Experimental implementation of a quantum walk on a circle with single photons

We experimentally implement a quantum walk on a circle in position space. Using a different arrangement of linear optical elements, our experiment realizes clockwise-cycling and counterclockwise-cycling walks. Periodic evolutions in quantum walks on three- and four-node circles with uniform coin flipping for each step and a localized initial walker state are observed, and the full revival of the walker+coin state occurs. Coherent information encoded in the coin state shows the periodic collapse and revival due to the interaction between the coin and walker. The technology to realize clockwise-cycling and counterclockwise-cycling walks can be expanded to simulate a quantum walk on a circle with arbitrary nodes.