An optical fiber network oracle for NP-complete problems

The modern information society is enabled by photonic fiber networks of huge coverage and complexity, from transcontinental submarine telecommunication cables to fiber to the home local segments. This world-wide network has yet to match the complexity of human brain containing a hundred billion neurons, with thousands synaptic connections each in average, but already exceeds the complexity of brains of primitive organisms, such as honey bee containing about one million neurons. With this paper we bring about a discussion on the computing potential of optical networks as information carriers. Using a simple fiber network we provide a proof-of-principle demonstration that it can be seen as an optical oracle for the Hamiltonian path problem, the famous mathematical complexity problem of finding if a map can be travelled so that each town is visited once only. Pronouncement of a Hamiltonian path is made by monitoring the delay of the optical pulse interrogating the network, which shall be equal to the sum of travel times visiting all the nodes (towns). We argue that the optical oracle could solve this NP-complete problem hundreds times faster than brute-force computing, discuss its secure communication applications, and propose possible implementation in silicon photonics and plasmonic networks