Consider a discrete time quantum walk on a 2-dimensional square lattice, with particles starting from point A and detected at point B. To establish an efficient channel for transport from A to B, which links (edges) in the lattice should you remove? We show that the counterintuitive strategy of picking a path that connects A and B, and removing links that cross this path, can create such a channel, that uses topologically protected edge states [1]. The existence of these edge states depends on the bulk properties of the quantum walk (including topological invariants other than the Chern number [2]), and on the way the links are removed (similarly to 1D quantum walks [3]), but not on the precise shape of the path. The channel ensures a transmission probability independent of the distance of A and B, even in the presence of static disorder, which induces Anderson localization. Time-dependent disorder, however, causes decoherence and thus makes the channel lossy.

References

[1] T. Kitagawa, Quant. Inf. Proc. 1570-0755 (2012); arXiv:1112.1882

[2] M. S. Rudner, N. H. Lindner, E. Berg, M. Levinot, arXiv:1212.3324 (2012)

[3] J. K. Asboth, Phys. Rev. B 86, 195414 (2012)