  We propose an integrated nonlinear superconducting device based on a
nanoelectromechanical shuttle. The system can be described as a qubit coupled
to a bosonic mode. The topology of the circuit gives rise to an adjustable
qubit/mechanical coupling, allowing the experimenter to tune between linear and
quadratic coupling in the mechanical degrees of freedom. Owing to its
flexibility and potential scalability, the proposed setup represents an
important step towards the implementation of bosonic error correction with
mechanical elements in large-scale superconducting circuits. We give
preliminary evidence of this possibility by discussing a simple state-swapping
protocol that uses this device as a quantum memory element.
