The Witten index for 1D supersymmetric quantum walks with anisotropic coins

Chiral symmetric discrete-time quantum walks possess supersymmetry, and their associated Witten indices can be naturally defined. The Witten index is known to give a lower bound for the number of topologically protected bound states. The purpose of this paper is to give a complete classification of...

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Bibliographic Details
Published in:Quantum information processing 2019-12, Vol.18 (12), p.1-36, Article 377
Main Authors: Suzuki, Akito, Tanaka, Yohei
Format: Article
Language:English
Subjects:
Coins
Data Structures and Information Theory
Lower bounds
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum mechanics
Quantum Physics
Spintronics
Supersymmetry
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Summary:Chiral symmetric discrete-time quantum walks possess supersymmetry, and their associated Witten indices can be naturally defined. The Witten index is known to give a lower bound for the number of topologically protected bound states. The purpose of this paper is to give a complete classification of the Witten index for a one-dimensional split-step quantum walk. It turns out that the Witten index of this model exhibits a striking similarity to that of a Dirac particle model in supersymmetric quantum mechanics.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-019-2485-1