  Silicon nanomechanical resonators display ultra-long lifetimes at cryogenic
temperatures and microwave frequencies. Achieving quantum control of
single-phonons in these devices has so far relied on nonlinearities enabled by
coupling to ancillary qubits. In this work, we propose using atomic forces to
realize a silicon nanomechanical qubit without coupling to an ancillary qubit.
The proposed qubit operates at 60 MHz with a single-phonon level anharmonicity
of 5 MHz. We present a circuit quantum acoustodynamics architecture where
electromechanical resonators enable dispersive state readout and multi-qubit
operations. The combination of strong anharmonicity, ultrahigh mechanical
quality factors, and small footprints achievable in this platform could enable
quantum-nonlinear phononics for quantum information processing and
transduction.
