Heavy tails in the distribution of time-to-solution for classical and quantum annealing

TL;DR

This paper investigates the distribution of annealing times in classical and quantum annealing, revealing heavy tails indicating extremely hard problem instances, and shows that non-adiabatic schedules can significantly improve quantum annealing performance.

Contribution

It provides a comparative analysis of the time-to-solution distributions for classical and quantum annealing on spin glass problems, highlighting the impact of schedule choices.

Findings

Quantum annealing exhibits broader, heavier-tailed distributions than classical annealing.

Non-adiabatic schedules can drastically reduce the time-to-solution for hard instances.

Power-law distributions characterize the difficulty landscape of annealing algorithms.

Abstract

For many optimization algorithms the time-to-solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and especially its tail. Here we analyze the distributions of annealing times for simulated annealing and simulated quantum annealing (by path integral quantum Monte Carlo) for random Ising spin glass instances. We find power-law distributions with very heavy tails, corresponding to extremely hard instances, but far broader distributions - and thus worse performance for hard instances - for simulated quantum annealing than for simulated annealing. Fast, non-adiabatic, annealing schedules can improve the performance of simulated quantum annealing for very hard instances by many orders of magnitude.