Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

TL;DR

This paper evaluates the D-Wave 2X quantum annealer's ability to uniformly sample degenerate ground states, revealing limitations of naive transverse-field approaches and suggesting the need for more complex Hamiltonians.

Contribution

It demonstrates the inadequacy of simple transverse-field quantum annealing in uniformly sampling all ground states and highlights the necessity for advanced driving Hamiltonians.

Findings

Naive transverse-field annealing poorly samples degenerate ground states.

Some ground states are exponentially suppressed in sampling.

Complex driving Hamiltonians are required for fair ground-state sampling.

Abstract

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.