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arXiv:2407.02864 · Quantum Information Processing

A quantum approach for optimal control

Hirmay Sandesara, Alok Shukla, Prakash Vedula

Published Mar 20, 2025• 2 citations
arXivHTMLPDF
DOI
10.1007/s11128-025-04710-z

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Quantum optimal control (QOC) aims to find control functions that optimally steer a quantum system toward a target operation. We introduce a \emph{randomized} QOC framework where optimization is carried over an ensemble of control functions and their probabilities, instead of a single set of functions. Using this framework, we prove that randomized QOC can reach a target accuracy faster than any deterministic protocol under the same resource constraints. We also develop general symmetry-based constructions that convert a given control into an ensemble of controls that can systematically reduce the error. We benchmark these constructions for CNOT implementation and find that the resulting randomized protocol quadratically suppresses the error of the optimized deterministic solution. In addition, we introduce randomized GRAPE, which generalizes GRAPE to directly optimize control ensembles and their associated probabilities. Finally, as a related application, we discuss randomized boundary-pulse constructions {that enhance} robustness against coherent noise.
Quantum optimal control (QOC) enables the realization of accurate operations, such as quantum gates, and supports the development of quantum technologies. To date, many QOC frameworks have been developed, but those remain only naturally suited to optimize a single targeted operation at a time. We extend this concept to optimal control with a continuous family of targets, and demonstrate that an optimization based on neural networks can find families of time-dependent Hamiltonians realizing desired classes of quantum gates in minimal time.
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