A Mechanical Qubit

Strong nonlinear interactions between quantized excitations are crucial for quantum technologies that utilize bosonic oscillator modes. However, inherent mechanical nonlinearities are typically too weak to observe nonlinear effects at the single-quantum level. In this work, we overcome this limitation by dispersively coupling a solid-state mechanical resonator to a superconducting qubit, thereby realizing the single-phonon nonlinear regime. We measure the phonon anharmonicity using spectroscopy and Ramsey sequences and show that the anharmonicity exceeds the phonon decoherence rate by a factor of 6.8. At the same time, the dispersive coupling ensures that the system's mechanical nature is preserved. This enables us to operate the system as a mechanical qubit, allowing us to drive Rabi oscillations between its two lowest energy levels and demonstrate initialization, readout, and the implementation of a complete 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.