The three phases of quantum annealing: fast, slow, and very slow

TL;DR

This paper characterizes the different dynamical regimes of quantum annealing in Ising chains, identifying fast, slow, and very slow phases and their underlying physical mechanisms to optimize quantum annealer performance.

Contribution

It introduces a phase diagram for driven Ising chains that delineates the scaling behavior of excess work across different annealing speeds, integrating multiple theoretical frameworks.

Findings

Fast processes follow the Kibble-Zurek mechanism.

Slow processes are governed by Landau-Zener dynamics.

Very slow processes are well described by adiabatic perturbation theory.

Abstract

Currently, existing quantum annealers have proven themselves as viable technology for the first practical applications in the noisy-intermediate-scale-quantum era. However, to fully exploit their capabilities, a comprehensive characterization of their finite-time excitations is instrumental. To this end, we develop a phase diagram for driven Ising chains, from which the scaling behavior of the excess work can be read off as a function of process duration and system size. "Fast" processes are well described by the Kibble-Zurek mechanism; "slow" processes are governed by effective Landau-Zener dynamics; and "very slow" processes can be approximated with adiabatic perturbation theory.