Systems and methods for utilizing photonic degrees of freedom in a photonic processor

A method for performing a mathematical operation, the method comprising:

• performing matrix-matrix multiplication between a first matrix and a second matrix, wherein performing the matrix-matrix multiplication comprises:
• obtaining first numeric values representing at least a portion of the first matrix and second numeric values representing at least a portion of the second matrix;
• generating encoded optical signals by modifying input optical signals using the first numeric values;
• multiplexing, using at least one photonic degree of freedom, the encoded optical signals to generate multiplexed optical signals;
• generating first currents by detecting, using detectors, the multiplexed optical signals;
• and
• generating second currents, using modulators and the first currents, by setting a characteristic of the modulators based on the second numeric values, wherein the second currents represent a portion of a result of the matrix-matrix multiplication;
• and
• obtaining a result of the matrix-matrix multiplication using the second currents.

A photonic processor, comprising:

• a device configured to perform matrix-matrix multiplication, comprising:
• a multiplexer configured to multiplex, using at least one photonic degree of freedom, multiple encoded optical signals into a multiplexed optical signal;
• a demultiplexer configured to demultiplex the multiplexed optical signal using the at least one photonic degree of freedom;
• a detector coupled to an output of an optical path including the multiplexer, wherein the detector is configured to generate a first current based on the demultiplexed optical signal;
• and
• a modulator coupled to an output of the detector and configured to generate a second current by modulating the first current, wherein the second current represents a portion of a result of the matrix-matrix multiplication.