Exploring Topological Phases With Quantum Walks

TL;DR

This paper demonstrates that discrete time quantum walks can simulate and explore various topological phases, including the realization of robust edge modes, serving as a versatile platform for topological matter research.

Contribution

It shows how quantum walks can be engineered to realize all classified topological phases in one and two dimensions, linking quantum simulation with topological physics.

Findings

Experimental realization of non-trivial 1D topological phase

Quantum walks can be modified to simulate all classified topological phases

Presence of robust edge modes at phase boundaries

Abstract

The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigation. In particular, we demonstrate that recent experimental realizations of quantum walks simulate a non-trivial one dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the non-trivial topological character of the system.