**Quantum control of acoustic phonons**

Superconducting qubits provide an excellent approach to building quantum computing systems, due to their good performance metrics and their easy lithographic scaling to large qubit numbers. In addition, these qubits provide unique opportunities as testbed systems for quantum communication as well as developing hybrid quantum systems. Here, I will discuss applications for superconducting qubits in generating and detecting individual phonons, in the form of quantum surface acoustic wave (SAW) excitations, and using these phonon states to generate remote quantum entanglement. Specifically, I will describe recent experiments [1,2] where we have demonstrated the use of reasonably high finesse acoustic Fabry-Perot structures to store acoustic phonon Fock states, in which we can measure the Wigner tomograms of individual Fock states as well as their superpositions. In more recent work, we have coupled two superconducting qubits to a long SAW resonator with a 500 ns phonon bounce time. We can release and recapture individual itinerant phonons using one of the two qubits, as well as transfer quantum states between the two qubits [2].

[1] K. J. Satzinger et al., “Quantum control of surface acoustic wave phonons”, *Nature* **563**, 661–665 (2018).

[2] A. Bienfait et al., “Phonon-mediated quantum state transfer and remote qubit entanglement”, *Science* **364**, 368-371 (2019).