Edge-state-enhanced transport in a two-dimensional quantum walk

• 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 two-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.

Subject headings

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

Hamiltonians

Quantum chemistry

Topology Chern numbers

Classical counterpart

Enhanced transports

Lattice Hamiltonians

Regular graphs

Topological invariants

Translation invariants

Transport channel

Publication and Content Type

ref (subject category)

art (subject category)