Gradient evaluation of analytic control for quantum systems with large Hilbert space

Open loop optimization of a quantum system involves computing gradients of propagators with respect to control parameters. One of the most commonly used optimal control methods is GRAPE, which assumes a piece-wise constant (PWC) pulse ansatz. While GRAPE allows for an easy evaluation of the gradients, it is harder to implement in experiments due to deviation from the ideal pulse shape. These pulses are also susceptible to be problem specific and hard to interpret. Analytic controls on the other hand have fewer parameters, making it easier to implement, and provide interpretable results.

In this work, we construct a general framework for computing analytical gradients of quantum dynamics for both open and closed system, for any general pulse shape. These are derived from the analytic solution to gradients, and can be evaluated in parallel using only a few state propagation. Additionally, we present cases where the computation of the gradients can be done by propagating only a single state, hence making it useful for systems with large Hilbert space where computing the propagators is expensive. Finally, we discuss cases in which the gradients can be computed efficiently for open systems with large Hilbert space dimension.