Latency considerations for stochastic optimizers in variational quantum algorithms

TL;DR

This paper explores the use of stochastic optimization algorithms in variational quantum algorithms, analyzing the trade-offs between iteration complexity and shot complexity, and how latency influences optimizer choice.

Contribution

It introduces stochastic optimization methods that emulate deterministic dynamics, providing a theoretical basis for optimizer selection based on latency and shot times.

Findings

Stochastic algorithms can have better worst-case iteration complexity.

Trade-offs exist between iteration complexity and shot complexity.

Optimizer choice should consider latency and shot execution times.

Abstract

Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of greater per-iteration sample (shot) complexities. We investigate this trade-off both theoretically and empirically and conclude that preferences for a choice of stochastic optimizer should explicitly depend on a function of both latency and shot execution times.