Robust gates in holonomic quantum computation

Quantum algorithms based on geometric phases areattracting increasing interest in quantum computation.The related quantum gates representing the unitarytransformations on a register of qubits do not have adynamical origin: the Hamiltonian depends on timethrough a set of control parameters that change by followingsuitable closed loops in the associated parameter space;in the adiabatic limit the dynamical contribution to theevolution can be factorized and the features of the quantumgate depend only on the topological structure of the manifold.Geometric phases are an interesting resource for quantumcomputation in view of their robustness against decoherenceeffects. We study here the effects of the environmenton a class of one-qubit holonomic gates that have beenrecently shown to be characterized by “optimal” workingtimes. We numerically analyze the behavior of these optimalpoints and focus on their robustness against noise.