  Higher-order topological insulators not only exhibit exotic bulk-boundary
correspondence principle, but also have an important application in quantum
computing. However, they have never been achieved in quantum walk. In this
paper, we construct a two-dimensional coinless discrete-time quantum walk to
simulate 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 multi-step discrete-time
quantum walks. Furthermore, we demonstrate the robustness of the topological
corner states by introducing the static disorder. Finally, we propose a
possible experimental implementation to realize this discrete-time quantum walk
in a three-dimensional integrated photonic circuits. Our work offers a new
route to explore exotic higher-order topological matters using discrete-time
quantum walks.
