Residue number system in a photonic matrix accelerator

A photonic processor for representing numbers using a redundant residue number system (RRNS) that includes a set of moduli, the set of moduli including n moduli and k redundant moduli, the photonic processor comprising:

• at least one optical transmitter configured to, for each modulus of the set of moduli:
• provide a first value associated with the modulus;
• and
• provide a second value associated with the modulus;
• at least one phase shifter configured to, for each modulus of the set of moduli:
• shift, by each of the first value and the second value, a phase of a light signal;
• and
• at least one receiver configured to, for each modulus of the set of moduli:
• detect the shifted phase of the light signal;
• and
• output the detected phase of the light signal as representing a residue of a sum of the first value and the second value, the residue being associated with the modulus,
• wherein the photonic processor is further configured to use a residue associated with a modulus of the k redundant moduli to detect and/or correct an error of a residue associated with a modulus of the n moduli,
• wherein the photonic processor is configured to detect and/or correct the error by:
• forming a plurality of sets of moduli, each set of moduli comprising p moduli;
• determining a plurality of representations by, for each set of moduli of the plurality of sets of moduli, converting a set of residues associated with the set of moduli to a representation of the set of residues;
• determining a correct representation using the plurality of representations.