Continuous-time limit of topological quantum walks
Radhakrishnan Balu, Daniel Castillo, George Siopsis, Christian Weedbrook · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2017
We derive the continuous-time limit of discrete quantum walks with topological phases. We show the existence of a continuous-time limit that preserves their topological phases. We consider both simple-step and splitstep walks, and derive analytically equations of motion governing their behavior. We obtain simple analytical solutions showing the existence of bound states at the boundary of two phases, and solve the equations of motion numerically in the bulk.