  Hybrid quantum systems in which acoustic resonators couple to superconducting
qubits are promising quantum information platforms. High quality factors and
small mode volumes make acoustic modes ideal quantum memories, while the
qubit-phonon coupling enables the initialization and manipulation of quantum
states. We present a scheme for quantum computing with multimode quantum
acoustic systems, and based on this scheme, propose a hardware-efficient
implementation of a quantum random access memory (QRAM). Quantum information is
stored in high-Q phonon modes, and couplings between modes are engineered by
applying off-resonant drives to a transmon qubit. In comparison to existing
proposals that involve directly exciting the qubit, this scheme can offer a
substantial improvement in gate fidelity for long-lived acoustic modes. We show
how these engineered phonon-phonon couplings can be used to access data in
superposition according to the state of designated address modes--implementing
a QRAM on a single chip.
