A mechanical qubit

Strong nonlinear interactions between quantized excitations are an important resource for quantum technologies based on bosonic oscillator modes. However, inherent mechanical nonlinearities are typically too weak to observe nonlinear effects at the single-quantum level. By dispersively coupling a bulk acoustic wave resonator to a superconducting qubit, we demonstrate the realization of the single-phonon nonlinear regime in a solid-state mechanical system, where the anharmonicity exceeds the decoherence rate by a factor of 6.8. This allows us to operate the system as a mechanical qubit, by enabling us to drive Rabi oscillations between its two lowest energy levels and demonstrate initialization, readout and implementation of a full set of single-qubit gates. Our results facilitate the use of existing quantum sensing protocols for two level systems, which makes our system suitable for force sensing and tests of fundamental physics.