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 fix...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2015, Vol.91 (2)
Main Authors: Asboth, Janos K., Edge, Jonathan M.
Format: Article
Language:English
Subjects:
Classical counterpart
Enhanced transports
Hamiltonians
Lattice Hamiltonians
Quantum chemistry
Regular graphs
Topological invariants
Topology Chern numbers
Translation invariants
Transport channel
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Summary: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.
ISSN:1094-1622
1050-2947
DOI:10.1103/PhysRevA.91.022324