A mechanical qubit is demonstrated using a solid-state mechanical system where the single-phonon nonlinear regime is realized. The system's single-phonon anharmonicity exceeds the decoherence rate by a factor of 6.8, enabling the use of the lowest two energy levels of the resonator as a mechanical qubit. The qubit supports initialization, readout, and a complete set of direct single-qubit gates. This work enhances a powerful quantum acoustics platform for quantum simulations, sensing, and information processing. Mechanical systems are typically treated as harmonic oscillators, with phonons as non-interacting quanta. However, coherent interactions at the single-quantum level in bosonic modes can lead to new physical phenomena and applications in quantum technologies. In electromagnetic systems, weak intrinsic optical nonlinearity has been overcome by coupling to strongly nonlinear media. In mechanical systems, the challenge is to achieve coherent phonon-phonon interactions, which is difficult due to the need for a long-lived, coherent mechanical mode. The study demonstrates a solid-state mechanical system with self-Kerr nonlinearity exceeding the decoherence rate. The system is a circuit quantum acoustodynamics (cQAD) system with a high-overtone bulk acoustic wave resonator (HBAR) coupled to a transmon superconducting circuit. The system is described by the Jaynes-Cummings Hamiltonian, with the anharmonicity of the phonon mode being much greater than the decoherence rate, allowing for coherent quantum operations. The mechanical qubit is operated as a qubit, with direct operations on the mechanical mode at a rate satisfying the condition Γ₂ << Ω << α, enabling coherent operations on a two-level system. The system supports Rabi oscillations, with the Rabi frequency and π-pulse fidelity measured. The mechanical qubit also supports Wigner tomography, showing that the generated state is not a coherent state, confirming the qubit behavior. The study demonstrates the ability to tune the anharmonicity of the mechanical system, enabling qubit operations and state visualization. The results show a strong tunable anharmonicity achieved through dispersive coupling with a superconducting qubit. The mechanical qubit has applications in quantum metrology and quantum information processing, with potential for use in novel quantum computing platforms. The work highlights the importance of improving device parameters and coupling strengths to achieve the desired qubit regime.A mechanical qubit is demonstrated using a solid-state mechanical system where the single-phonon nonlinear regime is realized. The system's single-phonon anharmonicity exceeds the decoherence rate by a factor of 6.8, enabling the use of the lowest two energy levels of the resonator as a mechanical qubit. The qubit supports initialization, readout, and a complete set of direct single-qubit gates. This work enhances a powerful quantum acoustics platform for quantum simulations, sensing, and information processing. Mechanical systems are typically treated as harmonic oscillators, with phonons as non-interacting quanta. However, coherent interactions at the single-quantum level in bosonic modes can lead to new physical phenomena and applications in quantum technologies. In electromagnetic systems, weak intrinsic optical nonlinearity has been overcome by coupling to strongly nonlinear media. In mechanical systems, the challenge is to achieve coherent phonon-phonon interactions, which is difficult due to the need for a long-lived, coherent mechanical mode. The study demonstrates a solid-state mechanical system with self-Kerr nonlinearity exceeding the decoherence rate. The system is a circuit quantum acoustodynamics (cQAD) system with a high-overtone bulk acoustic wave resonator (HBAR) coupled to a transmon superconducting circuit. The system is described by the Jaynes-Cummings Hamiltonian, with the anharmonicity of the phonon mode being much greater than the decoherence rate, allowing for coherent quantum operations. The mechanical qubit is operated as a qubit, with direct operations on the mechanical mode at a rate satisfying the condition Γ₂ << Ω << α, enabling coherent operations on a two-level system. The system supports Rabi oscillations, with the Rabi frequency and π-pulse fidelity measured. The mechanical qubit also supports Wigner tomography, showing that the generated state is not a coherent state, confirming the qubit behavior. The study demonstrates the ability to tune the anharmonicity of the mechanical system, enabling qubit operations and state visualization. The results show a strong tunable anharmonicity achieved through dispersive coupling with a superconducting qubit. The mechanical qubit has applications in quantum metrology and quantum information processing, with potential for use in novel quantum computing platforms. The work highlights the importance of improving device parameters and coupling strengths to achieve the desired qubit regime.