Quantum annealing: the fastest route to quantum computation?

TL;DR

This review analyzes the performance of quantum adiabatic algorithms, highlighting how many-body localization phases lead to exponentially small energy gaps, which impact the efficiency of quantum annealing.

Contribution

It provides a detailed discussion on failure mechanisms in quantum annealing, especially emphasizing the role of Many-Body Localized phases and their effect on energy gap scaling.

Findings

Small gaps due to quantum phase transitions are not predictive of scaling.

Many-Body Localized phases cause exponentially small gaps.

Thermodynamic order does not determine gap size.

Abstract

In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to avoided crossings inside a phase. We argue that the thermodynamic order of the phase transitions is not predictive of the scaling of the gap with the system size. On the contrary, we also argue that, if the phase surrounding the problem Hamiltonian is a Many-Body Localized (MBL) phase, the gaps are going to be typically exponentially small and that this follows naturally from the existence of local integrals of motion in the MBL phase.