Intrinsic leakage of the Josephson flux qubit and breakdown of the two-level approximation for strong driving

Abstract

Solid-state devices for quantum-bit computation qubits are not perfect isolated two-level systems sinceadditional higher energy levels always exist. One example is the Josephson flux qubit, which consists on amesoscopic superconducting quantum interference device loop with three Josephson junctions operated at ornear a magnetic flux of half quantum. We study intrinsic leakage effects, i.e., direct transitions from theallowed qubit states to higher excited states of the system during the application of pulses for quantumcomputation operations. The system is started in the ground state and rf-magnetic field pulses are applied at thequbit resonant frequency with pulse intensity f p. A perturbative calculation of the average leakage for small f pis performed for this case, obtaining that the leakage is quadratic in f p, and that it depends mainly on the matrixelements of the supercurrent. Numerical simulations of the time-dependent Schrödinger equation correspondingto the full Hamiltonian of this device were also performed. From the simulations we obtain the value of f pabove which the two-level approximation breaks down, and we estimate the maximum Rabi frequency that canbe achieved. We study the leakage as a function of the ratio among the Josephson energies of the junctionsof the device, obtaining the best value for minimum leakage 0.85. The effects of flux noise on the leakageare also discussed.