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CN-122021961-A - Digital quantum simulation method

CN122021961ACN 122021961 ACN122021961 ACN 122021961ACN-122021961-A

Abstract

The invention provides a digital quantum simulation method which comprises the steps of carrying out symmetry analysis and subspace decomposition on a target Hamiltonian volume to obtain an effective Hamiltonian volume and symmetry constraint conditions, constructing a quantum line population of a target unitary operator according to the effective Hamiltonian volume, calculating entanglement characteristics of each quantum line in the quantum line population, carrying out structural variation on the quantum line population based on the entanglement characteristics, carrying out line segment intersection on the symmetry constraint conditions to obtain a candidate line set, carrying out line parameter optimization on the candidate line set based on a fidelity gradient to obtain an optimized line set, extracting gate distribution structural characteristics of the optimized line set, carrying out non-uniform sampling on the optimized line set based on the gate distribution structural characteristics to obtain a sampling line subset, screening out optimal quantum lines from the sampling line subset based on deviation of experimental observation values and theoretical expected values, and carrying out quantum simulation based on the optimal quantum lines.

Inventors

  • WANG ZHEN
  • ZHANG XU
  • DENG JINFENG

Assignees

  • 浙江大学

Dates

Publication Date
20260512
Application Date
20260202

Claims (10)

