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
$\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth
$O(1/\epsilon)$, whereas each expectation estimation subroutine within VQE
requires $O(1/\epsilon^2)$ samples from circuits with depth $O(1)$. We
propose a generalised VQE algorithm that interpolates between these two regimes
via a free parameter $\alphaın0,1$ which can exploit quantum coherence over
a circuit depth of $O(1/\epsilon^\alpha)$ to reduce the number of samples to
$O(1/\epsilon^2(1-\alpha))$. Along the way, we give a new routine for
expectation estimation under limited quantum resources that is of independent
interest.
%0 Generic
%1 wang2018accelerated
%A Wang, Daochen
%A Higgott, Oscar
%A Brierley, Stephen
%D 2018
%K quantumcomputing
%R 10.1103/PhysRevLett.122.140504
%T Accelerated Variational Quantum Eigensolver
%U http://arxiv.org/abs/1802.00171
%X 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
$\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth
$O(1/\epsilon)$, whereas each expectation estimation subroutine within VQE
requires $O(1/\epsilon^2)$ samples from circuits with depth $O(1)$. We
propose a generalised VQE algorithm that interpolates between these two regimes
via a free parameter $\alphaın0,1$ which can exploit quantum coherence over
a circuit depth of $O(1/\epsilon^\alpha)$ to reduce the number of samples to
$O(1/\epsilon^2(1-\alpha))$. Along the way, we give a new routine for
expectation estimation under limited quantum resources that is of independent
interest.
@misc{wang2018accelerated,
abstract = {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
$\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth
$O(1/\epsilon)$, whereas each expectation estimation subroutine within VQE
requires $O(1/\epsilon^{2})$ samples from circuits with depth $O(1)$. We
propose a generalised VQE algorithm that interpolates between these two regimes
via a free parameter $\alpha\in[0,1]$ which can exploit quantum coherence over
a circuit depth of $O(1/\epsilon^{\alpha})$ to reduce the number of samples to
$O(1/\epsilon^{2(1-\alpha)})$. Along the way, we give a new routine for
expectation estimation under limited quantum resources that is of independent
interest.},
added-at = {2020-03-12T11:14:57.000+0100},
author = {Wang, Daochen and Higgott, Oscar and Brierley, Stephen},
biburl = {https://www.bibsonomy.org/bibtex/2821ff3bffa67a80e837923c8f71c7331/cmcneile},
description = {Accelerated Variational Quantum Eigensolver},
doi = {10.1103/PhysRevLett.122.140504},
interhash = {73e63187a611ca063b5b2910ac72d241},
intrahash = {821ff3bffa67a80e837923c8f71c7331},
keywords = {quantumcomputing},
note = {cite arxiv:1802.00171Comment: 11 pages},
timestamp = {2020-03-12T11:14:57.000+0100},
title = {Accelerated Variational Quantum Eigensolver},
url = {http://arxiv.org/abs/1802.00171},
year = 2018
}