Decoherence in a superconducting flux qubit with a pi-junction

We consider the use of a pi-junction for flux qubits to realize degenerate quantum levels without external magnetic field. On the basis of the Caldeira-Leggett model, we derive an effective spin-Boson model, and study decoherece of this type of qubits. We estimate the dephasing time by using parameters from recent experiments of SIFS junctions, and show that high critical current and large subgap resistance are required for the pi-junction to realize a long coherent time.