Synthesizing arbitrary mechanical quantum states using flux-mediated three-body interactions with superconducting qubits

We propose a scheme for generating arbitrary quantum states in a mechanical resonator using tuneable three-body interactions with two superconducting qubits. The coupling relies on embedding a suspended nanobeam in one of the arms of a superconducting quantum interference device that galvanically connects two transmon qubits, in combination with an in-plane magnetic field. Using state-of-the-art parameters and single-qubit operations, we demonstrate the possibility of ground-state cooling as well as high-fidelity preparation of arbitrary mechanical states and qubit-phonon entanglement, significantly extending the quantum control toolbox of radio-frequency mechanical oscillators.