From Pulses to Circuits and Back Again: A Quantum Optimal Control Perspective on Variational 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 progress toward this potential crossover point 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.

On Assessing the Quantum Advantage for MaxCut Provided by Quantum Neural Network Ansätze

“…Theorem (3) shows that an exponentially parameterized simple Ansatz yields a trap-free landscape, which (as will be discussed briefly in section 6) closely relates to similar results found in the setting of quantum control landscapes [32,33,34,16] and classical neural network landscapes [35,36,37]. Nevertheless, while this is an interesting result and in particular holds for any graph G, it only holds for an exponentially-sized Ansatz, and therefore requires an exponential number of parameters in θ, thus prohibiting its scalability.…”

“…Since their inception in the early 2010s [11,12], significant attention has been paid to the quantum component of variational quantum algorithms, particularly in developing ways to evaluate the objective function associated with different problems of interest, and designing Ansätze for either specific applications or hardware implementation settings [13]. For comprehensive overviews of the theory and experiments done in this regard, we refer to [14,15,16], and for a recent review we turn to [17]. In this subsection we reformulate variational quantum algorithms in the context of focusing on the classical optimization component, similar to the setting of [18], by viewing the output of the parameterized quantum circuit as an oracle.…”

Towards Single Atom Computing via High Harmonic Generation

“…The crosspollination of information theory and physics has been particularly fruitful. Considering physical systems as information processors has allowed for the formulation of physical bounds based on informational principles [3][4][5], but perhaps the most important consequence of this synthesis has been the realisation that with suitable interpretation, all physical systems can act as computers [6,7]. The appeal of using physical systems for computation lies in the trade off it performs between the computational and energetic costs of a problem.…”

Optimal solutions to quantum annealing using two independent control functions

“…In Ref. [29] a comprehensive perspective of the possible connections between VQA with quantum control has been presented. Specifically, the authors indicate that the quantum optimal theory background can extract a rich variational structures of VQA and provide a better understanding of variational experiments.…”