Optimizing quantum gates within decoherence-free subspaces

A scheme for optimizing quantum gates in quantum computation on decoherence-free subspaces using optimal control theory is presented. Compared with the previous scheme, this scheme possesses the following properties: (i) efficiency in finding control sequences, specifically in a system without controllable exchange interaction where the previous method is difficult to handle; (ii) robustness against control errors; and (iii) showing better performance than the robust GRAPE method under stochastic noise. As an application, we work out the control sequences for the not, quantum phase, and cnot gates.