  Quantum random walks use interference to obtain faster state space
exploration, which can be used for algorithmic purposes. Photonic technologies
provide a natural platform for many recent experimental demonstrations. Here we
analyze quantum random walks implemented by coherent light propagation in
series-coupled photonic ring resonators. We propose a family of graphs modeling
these devices and compare quantum and classical random walks on these
structures, calculating steady-state and time-dependent solutions. We obtain
conditions for quantum advantage in this setting and show how to recover
classical random walks by averaging over quantum phases. Preliminary device
feasibility tests are carried out via simulations and experimental results
using polymeric directional couplers.
