Minimization of environment-induced decoherence in quantum subsystems and application to solid-state-based quantum gates

A general formulation of optimal control theory for open quantum systems (quantum subsystems) based on a superoperator method is presented. This approach is applied to a computation of optimized time-dependent fields for solid-state-based realizations of quantum gates. Decoherence is incorporated within the spin-boson model and treated within, essentially, the Bloch-Redfield formalism. Generating a decoherence-free subspace for the superoperator dynamically, we identify optimal trajectories in the phase space of the dynamical system for one- and two-qubit subsystems. Numerical analysis shows that, for the ideal case where one has full control over the subsystem's Hamiltonian, any gate operation can be realized with arbitrary small loss of coherence due to dephasing and optimal solutions exist which are independent of both spectral density and the temperature of the environment. At the example of a Josephson charge quantum gate we study the more realistic situation where one has a restricted number of control fields which, while providing a universal gate, cannot completely eliminate dephasing.