Time-Domain Simulations of Itinerant Phonons Interacting with Superconducting Qubits

We describe an approach to simulating itinerant phonons-as-qubits traveling in acoustic waveguides and interacting with superconducting qubits. We adapt the novel time-domain simulation capabilities of the Julia package WaveguideQED.jl, a package developed for time-domain visualizations of photon quantum states in optical waveguides. Specifically, we investigate the Hong-Ou-Mandel (HOM) effect with phonons, treating the finite-distance acoustic waveguide as a time-loop to model the phonon quantum state evolution. By also simulating the catch and release processes of phonons by superconducting qubits, and the interference of phonons at an acoustic beamsplitter, we provide new insights into the control of phonons, targeting the development of phonon-based quantum computing.