  We introduce the `displacemon' electromechanical architecture that comprises
a vibrating nanobeam, e.g. a carbon nanotube, flux coupled to a superconducting
qubit. This platform can achieve strong and even ultrastrong coupling enabling
a variety of quantum protocols. We use this system to describe a protocol for
generating and measuring quantum interference between two trajectories of a
nanomechanical resonator. The scheme uses a sequence of qubit manipulations and
measurements to cool the resonator, apply an effective diffraction grating, and
measure the resulting interference pattern. We simulate the protocol for a
realistic system consisting of a vibrating carbon nanotube acting as a junction
in a superconducting qubit, and we demonstrate the feasibility of generating a
spatially distinct quantum superposition state of motion containing more than
$10^6$ nucleons.
