Experimental Determination of Multi-Qubit Ground State via a Cluster Mean-Field Algorithm

TL;DR

This paper introduces a cluster mean-field quantum eigensolver that partitions multi-qubit systems into clusters to efficiently approximate ground states, validated through numerical and experimental studies.

Contribution

It proposes a novel multi-layer cluster mean-field algorithm for quantum ground state determination, combining partial environment averaging with effective Hamiltonian diagonalization.

Findings

Accurately predicts ground states in multi-spin chains.

Successfully applied to a three-spin network experimentally.

Demonstrates efficiency of the CMF approach in quantum systems.

Abstract

A quantum eigensolver is designed under a multi-layer cluster mean-field (CMF) algorithm by partitioning a quantum system into spatially-separated clusters. For each cluster, a reduced Hamiltonian is obtained after a partial average over its environment cluster. The products of eigenstates from different clusters construct a compressed Hilbert space, in which an effective Hamiltonian is diagonalized to determine certain eigenstates of the whole Hamiltonian. The CMF method is numerically verified in multi-spin chains and experimentally studied in a fully-connected three-spin network, both yielding an excellent prediction of their ground states.