  A gradient ascent method for optimal quantum control synthesis is presented
that employs a gradient derived with respect to the coefficients of a
functional basis expansion of the control. Restricting the space of allowable
controls to weighted sums of the Slepian sequences efficiently parameterizes
the control in terms of bandwidth, resolution and pulse duration. A bound
showing minimum time evolutions scaling with the inverse of the control
bandwidth [S. Lloyd and S. Montangero, PRL, 113, 010502, (2014)] is recovered
and the method is shown numerically to achieve the bound on entangling
two-qubit quantum gates.

Quantum Physics