Bayesian Quantum Multiphase Estimation Algorithm

TL;DR

This paper introduces a Bayesian quantum algorithm for simultaneous estimation of multiple phases, improving sensitivity, noise resilience, and practical implementability in quantum computing and simulation.

Contribution

It presents a novel Bayesian multi-phase estimation algorithm that leverages correlations to outperform sequential strategies and is feasible with current optical technology.

Findings

Covariance matrix elements scale inversely with the square of resources

Parallel estimation surpasses sequential sensitivity for phase combinations

Algorithm shows resilience to noise and practical implementability

Abstract

Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a single phase, applications to the simultaneous estimation of several phases may bring substantial advantages; for instance, in the presence of spatial or temporal constraints. In this work, we study a Bayesian algorithm for the parallel (simultaneous) estimation of multiple arbitrary phases. The protocol gives access to correlations in the Bayesian multi-phase distribution resulting in covariance matrix elements scaling inversely proportional to the square of the total number of quantum resources. The parallel estimation allows to surpass the sensitivity of sequential single-phase estimation strategies for optimal linear combinations of phases. Furthermore, the algorithm proves a certain noise resilience and can be implemented using single photons and standard optical elements in currently accessible experiments.