Optical modular arithmetic

TL;DR

This paper introduces an optical circuit that performs phase-based arithmetic operations using nanoscale photonic devices, enabling ultra-low power computation for tasks like inner products and matrix operations.

Contribution

It proposes a novel optical circuit architecture for phase-based computation, extending to matrix operations and weighted readouts, utilizing coherence as a computational resource.

Findings

Demonstrates optical circuit for phase-based inner product computation

Extends to matrix-vector and matrix-matrix products

Potential applications in error correction and machine learning

Abstract

Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary "selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a "weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.