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A gradient ascent method for optimal quantum control synthesis is presentedthat employs a gradient derived with respect to the coefficients of afunctional basis expansion of the control. Restricting the space of allowablecontrols to weighted sums of the Slepian sequences efficiently parameterizesthe control in terms of bandwidth, resolution and pulse duration. A boundshowing minimum time evolutions scaling with the inverse of the controlbandwidth [S. Lloyd and S. Montangero, PRL, 113, 010502, (2014)] is recoveredand the method is shown numerically to achieve the bound on entanglingtwo-qubit quantum gates.

Quantum optimal control via gradient ascent in function space and the time-bandwidth quantum speed limit