Mechanical resonators can store quantum states for long times: aluminium drums a few tens of micrometres across, suspended above a chip, vibrate at megahertz frequencies with energy lifetimes of seconds. Controlling them at the level of single quanta requires a nonlinear element at the same frequency. Our team has developed such an element, the heavy fluxonium, a superconducting qubit with a transition frequency around 1 MHz, and has used it to read out and cool the motion of a mechanical resonator. During the internship, the student will design a drum–qubit chip with a coupling large enough for drum and qubit to exchange single quanta of vibration (strong-coupling regime), combining electromechanical and circuit modelling. The student will also become familiar with our ongoing experiments on fluxonium–mechanical devices at 10 mK. This design is the starting point of the PhD, which will address the preparation of Schrödinger-cat states of a megahertz mechanical mode and the encoding of an error-protected quantum bit in the motion of the drum.