Deterministic multi-phonon entanglement between two mechanical resonators on separate substrates

Mechanical systems have emerged as a compelling platform for applications in quantum information, leveraging advances in the control of phonons, the quanta of mechanical vibrations. Experiments have demonstrated the control and measurement of phonon states in mechanical resonators, and while dual-resonator entanglement has been demonstrated, more complex entangled states remain a challenge. Here, we demonstrate rapid multi-phonon entanglement generation and subsequent tomographic analysis, using a scalable platform comprising two surface acoustic wave resonators on separate substrates, each connected to a superconducting qubit. We synthesize a mechanical Bell state with a fidelity of $${{{{\mathcal{F}}}}}=0.872\pm 0.002$$ F = 0.872 ± 0.002 , and a multi-phonon entangled N = 2 N00N state with a fidelity of $${{{{\mathcal{F}}}}}=0.748\pm 0.008$$ F = 0.748 ± 0.008 . The compact, modular, and scalable platform we demonstrate will enable further advances in the quantum control of complex mechanical systems.