Edge-state enhanced transport in a 2-dimensional quantum walk
arXiv:1411.3958 · doi:10.1103/PhysRevA.91.022324
Abstract
Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder. We ask how to create an efficient transport channel from a fixed source site (A) to fixed target site (B) in a disordered 2-dimensional discrete-time quantum walk by cutting some of the links. We show that the somewhat counterintuitive strategy of cutting links along a single line connecting A to B creates such a channel. The efficient transport along the cut is due to topologically protected chiral edge states, which exist even though the bulk Chern number in this system vanishes. We give a realization of the walk as a periodically driven lattice Hamiltonian, and identify the bulk topological invariant responsible for the edge states as the quasienergy winding of this Hamiltonian.
References in corpus (7)
- Quantum walks of correlated particles
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Exploring Topological Phases With Quantum Walks
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Discrete single-photon quantum walks with tunable decoherence
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Implementation of a spatial two-dimensional quantum random walk with tunable decoherence