Leakage of the Josephson flux qubit

We study the dynamics of the Josephson flux qubit, which consists on a SQUID loop with three Josephson junctions operated at or near a magnetic flux of half quantum. We perform simulations of the time dependent Schroedinger equation when the system is started in the ground state. The leakage from the two lowest energy levels of the qubit computational subspace to higher energy levels is calculated, when pulses in the magnetic field are applied. We obtain, as expected, that constant field pulses have a higher leakage than rf field pulses at the resonant Rabi frequency. In the case of the constant field pulse we study the average leakage as a function of the pulse intensity, fp. For low fp we obtain that the leakage is quadratic in fp and we compare with a perturbative calculation.