  Linear optical quantum computing provides a desirable approach to quantum
computing, with a short list of required elements. The similarity between
photons and phonons points to the interesting potential for linear mechanical
quantum computing (LMQC), using phonons in place of photons. While
single-phonon sources and detectors have been demonstrated, a phononic
beamsplitter element remains an outstanding requirement. Here we demonstrate
such an element, using two superconducting qubits to fully characterize a
beamsplitter with single phonons. We further use the beamsplitter to
demonstrate two-phonon interference, a requirement for two-qubit gates,
completing the toolbox needed for LMQC. This advance brings linear quantum
computing to a fully solid-state system, along with straightforward conversion
between itinerant phonons and superconducting qubits.
