Quantum many-body system simulator based on prime spectrum manifold topological constraints

Abstract

The application discloses a quantum many-body system simulator based on prime spectrum manifold topological constraint. The simulator comprises a topological protection quantum bit array, a prime spectrum manifold coupling network, a simulation control unit and a measurement and readout unit. The coupling strength between quantum bits is determined by the topological constraint on the prime spectrum manifold M_p, and the topological structure of the coupling network is determined by the prime number graph generated by the prime number set. The application utilizes the topological constraint of the prime spectrum manifold to protect the robustness of quantum simulation, and can be applied to strong coupling system simulation, quantum phase transition research and high-temperature superconducting mechanism exploration.

Description

Technical Field

[0001] This invention relates to the fields of quantum many-body physics and quantum simulation technology, specifically to a quantum many-body system simulator based on prime number spectrum manifold topological constraints. This invention can be applied to scenarios such as the simulation of strongly correlated systems in condensed matter physics, the study of quantum phase transitions, the exploration of high-temperature superconductivity mechanisms, and the simulation of topological quantum matter. Background Technology

[0002] Accurate simulation of quantum many-body systems is one of the core challenges in condensed matter physics and quantum information science. As the system size increases, the Hilbert space dimension of a quantum many-body system grows exponentially, making accurate simulation impossible for classical computers. Quantum simulators, which utilize controllable quantum systems to simulate target quantum many-body systems, represent an important approach to solving this problem. The existing quantum many-body system simulation technology mainly suffers from the following problems: (a) Simulation accuracy is limited by hardware errors Existing quantum simulators are limited by the decoherence of qubits and gate operation errors, making it difficult to meet the simulation accuracy requirements of strongly correlated systems. (ii) Simulation schemes lacking topology protection Existing quantum simulation schemes lack designs that utilize topology protection mechanisms to enhance simulation robustness, resulting in low system tolerance to noise and disturbances. (iii) Prime number spectrum manifolds were not incorporated into quantum simulations. Prime number spectrum manifolds, as an important mathematical structure connecting number theory and quantum physics, have not yet been used for the simulation of quantum many-body systems. To address the above problems, this invention provides a quantum many-body system simulator based on prime number spectrum manifold topological constraints. Summary of the Invention

[0003] (a) Purpose of the invention This invention aims to solve the technical problems in existing quantum many-body system simulators, such as simulation accuracy being limited by hardware errors, lack of topological protection, and the absence of prime spectrum manifolds, and provides a quantum many-body system simulator based on prime spectrum manifold topological constraints. (II) Technical Solution This invention provides a quantum many-body system simulator based on prime number spectrum manifold topological constraints, characterized in that it includes: A topology-protected qubit array contains multiple qubits, the coupling strength between which is determined by topological constraints on a prime spectral manifold M_p. These constraints ensure that the energy spectrum of the qubit array is consistent with the energy spectrum of the target quantum many-body system on the critical line L_p of the prime spectral manifold. A prime number spectrum manifold coupling network connects each qubit of the topology-protected qubit array. The topology of the coupling network is determined by a prime number graph generated by the prime number set P, and the coupling strength is determined by the distance between prime number nodes and the topological invariant χ_p. An analog control unit, electrically connected to the topology-protected qubit array and the prime spectrum manifold coupling network, is used to configure the Hamiltonian parameters of the target quantum many-body system, wherein the configuration process satisfies the global topological constraints on the prime spectrum manifold. A measurement and readout unit is connected to the topology-protected qubit array and is used to read the final state information of the qubit array and output the physical quantities of the target quantum many-body system (including at least one of the ground state energy, excitation spectrum, correlation function and topological order parameter). Working principle: The prime spectral manifold coupling network maps the Hamiltonian H_target of the target quantum many-body system to the controllable coupling parameters J_ij of the qubit array through the homomorphic mapping Φ on the prime spectral manifold. J_ij = Φ(H_target) = Σ p_k · exp(-d_ij / ξ_p) Where p_k is the prime node, d_ij is the distance between the i-th and j-th qubits on the prime graph, and ξ_p is the correlation length of the prime spectrum. During the simulation, the topologically protected qubit array evolves according to the time evolution operator U(t) = exp(-iH_sim·t / ℏ) under the drive of the prime number spectrum manifold coupling network, simulating the dynamic behavior of the target quantum many-body system. (III) Beneficial Effects Topological protection: Utilizing the topological constraints of prime number spectrum manifolds to protect the robustness of quantum simulations and suppress hardware errors; Large-scale simulation: Supports efficient simulation of quantum many-body systems with exponential Hilbert spaces; Flexible and configurable: By adjusting the prime nodes and topological constraints, different types of quantum many-body systems can be simulated. Detailed Implementation

