Tradeoff between leakage and dephasing errors in the fluxonium qubit

We present a tradeoff between anharmonicity (related to leakage) and pure dephasing errors for the fluxonium circuit. We show that in the insulating regime, i.e., when the persistent current flowing across the circuit is suppressed, the pure dephasing rate induced by a Markovian environment decreases exponentially as the impedance of the circuit is increased. In contrast to this exponential decrease, the qubit remains sufficiently anharmonic so that gate times can still be short, allowing for significant reduction in the computational error rates. A transition from the insulating to the superconducting phases establishes an upper bound on the Josephson energy below which this tradeoff exists. © 2013 American Physical Society.