  We report the realization of quantum microwave circuits using hybrid
superconductor-semiconductor Josephson elements comprised of InAs nanowires
contacted by NbTiN. Capacitively-shunted single elements behave as transmon
qubits with electrically tunable transition frequencies. Two-element circuits
also exhibit transmon-like behavior near zero applied flux, but behave as flux
qubits at half the flux quantum, where non-sinusoidal current-phase relations
in the elements produce a double-well Josephson potential. These hybrid
Josephson elements are promising for applications requiring microwave
superconducting circuits operating in magnetic field.
