| CPC G06F 7/729 (2013.01) [G06E 1/00 (2013.01)] | 18 Claims |

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1. 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.
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