Optical systems comprising binary photonics lattices

A method of optically representing of a binary number, the method comprising directing a plurality of photons generated using a photon source into an input end of a central waveguide of a binary waveguide region of a waveguide array of a binary photonics lattice, wherein the waveguide array comprises:

• a plurality of single mode waveguides disposed in a substrate, the plurality of single mode waveguides including one or more first waveguides comprising a first V-number V1 and one or more second waveguides comprising a second V-number V2 wherein:
• the first V-number V1 is smaller than the second V-number V2;
• the one or more first waveguides and the one or more second waveguides are arranged in a linear distribution comprising the binary waveguide region, a first edge waveguide region, and a second edge waveguide region, wherein:
• the binary waveguide region is positioned between the first edge waveguide region and the second edge waveguide region;
• the binary waveguide region comprises a symmetrical binary representation of a decimal number;
• and
• the binary waveguide region comprises at least one first waveguide representing a digit 0 of the symmetrical binary representation, at least one second waveguide representing a digit 1 of the symmetrical binary representation, or both at least one first waveguide representing a digit 0 of the symmetrical binary representation and at least one second waveguide representing a digit 1 of the symmetrical binary representation;
• receiving the plurality of photons using one or more photon detectors, wherein each of the one or more photon detectors is optically coupled to an output end of at least one of the plurality of single mode waveguides;
• and
• measuring an output power distribution based on the plurality of photons received by the one or more photon detectors, wherein the output power distribution corresponds with the symmetrical binary representation of the decimal number.