Hybrid systems consisting of superconducting circuits and mechanical resonators are a promising platform for quantum technologies. However, realizing high-performance preparation and manipulation of phonon states remains an outstanding challenge due to the complex energy levels and interactions of hybrid systems. Here, we propose a noise-resistant phonon manipulation scheme. Using engineered superconducting-resonator dispersive interactions, we tailor a control sequence combined with dynamical decoupling pulses, which forms the basis for a universal set of phonon gate operations. Using this gate design, we demonstrate the preparation of Schrödinger cat states of phonons, the creation of complex phonon superposition states, and the encoding and transfer of quantum information into phonon states. In addition, we show that the fidelity of the state preparation can reach 95% under realistic parameters and that these designs significantly reduce the error effects compared to existing schemes. These results provide a complete toolbox for superconducting-mechanics hybrid systems.

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• Circuit quantum electrodynamics
• Quantum information with hybrid systems
• Quantum optics with artificial atoms