimization methods such as simulated annealing and genetic algorithms require extensive sampling and evaluation, which is particularly demanding for high-dimensional systems (dimensionality). The computational cost of ) grows exponentially. Lack of physical constraints: Existing methods rely solely on the shape of the energy function itself, without utilizing the inherent physical conservation quantities of the system (such as total topological charge conservation and finite energy boundary conditions) to compress the search space. Low efficiency of multi-scale search: In multi-scale and multi-volume systems, energy landscapes have long-range correlations and short-range fluctuations, and existing methods are difficult to effectively handle features at different scales simultaneously. Disconnected from the toolchain of topological cryptography: In post-quantum cryptosystems based on prime spectral manifolds (such as RH00201-RH00206), low-energy state search can serve as a tool for random seed optimization or cryptographic parameter mining, but existing methods are not associated with this framework. This invention proposes a constraint optimization method based on topological load constraints. The method uses the condition of total topological load returning to zero as a global constraint to guide the search process and uses constraint projection and iterative updates to quickly locate the low-energy configuration that satisfies the finite energy boundary conditions. Summary of the Invention

[0003] This addresses the technical problems of existing low-energy state search methods, such as easy getting trapped in local minima, large computational cost of global search, and lack of physical constraint guidance. Technical solution This invention is based on the following mathematical fact: a physically realizable low-energy state must satisfy the condition that the total topological charge returns to zero. (Equivalent to finite energy boundary conditions). This condition is embedded as a constraint term into the energy function to construct a constrained optimization problem: Constraints By alternately performing gradient descent and constraint projection, the search process is guided to converge quickly to a low-energy state that satisfies the physical constraints. This system consists of four main components: Many-body field encoding module: configured to encode the degrees of freedom (spin configuration, particle position, molecular configuration) of a many-body system into a prime-number spectral manifold. The sequence of coordinate points on ,in Encoding scale information, Encode phase / orientation information. Topology load calculation module: Configured to calculate the current configuration Total topological charge on prime number spectrum manifold This serves as the fundamental criterion for constraint verification. The constrained optimization solution module is configured to use the following iterative strategy: In each iteration, unconstrained gradient descent is first performed (based on the energy function). To obtain the intermediate configuration Then perform constraint projection: Projection to satisfy On the submanifold, a new configuration is obtained. . Convergence determination and output module: configured to determine energy changes and topological load Are they all less than the preset threshold? and If the condition is met, the current configuration is output as the low-energy state result; otherwise, the iteration continues. The method of constrained projection (core): In the projection step, the total topological load of the current configuration is calculated. Along the direction of topological load gradient Adjust the configuration parameters to make Move towards zero: in Projection step size (typical value) ), iteration Typical value (times) until . Overall process: Randomly initialize configuration → Map to prime spectral manifold → Calculate topological charge → Gradient descent update → Constrained projection → Check convergence → Output low-energy state Physical correctness guarantees: - The condition for zeroing the topological charge is guaranteed by the Chern-Gauss-Bonnet theorem and is a necessary condition for a physically admissible state; - The constrained projection process maintains the continuity of the system's energy function and does not introduce non-physical discontinuous jumps; - The converged configuration simultaneously satisfies energy minimization and zeroing the topological charge, directly corresponding to the low-energy state of the physical system. Beneficial effects By narrowing the search space through topological load constraints, the effective configuration space is compressed to meet the requirements. A subset of; To avoid local minima traps, constrained projections can escape local minima of the energy surface and search for physically permissible low-energy states. Applicable to any high-dimensional many-body system (dimension) ), not limited by system size; It can work in conjunction with RH00207 (spin field simulation) and RH00208 (eigenspectrum solving) to form a complete solution toolchain for multibody problems; The low-energy states obtained from the search automatically satisfy the finite energy boundary conditions and can be directly used for subsequent physical analysis. Terminology Explanation

[0004] Terminology Meaning Total topological load zeroing condition The global constraints that the physically permissible configuration of the system must satisfy are equivalent to finite energy boundary conditions, and are guaranteed by the Chern-Gauss-Bonnet theorem. Constraint projection: Projecting a configuration that does not satisfy constraints onto a configuration that does satisfy constraints. Mathematical operations on the submanifold are achieved by adjusting the configuration parameters along the direction of the topological load gradient. Gradient descent: along the negative gradient direction of the energy function An iterative method that updates configuration parameters to gradually reduce energy. Attached Figure Description

[0005] Figure 1 This is a flowchart illustrating the overall process of this invention. Figure 2 A comparison chart of search paths with and without topological constraints; Figure 3 To constrain the energy-topological charge distribution changes before and after projection; Figure 4 This is a comparison chart of convergence speeds across different system dimensions. Detailed Implementation

