Quantum Eigenstate Acquisition via Cluster Division and Compressed Hilbert Space
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Solution Overview
Problem
Current quantum eigenstate solving algorithms face challenges in efficiently computing eigenstates of high-dimensional quantum systems due to rapid increases in required quantum gate operations with increasing qubit numbers, leading to resource-intensive computations and diminished algorithmic advantages.
Innovation Solution
The method involves cluster division of a quantum system into multiple clusters, obtaining direct product states, and constructing a compressed Hilbert space with a reduced dimensionality, allowing for the equivalent Hamiltonian to be solved in a lower-dimensional space, thereby reducing the computational resources needed for eigenstate acquisition.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the quantum system is divided into multiple clusters and a compressed Hilbert space is constructed, then the computational efficiency is improved and the number of quantum gate operations is reduced, but the device complexity increases due to the need for cluster division and equivalent Hamiltonian calculation
Solution Approach 1:
The quantum system is divided into multiple clusters, each representing a subsystem with its own Hilbert space. This segmentation allows the original high-dimensional eigenstate problem to be decomposed into lower-dimensional problems that can be solved more efficiently, directly improving computational productivity while managing complexity through structured decomposition
Solution Approach 2:
The patent transforms the problem from the original high-dimensional Hilbert space to a compressed Hilbert space constructed from direct product states of cluster eigenstates. This dimensionality reduction technique projects the complex high-dimensional problem into a lower-dimensional space where calculations are more tractable, achieving better productivity without requiring proportional increases in quantum resources
2Loss of time
If the dimension number of Hilbert space is reduced by constructing compressed Hilbert space, then the number of quantum gate operations decreases, but the measurement precision may be affected by the approximation involved in compression
Solution Approach 1:
The method performs preliminary calculation of eigenstates for each individual cluster before constructing the compressed Hilbert space. These pre-computed cluster eigenstates serve as basis vectors for the compressed space, ensuring that the compression is based on physically meaningful states rather than arbitrary basis vectors, thereby maintaining accuracy while reducing computational time
Solution Approach 2:
The patent employs an iterative refinement process where the equivalent Hamiltonian is constructed in the compressed Hilbert space, its eigenstates are calculated, and these results are used to refine the understanding of the full system. This feedback mechanism allows the approximation to be systematically improved, ensuring that measurement precision is maintained even as computational time is reduced through compression
Data Source
AI summary
A method for acquiring an eigenstate of a quantum system includes performing cluster division on multiple particles included in a target quantum system to obtain multiple clusters, where each cluster includes one or more particles, obtaining multiple direct product states according to eigenstates respectively corresponding to the multiple clusters, selecting some direct product states from the multiple direct product states as a set of basis vectors to represent a compressed Hilbert space, acquiring a Hamiltonian of the target quantum system and an equivalent Hamiltonian in the compressed Hilbert space, and acquiring an eigenstate and eigenenergy of the equivalent Hamiltonian as an eigenstate and eigenenergy of the target quantum system.