  A general scheme to realize a perceptron for hardware neural networks is
presented, where multiple interconnections are achieved by a superposition of
Schrodinger waves. Spatially patterned potentials process information by
coupling different points of reciprocal space. The necessary potential shape is
obtained from the Hebbian learning rule, either through exact calculation or
construction from a superposition of known optical inputs. This allows
implementation in a wide range of compact optical systems, including: 1) any
non-linear optical system; 2) optical systems patterned by optical lithography;
and 3) exciton-polariton systems with phonon or nuclear spin interactions.
