  We investigate theoretically the dynamical behavior of a qubit obtained with
the two ground eigenstates of an ultrastrong coupling circuit-QED system
consisting of a finite number of Josephson fluxonium atoms inductively coupled
to a transmission line resonator. We show an universal set of quantum gates by
using multiple transmission line resonators (each resonator represents a single
qubit). We discuss the intrinsic 'anisotropic' nature of noise sources for
fluxonium artificial atoms. Through a master equation treatment with colored
noise and manylevel dynamics, we prove that, for a general class of anisotropic
noise sources, the coherence time of the qubit and the fidelity of the quantum
operations can be dramatically improved in an optimal regime of ultrastrong
coupling, where the ground state is an entangled photonic 'cat' state.
