Optimal working point in digitized quantum annealing

TL;DR

This paper investigates the optimal annealing time in digitized quantum annealing, revealing a linear scaling with Trotter steps and identifying a threshold beyond which the residual energy error increases sharply.

Contribution

The study provides an analytical and numerical analysis of the optimal working point in digitized quantum annealing, highlighting its dependence on Trotter steps and robustness to disorder.

Findings

Optimal annealing time scales linearly with Trotter steps.

Residual energy error increases sharply beyond the optimal point.

Scenario persists even with disorder in the system.

Abstract

We present a study of the digitized Quantum Annealing protocol proposed by R. Barends et al., Nature 534, 222 (2016). Our analysis, performed on the benchmark case of a transverse Ising chain problem, shows that the algorithm has a well defined optimal working point for the annealing time $\tau^{\mathrm{opt}}_\mathrm{P}$ --- scaling as $\tau^{\mathrm{opt}}_\mathrm{P}\sim \mathrm{P}$, where $\mathrm{P}$ is the number of digital Trotter steps --- beyond which, the residual energy error shoots-up towards the value characteristic of the maximally disordered state. We present an analytical analysis for the translationally invariant transverse Ising chain case, but our numerical evidence suggests that this scenario is more general, surviving, for instance, the presence of disorder.