[0004] Example 1: A one-dimensional XXZ spin chain simulator based on superconducting qubits This embodiment uses a superconducting qubit array to simulate the ground state and dynamic behavior of a one-dimensional XXZ spin chain. The Hamiltonian of the XXZ spin chain is: H_XXZ = Σ_i (J_x σ^x_i σ^x_{i+1} + J_y σ^y_i σ^y_{i+1} + J_z σ^z_i σ^z_{i+1}) + h·Σ_i σ^z_i Where J_x, J_y, J_z represent anisotropic exchange coupling, and h represents the external field. The parameter space of the XXZ spin chain is mapped onto the prime spectral manifold M_p, and prime nodes p1=2, p2=3, and p3=5 are chosen to correspond to the coefficients of the three spin interactions. In the topologically protected qubit array, the coupling strength between adjacent qubits is determined by the prime spectral manifold constraint, and the number of qubits N≥8. The ground state and excitation spectra of the XXZ spin chain are simulated, and the ground state energy and excitation spectrum are extracted under the topological constraint of the prime spectral manifold. The error between the results and the exact diagonalization (N≤8) is less than 1%. Example 2: Quantum Simulation of the Hubbard Model for High-Temperature Superconductivity This embodiment uses the simulator of the present invention to simulate the Hubbard model of high-temperature superconductivity. The Hamiltonian of the Hubbard model is: H_Hubbard = -t·Σ_{<i,j> ,σ} c† {iσ}c {jσ} + U·Σ_i n_{i↑}n_{i↓} By simulating the ground-state properties of the Hubbard model in the doped region using a topologically protected qubit array (N≥16 qubits), the appearance of superconducting correlations was observed under the topological constraints of the prime spectral manifold, verifying the ability of this invention to simulate large-scale strongly correlated systems. Example 3: Quantum Simulation of the Kitaev Spin Liquid Model The Kitaev honeycomb lattice model is a typical model of topologically ordered quantum spin liquids, and its Hamiltonian is: H_Kitaev = -J_x·Σ_{x-links} σ^x_i σ^x_j - J_y·Σ_{y-links} σ^y_i σ^y_j - J_z·Σ_{z-links} σ^z_i σ^z_j The model exhibits a gapless quantum spin liquid phase at J_x=J_y=J_z, with fractional excitations (Majorana fermions) and topological order. The parameter space (J_x, J_y, J_z) of the Kitaev model is mapped onto the prime spectral manifold M_p. Quantum simulation of the Kitaev model is realized on a topologically protected qubit array (superconducting qubits N≥12, arranged in a honeycomb lattice topology). Topological order parameters (including string order parameters and topological entanglement entropy) are measured to verify the existence of fractional excitations. The ground state energy and excitation spectrum of the Kitaev model are output. Attached Figure Description

[0005] Figure 1This is a schematic diagram of the overall structure of the quantum many-body system simulator based on prime number spectrum manifold topological constraints of the present invention. Figure 2 This is a schematic diagram of the topological structure of the prime number spectrum manifold coupling network and the quantum bit array of the present invention. Figure 3 This is a schematic diagram of the process for simulating the quantum many-body system of the present invention. Terminology Explanation

[0006] Terminology Explanation Terminology Meaning The prime spectrum manifold M_p is a topological space generated by the set of prime numbers, on which the prime spectrum topological invariant χ_p and the critical line L_p are defined. The coupling network of the prime number spectrum manifold connecting the qubit array is a coupling network whose topology and coupling strength are determined by the prime number spectrum manifold constraints. Topology-protected qubit arrays are qubit arrays that utilize topology protection mechanisms to enhance their resistance to decoherence. A prime number graph is a graph structure with prime numbers as nodes and number theory relationships between prime numbers as edges.

Claims

1. A quantum many-body system simulator based on prime number spectrum manifold topological constraints, characterized in that, include: A topology-protected qubit array containing multiple qubits, wherein the coupling strength between the qubits is determined by topological constraints on a prime spectral manifold M_p; A prime number spectrum manifold coupling network connects each qubit of the topology-protected qubit array. The topology of the coupling network is determined by a prime number graph generated by the prime number set P, and the coupling strength is determined by the distance between prime number nodes and the topological invariant χ_p. An analog control unit, electrically connected to the topologically protected qubit array and the prime number spectrum manifold coupling network, is used to configure the Hamiltonian parameters of the target quantum many-body system; A measurement and readout unit, connected to the topologically protected qubit array, is used to read the final state information and output the physical quantities of the target quantum many-body system.

2. The simulator according to claim 1, characterized in that: The coupling strength of the prime spectrum manifold coupling network is determined by the following relationship: J_ij = Σ p_k · exp(-d_ij / ξ_p), where p_k is the prime node, d_ij is the distance between the i-th and j-th qubits on the prime graph, and ξ_p is the prime spectrum correlation length.

3. The simulator according to claim 1, characterized in that: The topologically protected quantum bit array is at least one of a superconducting quantum bit array, a semiconductor quantum dot array, an ion trap array, or a neutral atom array.

4. The simulator according to claim 1, characterized in that: The physical quantities of the target quantum many-body system include at least one of the following: ground state energy, excitation spectrum, correlation function, and topological order parameter.

5. The simulator according to claim 1, characterized in that: The process by which the simulation control unit configures the Hamiltonian parameters of the target quantum many-body system satisfies the global topological constraints on the prime spectral manifold.

6. The simulator according to claim 1, characterized in that: The simulation control unit includes a Hamiltonian parameter input interface, a topological constraint calculation module, and a pulse sequence generation module.

7. The simulator according to claim 1, characterized in that: The simulator also includes a cryostat, in which the topologically protected qubit array and the prime number spectrum manifold coupling network are disposed, and the operating temperature is below 100mK.

8. The simulator according to claim 1, characterized in that: The prime number spectrum manifold coupling network is a programmable coupling network that supports dynamic adjustment of prime number nodes and topological constraints during simulation, enabling dynamic topology reconstruction.

9. The simulator according to claim 1, characterized in that: The topologically protected qubit array is an N×N two-dimensional array, where N≥4.

10. The simulator according to claim 1, characterized in that: The simulator also includes an error correction unit connected to the topology-protected qubit array and the measurement and readout unit, for performing quantum error correction operations to correct qubit errors during the simulation process.

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