Optimal control of dissipative quantum dynamics

In this thesis, we develop a perturbative approximation for the solution of Lindblad master equations with time-dependent generators that satisfies the fundamental property of complete positivity, as essential for quantum simulations and optimal control of open quantum systems. By probing our method to several explicit examples we show that ensuring this property not only improves the accuracy of the perturbative approximation substantially, but also it permits to read off the effective dissipative processes . Subsequently, we design optimal entangling quantum gates for trapped ions mediated by a bus mode which is subject to decoherence. We show that suitably designed polychromatic control pulses, help to suppress the qubit-phonon entanglement substantially while maintaining the mediated interaction. This leads to a considerable reduction in the gate infidelity, in particular, for multi-qubit gates this yields a significant improvement in the gate performance.Open Acces