  Harnessing multimode waves allows high information capacity through modal
expansions. Although passive multimode devices including waveguides, couplers,
and multiplexers have been demonstrated for broadband responses in momentum or
frequency domains, collective switching of multimodes remains a challenge, due
to the difficulty in imposing consistent dynamics on all eigenmodes. Here we
overcome this limitation by realizing digital switching of spatially random
waves, based on supersymmetric pairs of multimode potentials. We reveal that
supersymmetric transformations of any parity-symmetric potential derive the
parity reversal of all eigenmodes, which allows the complete isolation of
random waves at the 'off' state. Building blocks for binary and many-valued
logics are then demonstrated for random waves: a harmonic pair for binary
switching of arbitrary wavefronts and a P\"oschl-Teller pair for multi-level
switching which implements the fuzzy membership function. Our results
establishing global phase matching conditions for multimode dynamics will lay
the foundation of multi-channel digital photonics.
