  Precisely engineered mechanical oscillators keep time, filter signals, and
sense motion, making them an indispensable part of today's technological
landscape. These unique capabilities motivate bringing mechanical devices into
the quantum domain by interfacing them with engineered quantum circuits.
Proposals to combine microwave-frequency mechanical resonators with
superconducting devices suggest the possibility of powerful quantum acoustic
processors. Meanwhile, experiments in several mechanical systems have
demonstrated quantum state control and readout, phonon number resolution, and
phonon-mediated qubit-qubit interactions. Currently, these acoustic platforms
lack processors capable of controlling multiple mechanical oscillators' quantum
states with a single qubit, and the rapid quantum non-demolition measurements
of mechanical states needed for error correction. Here we use a superconducting
qubit to control and read out the quantum state of a pair of nanomechanical
resonators. Our device is capable of fast qubit-mechanics swap operations,
which we use to deterministically manipulate the mechanical states. By placing
the qubit into the strong dispersive regime with both mechanical resonators
simultaneously, we determine the resonators' phonon number distributions via
Ramsey measurements. Finally, we present quantum tomography of the prepared
nonclassical and entangled mechanical states. Our result represents a concrete
step toward feedback-based operation of a quantum acoustic processor.
