We investigated decoherence of a Josephson vortex quantum bit (qubit) in
dissipative and noisy environment. As the Josephson vortex qubit (JVQ) is
fabricated by using a long Josephson junction (LJJ), we use the perturbed
sine-Gordon equation to describe the phase dynamics representing a two-state
system and estimate the effects of quasiparticle dissipation and weakly
fluctuating critical and bias currents on the relaxation time T_1 and on the
dephasing time T_\phi. We show that the critical current fluctuation does not
contribute to dephasing of the qubit in the lowest order approximation.
Modeling the weak current variation from magnetic field fluctuations in the LJJ
by using the Gaussian colored noise with long correlation time, we show that
the coherence time T_2 is limited by the low frequency current noise at very
low temperatures. Also, we show that an ultra-long coherence time may be
obtained from the JVQ by using experimentally accessible value of physical
parameters.Comment: 13 pages,8 figures,to be appeared in Phys.Rev.