A variational quantum algorithm by Bayesian Inference with von Mises-Fisher distribution

TL;DR

This paper introduces a novel variational quantum algorithm that uses Bayesian inference with von Mises-Fisher distribution to efficiently identify ground states of Hamiltonians, addressing measurement challenges in quantum eigensolvers.

Contribution

It proposes a new quantum algorithm combining Bayesian inference and von Mises-Fisher distribution, demonstrating its effectiveness in ground state identification for random Hamiltonians.

Findings

Successfully identifies ground states with high probability

Demonstrates the potential of von Mises-Fisher distribution in quantum algorithms

Provides a theoretical foundation for future quantum information applications

Abstract

The variational quantum eigensolver algorithm has gained attentions due to its capability of locating the ground state and ground energy of a Hamiltonian, which is a fundamental task in many physical and chemical problems. Although it has demonstrated promising results, the use of various types of measurements remains a significant obstacle. Recently, a quantum phase estimation algorithm inspired measurement scheme has been proposed to overcome this issue by introducing an additional ancilla system that is coupled to the primary system. Based on this measurement scheme, we present a novel approach that employs Bayesian inference principles together with von Mises-Fisher distribution and theoretically demonstrates the new algorithm's capability in identifying the ground state with certain for various random Hamiltonian matrices. This also opens a new way for exploring the von Mises-Fisher distribution potential in other quantum information science problems.