  The unit of quantum information is the qubit, a vector in a two-dimensional
Hilbert space. On the other hand, quantum hardware often operates in
two-dimensional subspaces of vector spaces of higher dimensionality. The
presence of higher quantum states may affect the accuracy of quantum
information processing. In this Letter we show how to cope with {\em quantum
leakage} in devices based on small Josephson junctions. While the presence of
higher charge states of the junction reduces the fidelity during gate
operations we demonstrate that errors can be minimized by appropriately
designing and operating the gates.
