Entanglement and Fidelity for Holonomic Quantum Gates

Abstract

We study entanglement and fidelity of a two-qubit system when a noisy holonomic, non-Abelian, transformation is applied to one of them. The source of noise we investigate is of two types: one due to a stochastic error representing an imprecise control of the fields driving the evolution; the other due to an interaction between the two near qubits. The peculiar level structure underlying the holonomic operator leads us to introduce the reduced logical entanglement which is the fraction of entanglement in the logical space. The comparison between entanglement and fidelity shows how they are differently affected by the noise and that, in general, the first is more robust than the latter. We find a range of physical parameters for which both fidelity and reduced logical entanglement are well preserved.