Comparing relaxation mechanisms in quantum and classical transverse-field annealing

TL;DR

This paper investigates the relaxation mechanisms in quantum and classical transverse-field annealing by pausing the anneal, revealing that success probability improvements are not uniquely quantum and identifying a dominant relaxation time-scale.

Contribution

It introduces a method to probe dissipative dynamics during annealing and compares quantum and classical models, showing qualitative agreement and conditions for pausing to enhance solution times.

Findings

Pausing during annealing increases success probability in both quantum and classical models.

Relaxation is dominated by a single time-scale, enabling simplified analysis.

Temperature effects can help distinguish quantum from classical annealing behaviors.

Abstract

Annealing schedule control provides new opportunities to better understand the manner and mechanisms by which putative quantum annealers operate. By appropriately modifying the annealing schedule to include a pause (keeping the Hamiltonian fixed) for a period of time, we show it is possible to more directly probe the dissipative dynamics of the system at intermediate points along the anneal and examine thermal relaxation rates, for example, by observing the re-population of the ground state after the minimum spectral gap. We provide a detailed comparison of experiments from a D-Wave device, simulations of the quantum adiabatic master equation and a classical analogue of quantum annealing, spin-vector Monte Carlo, and we observe qualitative agreement, showing that the characteristic increase in success probability when pausing is not a uniquely quantum phenomena. We find that the relaxation in our system is dominated by a single time-scale, which allows us to give a simple condition for when we can expect pausing to improve the time-to-solution, the relevant metric for classical optimization. Finally, we also explore in simulation the role of temperature whilst pausing as a means to better distinguish quantum and classical models of quantum annealers.