  1. 1. A method of digitized quantum simulation, the method comprising: Carrying out symmetry analysis and subspace decomposition on a target Hamiltonian amount obtained in advance to obtain an effective Hamiltonian amount and a corresponding symmetry constraint condition; Constructing a target unitary operator according to the effective Hamiltonian quantity, and initializing a quantum circuit population of the target unitary operator by combining the symmetry constraint condition; calculating entanglement degree characteristics of each quantum circuit in the quantum circuit population, carrying out structural variation on the quantum circuit population based on the entanglement degree characteristics, and carrying out circuit segment intersection by combining the symmetry constraint condition to obtain a candidate circuit set; Performing line parameter optimization on the candidate line set based on fidelity gradient to obtain an optimized line set, and extracting gate distribution structure characteristics of the optimized line set; And carrying out non-uniform Clifford sampling on the optimized line set based on the gate distribution structure characteristics to obtain a sampling line subset, screening out an optimal quantum line from the sampling line subset based on the deviation of an experimental observation value and a theoretical expected value, and carrying out quantum simulation based on the optimal quantum line.
  2. 2. The digitized quantum simulation method of claim 1, wherein performing symmetry analysis and subspace decomposition on the pre-acquired target hamiltonian to obtain an effective hamiltonian and a corresponding symmetry constraint comprises: performing item level expansion and structural analysis on a target Hamiltonian volume obtained in advance, and identifying local items, interaction items and corresponding operators contained in the target Hamiltonian volume to obtain a Hamiltonian volume operator item set; Determining a symmetry operator set corresponding to the target Hamiltonian whole according to the Hamiltonian operator item set; Dividing Quan Xier Bert space into a plurality of mutually orthogonal intrinsic subspaces according to the symmetry operator set, and constructing projection operators for each intrinsic subspace to obtain a subspace projection operator set; Screening out a target subspace projection operator from the subspace projection operator set according to the initial state of the target Hamiltonian amount, and projecting the target Hamiltonian amount into the target subspace projection operator to obtain an effective Hamiltonian amount; and extracting mathematical constraint corresponding to each intrinsic subspace in the subspace projection operator set according to the range of the eigenvalue and the conservation condition corresponding to each intrinsic subspace, and obtaining symmetry constraint conditions.
  3. 3. A digitized quantum simulation method according to claim 1, wherein, constructing a target unitary operator according to the effective Hamiltonian amount, including: extracting evolution time parameters of a sub-simulation model of the output quantity; performing spectrum range analysis on the effective Hamiltonian amount to obtain a target spectrum range; normalizing and recalibrating the effective Hamiltonian according to the target spectrum range, performing index mapping on the recalibrated effective Hamiltonian based on the evolution time parameter to obtain a target unitary operator, and performing symmetry consistency verification on the target unitary operator according to the symmetry constraint condition.
  4. 4. A method of digitized quantum simulation according to claim 1, wherein initializing the quantum wire population of the target unitary in conjunction with the symmetry constraint comprises: screening a limited quantum gate set from the universal quantum gate set based on the symmetry constraint condition; Modeling the adjacency relation among the quantum bits according to the geometric structure of the quantum simulation model to obtain a quantum circuit topology communication diagram; randomly combining the quantum circuit topology connected graphs according to the limited quantum gate set to generate a symmetry maintaining circuit fragment set; Carrying out depth constraint-based diversity line assembly on each symmetry maintaining line segment in the symmetry maintaining line segment set to obtain a quantum line population, and distributing initial angle parameters for adjustable gates of each quantum line in the quantum line population to obtain a sub-line population containing parameters; Calculating the similar distance between each parameter-containing sub-line in the parameter-containing sub-line population and the target unitary operator, and screening out parameter-containing sub-lines with the similar distance larger than a preset distance threshold value in the parameter-containing sub-line population to obtain a quantum line population.
  5. 5. The digitized quantum simulation method of claim 1, wherein calculating entanglement characteristics of individual ones of the quantum wire populations comprises: Selecting quantum circuits in the quantum circuit population one by one as target quantum circuits, and performing bit partitioning according to the quantum bit quantity of the target quantum circuits to obtain target bit partitions; Performing gate calculation on the target quantum circuit according to the initial state of the target quantum circuit to obtain a target output state; performing trace offset operation on the target quantum circuits according to the target bit partitions and the target output states to obtain target density matrixes, and collecting the target density matrixes corresponding to all the target quantum circuits in the quantum circuit population under different bit partitions into a density matrix set; calculating entanglement index of each quantum circuit in the quantum circuit population according to the density matrix set to obtain a entanglement index set, wherein the entanglement index comprises quantum mutual information, negativity and Renyi entropy; And performing aggregation analysis on the entanglement degree index set to obtain an entanglement degree characteristic set.
  6. 6. The method of claim 5, wherein structurally mutating the quantum wire population based on the entanglement characteristics and intersecting wire segments in combination with the symmetry constraint to obtain a candidate wire set, comprising: Carrying out line layering on the quantum line population according to the entanglement degree characteristics to obtain quantum line subsets with different entanglement degree characteristic grades; Distributing a structure variation strategy for each quantum line subset according to the entanglement degree characteristic grade, and carrying out variation on the quantum lines in each quantum line subset according to the structure variation strategy and symmetry constraint conditions to obtain a variation line set; Screening out line segments with higher entanglement characteristics from the variant line set as cross segments to be gathered into a cross segment set; Under the symmetry constraint condition, performing cross combination on each cross segment in the cross segment set to obtain a cross line set; and carrying out structure effectiveness screening on the variant line set and the cross line set to obtain a candidate line set.
  7. 7. The digitized quantum simulation method of claim 1, wherein optimizing the line parameters for the candidate line set based on the fidelity gradient to obtain an optimized line set comprises: selecting candidate lines in the candidate line set one by one, and initializing line parameter vectors according to the number of adjustable quantum gates in the candidate lines and the quantum gate types; performing gate calculation on the candidate lines based on the line structures of the candidate lines and the line parameter vectors to obtain line unitary operators; Calculating the fidelity loss value of the target unitary operator and the line unitary operator, and judging whether the fidelity loss value is larger than a preset loss value threshold; if yes, carrying out gradient calculation on the line parameter vector based on the fidelity loss value to obtain a fidelity gradient; performing gradient descent update on the line parameter vector, and returning to the step of performing parameterized gate calculation on the candidate line based on the line structure of the candidate line and the line parameter vector to obtain a line unitary operator; If not, carrying out parameter optimization on the candidate lines according to the line parameter vector to obtain optimized lines, and collecting all the optimized lines in the candidate line set into an optimized line set.
  8. 8. The digitized quantum simulation method of claim 1, wherein non-uniform Clifford sampling of the optimized line set based on the gate distribution structure features results in a sampled line subset, comprising: acquiring hardware calibration parameters of the quantum simulation model, selecting optimized circuits in the optimized circuit set one by one as target optimized circuits, and identifying sensitive areas of the target optimized circuits according to gate distribution structural characteristics of the target optimized circuits and the hardware calibration parameters to obtain high-noise sensitive areas; distributing non-uniform sampling weights to the target optimized circuit according to the high noise sensitive area, and determining Clifford substitution probability corresponding to each quantum gate in the target optimized circuit according to the non-uniform sampling weights; Gate-level Clifford sampling is carried out on each quantum gate of the target optimization circuit according to the Clifford replacement probability, and a primary sampling circuit is obtained; And carrying out structural consistency check on the primary sampling lines according to the symmetry constraint to obtain sampling lines, and collecting the sampling lines of all target optimization lines in the optimization line set into a sampling line subset.
  9. 9. The digitized quantum simulation method of claim 8, wherein screening the subset of sampled lines for optimal quantum lines based on a deviation of experimental observations from theoretical expectations comprises: Decomposing the target Hamiltonian amount into a hardware measurable Brix operator item set to obtain an operator set to be observed; Compiling the sampling line subset into a pulse instruction executable by a quantum processor, loading and running, repeatedly measuring the sampling line subset for a plurality of times by using the quantum processor, and calculating experimental observation values corresponding to each operator to be observed in the operators to be observed in the plurality of times by using a statistical averaging method to obtain an experimental observation value set; calculating theoretical expected values corresponding to the sampling line subsets by using a classical simulator to obtain a theoretical expected value set; Calculating the deviation between the experimental observation value set and the theoretical expected value set to obtain a deviation loss value set; calculating the noise-resistant evaluation diversity of the line according to the deviation loss set and the variance distribution of the non-uniform Clifford sampling; and screening out an optimal anti-noise score from the line anti-noise score set, taking a sampling line corresponding to the optimal anti-noise score in the sampling line subset as an optimal sampling line, and taking an optimal line corresponding to the optimal sampling line before non-uniform Clifford sampling as an optimal quantum line.
  10. 10. A digitized quantum simulation system, comprising a symmetry decomposition module, a population initialization module, a line variation module, a parameter optimization module and a quantum simulation module, wherein: the symmetry decomposition module is used for carrying out symmetry analysis and subspace decomposition on the target Hamiltonian quantity obtained in advance to obtain an effective Hamiltonian quantity and a corresponding symmetry constraint condition; the population initialization module constructs a target unitary operator according to the effective Hamiltonian quantity, and initializes the quantum circuit population of the target unitary operator by combining the symmetry constraint condition; The line mutation module is used for calculating entanglement characteristics of each quantum line in the quantum line population, carrying out structural mutation on the quantum line population based on the entanglement characteristics, and carrying out line segment intersection by combining the symmetry constraint condition to obtain a candidate line set; The parameter optimization module is used for optimizing the line parameters of the candidate line set based on the fidelity gradient to obtain an optimized line set, and extracting the gate distribution structure characteristics of the optimized line set; and the quantum simulation module is used for carrying out non-uniform Clifford sampling on the optimized line set based on the gate distribution structure characteristics to obtain a sampling line subset, screening out an optimal quantum line from the sampling line subset based on the deviation of an experimental observation value and a theoretical expected value, and carrying out quantum simulation based on the optimal quantum line.

