Simulated outperforms quantum reverse annealing in mean-field models

TL;DR

This paper compares adiabatic reverse annealing (ARA) with a classical analogue, simulated reverse annealing (SRA), showing that SRA can outperform ARA in mean-field models, challenging claims of quantum advantage.

Contribution

The paper introduces a classical analogue to ARA called SRA and demonstrates that SRA can outperform ARA in mean-field models, questioning the quantum advantage of ARA.

Findings

SRA succeeds whenever ARA does, and sometimes where ARA fails.

In the p-spin model, ARA offers no advantage over SRA.

Classical SRA can outperform quantum ARA in certain parameter regimes.

Abstract

Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase transitions. Here we interpret the performance of ARA through its effects on the free energy landscape, and use the intuition gained to introduce a classical analogue to ARA termed ``simulated reverse annealing'' (SRA). This makes it more difficult to claim that ARA provides a quantum advantage in solving a given problem, as not only must ARA succeed but the corresponding SRA must fail. As a solvable example, we analyze how both protocols behave in the infinite-range (non-disordered) $p$-spin model. Through both the thermodynamic phase diagrams and explicit dynamical behavior, we establish that the quantum algorithm has no advantage over its classical counterpart: SRA succeeds not only in every case where ARA does but even in a narrow range of parameters where ARA fails.