Resonant Two-Mode Measurements in a Hybrid Quantum Acoustic Device

Circuit quantum acoustodynamics (cQAD) describes the interactions between mechanical resonators and superconducting circuits. In a device made of a bulk acoustic resonator and a transmon qubit, the large non-linearity of the Josephson junction allows the control of many high-quality phonon modes. This has enabled the preparation of Fock states and the demonstration of continuous variable operations such as squeezing and beamsplitter gates required for boson sampling experiments. However, a measurement scheme for sampling many-phonon states over multiple modes has been missing so far. In this talk, I will present a method to characterize the final state of boson sampling operations applied to two phonon modes with a measurement of fixed duration. Based on two consecutive resonant interactions, we extract the joint probability distribution of the two-mode state, which provides a necessary ingredient for a minimal boson sampler.