Robustness of optimal working points for nonadiabatic holonomic quantum computation

Geometric phases are an interesting resource for quantum computation in view of their robustness against decoherence effects. We study the effects of the environment on a class of one-qubit holonomic gates that have recently been shown to be characterized by 'optimal' working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise.