  Acoustic devices play an important role in classical information processing.
The slower speed and lower losses of mechanical waves enable compact and
efficient elements for delaying, filtering, and storing of electric signals at
radio and microwave frequencies. Discovering ways of better controlling the
propagation of phonons on a chip is an important step towards enabling larger
scale phononic circuits and systems. We present a platform, inspired by decades
of advances in integrated photonics, that utilizes the strong piezoelectric
effect in a thin film of lithium niobate on sapphire to excite guided acoustic
waves immune from leakage into the bulk due to the phononic analogue of
index-guiding. We demonstrate an efficient transducer matched to 50 ohm and
guiding within a 1-micron wide mechanical waveguide as key building blocks of
this platform. Putting these components together, we realize acoustic delay
lines, racetrack resonators, and meander line waveguides for sensing
applications. To evaluate the promise of this platform for emerging quantum
technologies, we characterize losses at low temperature and measure quality
factors on the order of 50,000 at 4 kelvin. Finally, we demonstrate phononic
four-wave mixing in these circuits and measure the nonlinear coefficients to
provide estimates of the power needed for relevant parametric processes.
