Quantum optimal control of the driven dissipative two-level system

This paper investigates the dynamics of a two-level system coupled to a super-Ohmic boson bath, which is the so-called driven spin-boson model. Using the polaron transformation we derive the Bloch vector of a master equation where the bar tunneling parameter is used as the basis for a perturbation expansion. Our method is based on the canonical quantization provided by the Bloch-Redfield formalism. We apply quantum optimal control theory to the realization of a quantum $Z$ gate and also the coherent destruction of tunneling. To solve our optimal control problem, we use the techniques of automatic differentiation as an alternative to Pontryagin's minimum principle. The latter is less straightforward since the master equation is complex.