Description

Digital quantum simulation method Technical Field The invention relates to the technical field of quantum computing, in particular to a digital quantum simulation method. Background The quantum simulation is used as a core application field of quantum computing, aims to simulate the evolution process of a complex quantum system through a controllable quantum system, and has great value in the fields of material design, drug research and development, quantum chemistry and the like. However, current quantum simulation methods still face significant challenges in noisy mid-scale quantum era. Firstly, the traditional digital simulation method based on quantum gate decomposition needs to map the target Hamiltonian amount into a deep quantum circuit, and as the number of quantum bits increases, the circuit depth and noise accumulation are aggravated, so that the simulation fidelity is drastically reduced. Secondly, the existing quantum circuit design is dependent on Trotter fixed templates, and the integration of hardware noise self-adaption and symmetry constraint is lacked, and high-precision evolution is difficult to realize in a limited coherence time. In addition, quantum hardware noise breaks down the physical conservation law of the simulation process, and the existing error mitigation technology generally consumes a large amount of resources, and cannot guarantee that the evolution process meets the symmetry requirement. Although hybrid quantum simulators promote flexibility by combining digital and analog modes, they are still limited in complex multi-body system simulations by line structure optimization deficiencies and noise robustness deficiencies. Disclosure of Invention (One) solving the technical problems Aiming at the defects of the prior art, the invention provides a digital quantum simulation method which has the advantages of high reliability, high simulation precision, strong robustness and the like, and solves the problems of deep line noise accumulation, low calculation efficiency and low quantum resource cooperative efficiency in a quantum simulation scene. (II) technical scheme In order to achieve the above purpose, the present invention provides the following technical solutions: the invention provides a digital quantum simulation method, which comprises the following steps: Carrying out symmetry analysis and subspace decomposition on a target Hamiltonian amount obtained in advance to obtain an effective Hamiltonian amount and a corresponding symmetry constraint condition; Constructing a target unitary operator according to the effective Hamiltonian quantity, and initializing a quantum circuit population of the target unitary operator by combining the symmetry constraint condition; calculating entanglement degree characteristics of each quantum circuit in the quantum circuit population, carrying out structural variation on the quantum circuit population based on the entanglement degree characteristics, and carrying out circuit segment intersection by combining the symmetry constraint condition to obtain a candidate circuit set; Performing line parameter optimization on the candidate line set based on fidelity gradient to obtain an optimized line set, and extracting gate distribution structure characteristics of the optimized line set; And carrying out non-uniform Clifford sampling on the optimized line set based on the gate distribution structure characteristics to obtain a sampling line subset, screening out an optimal quantum line from the sampling line subset based on the deviation of an experimental observation value and a theoretical expected value, and carrying out quantum simulation based on the optimal quantum line. According to one preferred embodiment of the present invention, symmetry analysis and subspace decomposition are performed on a target hamiltonian obtained in advance to obtain an effective hamiltonian and a corresponding symmetry constraint condition, including: performing item level expansion and structural analysis on a target Hamiltonian volume obtained in advance, and identifying local items, interaction items and corresponding operators contained in the target Hamiltonian volume to obtain a Hamiltonian volume operator item set; Determining a symmetry operator set corresponding to the target Hamiltonian whole according to the Hamiltonian operator item set; Dividing Quan Xier Bert space into a plurality of mutually orthogonal intrinsic subspaces according to the symmetry operator set, and constructing projection operators for each intrinsic subspace to obtain a subspace projection operator set; Screening out a target subspace projection operator from the subspace projection operator set according to the initial state of the target Hamiltonian amount, and projecting the target Hamiltonian amount into the target subspace projection operator to obtain an effective Hamiltonian amount; and extracting mathematical constraint corresponding to each intrinsic subspace in t