Using models to improve optimizers for variational quantum algorithms

TL;DR

This paper introduces two surrogate model-based optimization methods for variational quantum algorithms, aiming to improve efficiency and robustness in noisy, real-world quantum computing settings.

Contribution

The paper proposes novel surrogate model-based optimizers utilizing quadratic fits and trusted regions, tailored for noisy quantum hardware, with comprehensive performance comparisons.

Findings

The new methods outperform standard optimizers in simulated noisy environments.

Cost models tailored to quantum hardware improve optimizer selection and hyperparameter tuning.

One method was successfully applied to Google's Sycamore device in a practical experiment.

Abstract

Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized quantum circuit. In practice, finite sampling error and gate errors make this a stochastic optimization with unique challenges that must be addressed at the level of the optimizer. The sharp trade-off between precision and sampling time in conjunction with experimental constraints necessitates the development of new optimization strategies to minimize overall wall clock time in this setting. In this work, we introduce two optimization methods and numerically compare their performance with common methods in use today. The methods are surrogate model-based algorithms designed to improve reuse of collected data. They do so by utilizing a least-squares quadratic fit of sampled function values within a moving trusted region to estimate the gradient or a policy gradient. To make fair comparisons between optimization methods, we develop experimentally relevant cost models designed to balance efficiency in testing and accuracy with respect to cloud quantum computing systems. The results here underscore the need to both use relevant cost models and optimize hyperparameters of existing optimization methods for competitive performance. The methods introduced here have several practical advantages in realistic experimental settings, and we have used one of them successfully in a separately published experiment on Google's Sycamore device.