Topological delocalization in two-dimensional quantum walks

Quantum walks spread faster than classical random walks, which makes them interesting for quantum information applications. However, they are more sensitive to spatial disorder: they can undergo Anderson localization, which stops them from spreading off to infinity. We show that in two-dimensional discrete-time quantum walks with two internal states, increasing the disorder to the maximum possible value, i.e., using position-dependent rotation operators selected randomly and Haar uniformly, does not lead to Anderson localization, but rather, to a critical dynamical system where the quantum walk spreads diffusively. The reason behind this has to do with the topological invariants of the quantum walk: maximal disorder tunes the quantum walk to a critical point between phases with different topological invariants. We calculate these invariants by detecting edge states. We characterize the critical state of the quantum walk, by numerical calculation of the critical exponent η in three different ways, obtaining η=0.52 as in the integer quantum Hall effect.

JK Asbóth, A Mallick, arXiv:2005.00203, accepted for publication in Phys. Rev. B