Aspects of Qubit Dynamics in the Presence of Leakage

Nano-electronics devices such as small-capacitance Josephsonjunction circuits appear to be promising systems to implementquantum logic. While the elementary unit of a quantum computeris a two-state system (the qubit) the computational space of aJosephson junction qubit is a subset of a larger Hilbertspace. Therefore quantum leakage may occur, i.e. during theoperation of the device the quantum state may escape partiallyfrom the computational subspace. We study the consequences ofleakage for the fidelity of Josephson qubits and discuss howthe gate design can be optimized.