The Theory of Variational Hybrid Quantum-Classical Algorithms
Venue
New Journal of Physics, vol. 18 (2016), pp. 023023
Publication Year
2016
Authors
Jarrod McClean, Jonathan Romero, Ryan Babbush, Alán Aspuru-Guzik
BibTeX
Abstract
Many quantum algorithms have daunting resource requirements when compared to what
is available today. To address this discrepancy, a quantum-classical hybrid
optimization scheme known as "the quantum variational eigensolver" was developed
with the philosophy that even minimal quantum resources could be made useful when
used in conjunction with classical routines. In this work we extend the general
theory of this algorithm and suggest algorithmic improvements for practical
implementations. Specifically, we develop a variational adiabatic ansatz and
explore unitary coupled cluster where we establish a connection from second order
unitary coupled cluster to universal gate sets through relaxation of exponential
splitting. We introduce the concept of quantum variational error suppression that
allows some errors to be suppressed naturally in this algorithm on a pre-threshold
quantum device. Additionally, we analyze truncation and correlated sampling in
Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we
show how the use of modern derivative free optimization techniques can offer
dramatic computational savings of up to three orders of magnitude over previously
used optimization techniques.
