  We describe a quantum computational architecture based on integrating
nanomechanical resonators with Josephson junction phase qubits, with which we
implement single- and multi-qubit operations. The nanomechanical resonator is a
GHz-frequency, high-quality-factor dilatational resonator, coupled to the
Josephson phase through a piezoelectric interaction. This system is analogous
to one or more few-level atoms (the Josephson qubits) in a tunable
electromagnetic cavity (the nanomechanical resonator). Our architecture
combines the best features of solid-state and cavity-QED approaches, and may
make possible multi-qubit processing in a scalable, solid-state environment.
