Optimal control for non-Markovian open quantum systems

An efficient optimal-control theory based on the Krotov method is introduced for a non-Markovian open quantum system with a time-nonlocal master equation in which the control parameter and the bath correlation function are correlated. This optimal-control method is developed via a quantum dissipation formulation that transforms the time-nonlocal master equation to a set of coupled linear time-local equations of motion in an extended auxiliary Liouville space. As an illustration, the optimal-control method is applied to find the control sequences for high-fidelity Z gates and identity gates of a qubit embedded in a non-Markovian bath. Z gates and identity gates with errors less than 10^{-5} for a wide range of bath decoherence parameters can be achieved for the non-Markovian open qubit system with control over only the {\sigma}z term. The control-dissipation correlation and the memory effect of the bath are crucial in achieving the high-fidelity gates.