Why and how to add direction to a quantum walk

We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral graph theory. We display results and simulations which highlight the conceptual differences between having directions en...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Chaves, Rodrigo, Bruno Oliveira Chagas, Coutinho, Gabriel
Format: Article
Language:English
Subjects:
Graph theory
Quantum phenomena
Online Access:Get full text
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Summary:We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral graph theory. We display results and simulations which highlight the conceptual differences between having directions encoded in the Hamiltonians or not. This leads to a construction of a new type of quantum phenomenon: zero transfer between pairs of sites in a connected coupled network, which is only possible in the directed model we study. Our main result is a description of several families of directed cycles that admit zero transfer.
ISSN:2331-8422