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Gradient Ascent Pulse Engineering (GRAPE) is a popular technique in quantumoptimal control, and can be combined with automatic differentiation (AD) tofacilitate on-the-fly evaluation of cost-function gradients. We illustrate thatthe convenience of AD comes at a significant memory cost due to the cumulativestorage of a large number of states and propagators. For quantum systems ofincreasing Hilbert space size, this imposes a significant bottleneck. Werevisit the strategy of hard-coding gradients in a scheme that fully avoidspropagator storage and significantly reduces memory requirements. Separately,we present improvements to numerical state propagation to enhance runtimeperformance. We benchmark runtime and memory usage and compare this approach toAD-based implementations, with a focus on pushing towards larger Hilbert spacesizes. The results confirm that the AD-free approach facilitates theapplication of optimal control for large quantum systems which would otherwisebe difficult to tackle.

Optimal control of large quantum systems: assessing memory and runtime performance of GRAPE