Integrated Nanophotonics Architecture for Residue Number System Arithmetic

TL;DR

This paper presents an integrated nanophotonic architecture for residue number system arithmetic, enabling high-speed, parallel optical processing for applications in linear algebra, vision, and neural networks.

Contribution

It introduces a novel optical RNS hardware design using integrated nanophotonics and photonic switches for fast, parallel arithmetic operations.

Findings

Achieves 10's ps computational speed due to optical propagation delay.

Demonstrates a photonic RNS adder and multiplier with all-to-all sparse network topology.

Leverages natural optical parallelism for efficient in-network processing.

Abstract

Residue number system (RNS) enables dimensionality reduction of an arithmetic problem by representing a large number as a set of smaller integers, where the number is decomposed by prime number factorization using the moduli as basic functions. These reduced problem sets can then be processed independently and in parallel, thus improving computational efficiency and speed. Here we show an optical RNS hardware representation based on integrated nanophotonics. The digit-wise shifting in RNS arithmetic is expressed as spatial routing of an optical signal in 2x2 hybrid photonic-plasmonic switches. Here the residue is represented by spatially shifting the input waveguides relative to the routers outputs, where the moduli are represented by the number of waveguides. By cascading the photonic 2x2 switches, we design a photonic RNS adder and a multiplier forming an all-to-all sparse directional network. The advantage of this photonic arithmetic processor is the short (10's ps) computational execution time given by the optical propagation delay through the integrated nanophotonic router. Furthermore, we show how photonic processing in-the-network leverages the natural parallelism of optics such as wavelength-division-multiplexing or optical angular momentum in this RNS processor. A key application for photonic RNS is the functional analysis convolution with widespread usage in numerical linear algebra, computer vision, language- image- and signal processing, and neural networks.