Residue number system arithmetic based on integrated nanophotonics

The 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. 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 $2\times 2$ 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 $2\times 2$ 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 in this RNS processor. A key application for such a photonic RNS engine is the functional analysis of convolutional neural networks.