An Aharonov—Anandan phase gate in the sub-Hilbert space of a coupling flux qubits system

Abstract

We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states |01〉 and |10〉. In this subspace, we illustrate how to generate an Aharnov—Anandan phase, based on which, we can construct a NOT gate (as effective as a C-NOT gate) in this coupling flux qubits system. Finally, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.