  Phononic computing -- the use of (typically thermal) vibrations for
information processing -- is a nascent technology; its capabilities are still
being discovered. We analyze an alternative form of phononic computing inspired
by optical, rather than electronic, computing. Using the acoustic Faraday
effect, we design a phonon gyrator and thereby a means of performing
computation through the manipulation of polarization in transverse phonon
currents. Moreover, we establish that our gyrators act as generalized
transistors and can construct digital logic gates. Exploiting the wave nature
of phonons and the similarity of our logic gates, we demonstrate parallel
computation within a single circuit, an effect presently unique to phonons.
Finally, a generic method of designing these parallel circuits is introduced
and used to analyze the feasibility of magneto-acoustic materials in realizing
these circuits.
