Effects of nuclear spins on the coherent evolution of a phase qubit

The role of nuclear spins in decoherence and dephasing of a solid state phase qubit is investigated. Both effects of static spin environment and spin polarization fluctuations in time are considered on the basis of non-Markovian Langevin-Bloch equations. We find conditions when coupling of a phase qubit to a bath of nuclear spins does not impair coherent evolution of the qubit.