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Parity measurement in the strong dispersive regime of circuit quantum acoustodynamics

Mechanical resonators are emerging as an important new platform for quantum science and technologies. A large number of proposals for using them to store, process, and transduce quantum information motivates the development of increasingly sophisticated techniques for controlling mechanical motion in the quantum regime. By interfacing mechanical resonators with superconducting circuits, circuit quantum acoustodynamics (cQAD) can make a variety of important tools available for manipulating and measuring motional quantum states. Here we demonstrate direct measurements of the phonon number distribution and parity of nonclassical mechanical states. We do this by operating our system in the strong dispersive regime, where a superconducting qubit can be used to spectroscopically resolve phonon Fock states. These measurements are some of the basic building blocks for constructing acoustic quantum memories and processors. Furthermore, our results open the door to performing even more complex quantum algorithms using mechanical systems, such as quantum error correction and multi-mode operations.