Quantum annealing speedup over simulated annealing on random Ising chains

TL;DR

This paper demonstrates a quadratic speedup of quantum annealing over simulated annealing in a 1D random Ising model, with additional exponential speedup from a quantum-inspired imaginary-time approach, challenging previous assumptions.

Contribution

It provides the first exact comparison showing quantum annealing's advantage over classical simulated annealing in a 1D random Ising chain, including novel quantum-inspired methods.

Findings

Quantum annealing achieves quadratic speedup over simulated annealing.

Quantum-inspired imaginary-time QA yields exponential speedup.

SA does not encounter phase transitions, unlike QA.

Abstract

We show clear evidence of a quadratic speedup of a quantum annealing (QA) Schroedinger dynamics over a Glauber master-equation simulated annealing (SA) for a random Ising model in one dimension, via an equal-footing exact deterministic dynamics of the Jordan-Wigner fermionized problems. This is remarkable, in view of the arguments of Katzgraber et al., PRX 4, 021008 (2014), since SA does not encounter any phase transition, while QA does. We also find a second remarkable result: that a "quantum-inspired" imaginary-time Schroedinger QA provides a further exponential speedup, i.e., an asymptotic residual error decreasing as a power-law $\tau^{-\mu}$ of the annealing time $\tau$.