Accelerated Variational Quantum Eigensolver

TitleAccelerated Variational Quantum Eigensolver
Publication TypeJournal Article
Year of Publication2019
AuthorsWang, D, Higgott, O, Brierley, S
JournalPhys. Rev. Lett.
Date Published3/25/2019

The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision ε, QPE requires O(1) repetitions of circuits with depth O(1/ε), whereas each expectation estimation subroutine within VQE requires O(1/ε2) samples from circuits with depth O(1). We propose a generalised VQE algorithm that interpolates between these two regimes via a free parameter α∈[0,1] which can exploit quantum coherence over a circuit depth of O(1/εα) to reduce the number of samples to O(1/ε2(1−α)). Along the way, we give a new routine for expectation estimation under limited quantum resources that is of independent interest.