An optical fiber network oracle for NP-complete problems

Abstract

The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the home and local segments. This world-wide network has yet to match the complexity of the human brain, which contains a hundred billion neurons, each with thousands of synaptic connections on average. However, it already exceeds the complexity of brains from primitive organisms, i.e., the honey bee, which has a brain containing approximately one million neurons. In this study, we present a discussion of the computing potential of optical networks as information carriers. Using a simple fiber network, we provide a proof-of-principle demonstration that this network can be treated as an optical oracle for the Hamiltonian path problem, the famous mathematical complexity problem of finding whether a set of towns can be travelled via a path in which each town is visited only once. Pronouncement of a Hamiltonian path is achieved by monitoring the delay of an optical pulse that interrogates the network, and this delay will be equal to the sum of the travel times needed to visit all of the nodes (towns). We argue that the optical oracle could solve this NP-complete problem hundreds of times faster than brute-force computing. Additionally, we discuss secure communication applications for the optical oracle and propose possible implementation in silicon photonics and plasmonic networks.