From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms

TL;DR

This paper explores how quantum optimal control theory can enhance variational quantum algorithms by connecting circuit and pulse level optimizations, addressing challenges like noise and ansatz selection on near-term quantum devices.

Contribution

It introduces a unified framework linking variational quantum algorithms and quantum optimal control, proposing methods to improve VQA performance through multi-level control strategies.

Findings

Identifies the connection between VQAs and quantum optimal control as a hierarchy of variational optimization levels.

Suggests strategies for integrating control resources to improve VQA robustness and efficiency.

Highlights open questions and future directions for control-based enhancements in quantum algorithms.

Abstract

The last decade has witnessed remarkable progress in the development of quantum technologies. Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes. Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities. In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory. To set the stage, we identify VQAs and quantum optimal control as formulations of variational optimization at the circuit level and pulse level, respectively, where these represent just two levels in a broader hierarchy of abstractions that we consider. In this unified picture, we suggest several ways that the different levels of abstraction may be connected, in order to facilitate the application of quantum optimal control theory to VQA challenges associated with ansatz selection, optimization landscapes, noise, and robustness. A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and conclude with a look to the future.