Photonic and electronic hamiltonian machines

A method of calculating a second-order Hamiltonian H(2)(u|M) with a matrix M and an input vector u, the method comprising:

• generating a first array of optical signals modulated to encode the input vector u;
• generating, with an optical matrix multiplication unit, a second array of optical signals from the first array of optical signals, the second array of optical signals representing a product Mu of the input vector u and the matrix M;
• and
• transducing interference between the second array of optical signals and a third array of optical signals modulated to encode the input vector u into an electrical signal, the interference representing the second-order Hamiltonian H(2)(u|M).

A photonic processor for calculating a second-order Hamiltonian H(2)(u|M) with a matrix M and an input vector u, the photonic processor comprising:

• an array of input optical paths to receive a first array of optical signals;
• optical modulators coupled to the input optical paths to modulate the first array of optical signals and form a second array of optical signals representative of components of the input vector u;
• an optical matrix multiplication unit, in optical communication with the array of input optical paths, to generate a third array of optical signals from the first array of optical signals, the third array of optical signals representing a vector-matrix product Mu of the input vector u and the matrix M;
• an array of optical splitters to couple portions of the second array of optical signals onto an array of feedforward optical paths;
• an array of optical combiners to interfere the portions of the second array of optical signals from the feedforward optical paths with the third array of optical signals from the optical matrix multiplication unit;
• an array of photodetectors, in optical communication with the optical matrix multiplication unit, to detect the interference between the third array of optical signals and the portions of the second array of optical signals;
• and
• a summing circuit coupled to the array of photodetectors to sum electrical outputs from the array of photodetectors to produce a value representative of the second-order Hamiltonian H(2)(u|M).