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The interaction between a quantum system and its environment limits ourability to control it and perform quantum operations on it. We present anefficient method to find optimal controls for quantum systems coupled tonon-Markovian environments, by using the process tensor to compute the gradientof an objective function. We consider state transfer for a driven two-levelsystem coupled to a bosonic environment, and characterize performance in termsof speed and fidelity. We thus determine the best achievable fidelity as afunction of process duration. We show there is a trade-off between speed andfidelity, and that slower processes can have higher fidelity by exploitingnon-Markovian effects.

Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?