Accurate control of Josephson phase qubits

A quantum bit is a closed two-dimensional Hilbert space, but often experimental systems have three or more energy levels. In a Josephson phase qubit the energy differences between successive levels differ by only a few percent, and hence care must be taken to isolate the two desired levels from the remaining Hilbert space. Here we show via numerical simulations how to restrict operations to the qubit subspace of a three-level Josephson junction system requiring shorter time duration and suffering less error compared with traditional methods. This is achieved by employing amplitude modulated pulses as well as carefully designed sequences of square wave pulses. We also show that tunneling out of higher lying energy levels represents a significant source of decoherence that can be reduced by tuning the system to contain four or more energy levels.