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 can make a variety of important tools available for manipulating and measuring motional quantum states. Here we demonstrate the direct measurements of phonon number distribution and parity of non-classical mechanical states. We do this by operating our system in the strong dispersive regime, where a superconducting qubit can be used to spectroscopically resolve the 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 for performing even more complex quantum algorithms using mechanical systems, such as quantum error correction and multimode operations. Mechanical resonators combined with superconducting circuits are a promising platform for controlling non-classical mechanical states. Here this platform is used to directly measure the parity of a motional quantum state.