A Quantum-classical Hybrid Clustering Algorithm for Excited States Preparation - RMGS

Description

Quantum computers have been widely speculated to offer significant advantages in obtaining the eigenstates of many-body Hamiltonians in chemistry and physics. In this proposal, we propose a quantum-classical hybrid strategy for quick eigenspectrum preparation. Different from the typical setting of performing the accurate but cost-consuming excited state finding method, we extend the imaginary-time method to the quantum-classical hybrid clustering for the rough preparation of the eigenspectrum. To make the method accessible in the noisy intermediate-scale quantum era, we plan to use a type of measurement-friendly parameterized quantum circuit where parameters scale linearly with the system as a kernel to extract eigenspectrum information for following classical clustering like K-means. Through numerical examples and theoretical analysis, we expect to show that the quantum-classical hybrid clustering can obtain the eigenspectrum distribution more efficiently than the existing excited state methods. And, it can be used as a subroutine to speed up existing classical or quantum methods to approximately find exact eigenstates.