[0006] Example 1: Search for low-energy states in high-dimensional energy landscapes (mathematical test function) This embodiment is applicable to verifying the algorithm's search capability in high-dimensional non-convex energy landscapes. Step S1, Objective Function Setting: Set an objective function. Rosenbrock function variant of dimension Its energy landscape has a complex gully structure, making it extremely prone to getting trapped in local minima. Step S2, Topology load constraint configuration: Define the topology load function Map each variable to a phase coordinate on the torus. The total topological charge is the sum of the sine values ​​of that phase angle. Step S3, Constraint Optimization: Execute an iterative loop (gradient descent + constraint projection), with a projection step size of... Convergence threshold , . Step S4, Output Result: The output satisfies... And energy The smallest configuration. Technical effect: Traditional gradient descent achieves approximately After stepping into a local minimum (energy) The method of the present invention is approximately... After the step, it converges to a lower energy ( ), and the final configuration satisfies . Example 2: Conformation Search in Protein Folding Simulation This embodiment is applicable to the low-energy configuration search of protein potential surfaces. Step P1, Potential Energy Input: Input the protein amino acid sequence and its molecular force field potential energy function. (Including bond length, bond angle, dihedral angle, van der Waals force, and electrostatic interaction). Step P2, Topological Charge Mapping: Map the torsion angle of each amino acid residue. Mapped to toroidal phase Scale coordinates . Step P3, Constraint Optimization: Perform topological load constraint optimization, alternating between energy gradient descent and topological load constraint projection in each iteration cycle. Step P4, Output low-energy configuration: Output multiple satisfying The low-energy configuration candidates are provided for subsequent molecular dynamics verification. Technical effect: In the testing of small proteins (50 residues), the method of this invention achieves results in approximately [timeframe missing]. Within the step, a low-energy folded state close to the natural configuration was discovered, which is faster than that of conventional simulated annealing (approximately). (Step) Fast times. Example 3: Joint solution of multibody systems in coordination with RH00207 / 00208 This embodiment is applicable to the combined use of the present invention with RH00207 (spin field simulation) and RH00208 (eigenspectral solving) to form a complete multibody problem solution chain. Step J1, RH00207 Initial Screening: Using the two-dimensional spin field simulation of RH00207, a set of possible ground state candidate configurations are generated under topological load constraints. Step J2, RH00209 Fine Search: Using the candidate configurations output by RH00207 as the initial point, a fine low-energy state search is performed using the constraint optimization method of this invention to further reduce the energy. Step J3, RH00208 Verification: Using the eigenspectral solution method of RH00208, verify whether the eigenenergy and topological charge of the low-energy configuration meet the physical requirements. Technical effect: The joint solution chain can shorten the overall time of ground state search for multibody systems. - Furthermore, the output results have higher physical confidence.

Claims

1. A fast search method for low-energy states in a multibody field based on topological load constraints and constraint optimization, characterized in that, The process includes the following steps: Initialization step: The processor initializes the configuration parameters of the multibody system. ; Mapping step: Assign the configuration parameters Mapped to a prime spectral manifold The sequence of coordinate points on ; Topology load calculation steps: Calculate the total topology load of the coordinate point sequence. Constrained optimization iteration steps: The following two sub-steps are executed alternately until the convergence condition is met: (1) Energy gradient descent sub-step: along the objective energy function Update the configuration parameters in the negative gradient direction to obtain the intermediate configuration. (2) Constraint projection sub-step: Projection to satisfy On the submanifold, a new configuration is obtained. ; Output steps: Output the low-energy configuration that satisfies the convergence condition.

2. The method according to claim 1, characterized in that, In the constrained projection sub-step, the configuration parameters are adjusted along the topological load gradient direction: ,in This represents the projection step size.

3. The method according to claim 2, characterized in that, The projection step size The range of values ​​is to Typical value .

4. The method according to claim 1, characterized in that, The convergence condition includes: energy change And the absolute value of the topological charge ,in and This is a preset threshold.

5. The method according to claim 1, characterized in that, The constraint projection substep is executed repeatedly in each iteration. Second-rate, The range of values ​​is to Typical value .

6. The method according to claim 1, characterized in that, The configuration parameters of the many-body system include at least one of spin orientation, particle coordinates, and molecular twist angle.

7. A fast search system for low-energy states in a multibody field based on topological load constraints and constraint optimization, characterized in that, include: The configuration initialization module is configured to generate the initial configuration parameters of the multibody system. The topology load calculation module is configured to calculate the total topology load of the configuration on the prime spectrum manifold. The energy gradient descent module is configured to update the configuration parameters along the negative gradient direction of the energy function. The constraint projection module is configured to project the configuration onto a plane that satisfies... On the submanifold; The convergence determination module is configured to check whether the energy change and topological charge meet the convergence conditions. The output module is configured to output a low-energy state configuration that meets the conditions.

8. The system according to claim 7, characterized in that, The topology load calculation module is implemented in the form of a hardware accelerator and shares the same hardware unit with RH00200, RH00207, and RH00208.

9. The system according to claim 7, characterized in that, The system is deployed on a GPU cluster, FPGA accelerator card, or quantum computing simulation platform.

10. The system according to claim 7, characterized in that, The system works in cascade with RH00207 and RH00208 to form a complete toolchain for solving multibody problems.

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