Variational quantum algorithm with information sharing

Chris N Self,Alistair W R Smith,Florian Mintert,M S Kim,Peter D Haynes,Kiran E Khosla,Frédéric Sauvage,Johannes Knolle

doi:10.1038/s41534-021-00452-9

Abstract

We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to the next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.

Highlights

Rapid developments in quantum computing hardware[1,2,3] have led to an explosion of interest in near-term applications[4,5,6,7,8]
We introduce a parallel optimisation scheme for VQA problems where the cost function is parameterised by some physical parameter(s)
Using our Bayesian optimisation with information sharing (BOIS) approach, we demonstrate a significant reduction in the number of circuits required to obtain a good solution at all parameter points

Summary

Introduction

Rapid developments in quantum computing hardware[1,2,3] have led to an explosion of interest in near-term applications[4,5,6,7,8]. Variational algorithms use low depth quantum circuits as a subroutine in a larger classical optimisation and have been applied broadly, including to binary optimisation problems[10,11,12], training machine learning models[13,14,15], and obtaining energy spectra[16,17,18]. While low depth circuits lessen the effect of errors, error rates are still a challenge for current practical implementations. Addressing these errors has been a focus within the literature, with many sophisticated error mitigation approaches being developed[19,20,21]. Other obstacles include ansatz construction[22,23], optimisation challenges[24,25] and integrated hardware design[26]

Objectives

Methods

Results

Conclusion