Controlled information transfer in continuous-time chiral quantum walks

Abstract

In this paper we investigate properties of continuous time chiral quantum walks, which possess complex valued edge weights in the underlying graph structure, together with an initial Gaussian wavefunction spread over a number of vertices. We demonstrate that, for certain graph topology and phase matching conditions, we are able to direct the flow of probability amplitudes in a specific direction inside the graph network. We design a quantum walk graph analogue of an optical circulator which is a combination of a cycle and semi-infinite chain graphs. Excitations input into the circulator from a semi-infinite chain are routed in a directionally biased fashion to output to a different semi-infinite chain. We examine in detail a two port circulator graph which spatially separates excitations flowing back in forth between the two semi-finite chains to directionally occupy the top or bottom half of the cycle portion of the circulator. This setup can be used, for example, to detect non-Markovian processes, which leads to information and energy back-flow from the bath back into the system.