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The last decade has witnessed remarkable progress in the development ofquantum technologies. Although fault-tolerant devices likely remain years away,the noisy intermediate-scale quantum devices of today may be leveraged forother 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 todemonstrate improvements over classical capabilities. In this Perspective, wepropose a variety of ways that the performance of VQAs could be informed byquantum optimal control theory. To set the stage, we identify VQAs and quantumoptimal control as formulations of variational optimization at the circuitlevel and pulse level, respectively, where these represent just two levels in abroader hierarchy of abstractions that we consider. In this unified picture, wesuggest several ways that the different levels of abstraction may be connected,in order to facilitate the application of quantum optimal control theory to VQAchallenges associated with ansatz selection, optimization landscapes, noise,and robustness. A major theme throughout is the need for sufficient controlresources in VQA implementations; we discuss different ways this need canmanifest, outline a variety of open questions, and conclude with a look to thefuture.

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