<p>Approaches to quantum computing that use itinerant photons are appealing because they have relatively few physical requirements. However, at present, many elements of photonic quantum computers are nondeterministic, presenting a challenge for large-scale devices. One alternative is to use similar schemes with itinerant phonons in solid-state devices, rather than photons, combined with superconducting transmon devices. Here we present an advancement in the ability to deterministically manipulate and measure acoustic phonon quantum states. First, we demonstrate the deterministic phase control of itinerant one- and two-phonon qubit states, which we measure using an acoustic Mach–Zehnder interferometer. We implement phonon phase control using the frequency-dependent scattering of phonon states from a superconducting transmon qubit. Additionally, we propose and implement a multiphonon detection scheme that enables coherent conversion between itinerant one- and two-phonon Fock states and transmon qutrit states, for example, transforming an entangled two-phonon output state into the entangled state of two transmons. The integration of quantum acoustics with superconducting circuits in our implementation promises further advances, including deterministic phonon quantum gates with direct applications to quantum computing.</p>