Second-order topological insulator in a coinless discrete-time quantum walk
Ya Meng, Gang Chen, Suotang Jia · Physical Review A · 2020
Higher-order topological insulators not only exhibit the exotic bulk-boundary correspondence principle but also have an important application in quantum computing. However, it seems they have not been achieved in the discrete-time quantum walk. In this paper we construct a two-dimensional coinless discrete-time quantum walk to simulate the second-order topological insulator with zero-dimensional corner states. We show that both of the corner and edge states can be observed through the probability distribution of the walker after a multistep coinless discrete-time quantum walk. Finally, we propose a possible experimental implementation to realize this coinless discrete-time quantum walk in a three-dimensional integrated photonic circuit and verify the robustness of the corner states against the small disorder. Our work offers an alternative route to explore exotic higher-order topological matters using discrete-time quantum walks.