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Quantum Information Processing
Erschienen in: Quantum Information Processing 9/2021

01.09.2021

An index theorem for one-dimensional gapless non-unitary quantum walks

verfasst von: Keisuke Asahara, Daiju Funakawa, Motoki Seki, Yohei Tanaka

Erschienen in: Quantum Information Processing | Ausgabe 9/2021

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Abstract

Recent developments in the index theory of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric index to a unitary time evolution U and a \(\mathbb {Z}_2\)-grading operator \(\varGamma \) satisfying the chiral symmetry condition, \(U^* = \varGamma U \varGamma .\) In the present article, we extend this index theory to encompass non-unitary time evolutions U. The existing literature for unitary U assumes that U is essentially gapped to define the associated index, that is, the essential spectrum of U contains neither \(-1\) nor \(+1\). We show this assumption is not necessary if U fails to be unitary. As a concrete example, we consider the well-known non-unitary quantum walk model on the integer lattice \(\mathbb {Z}\) introduced by Mochizuki–Kim–Obuse.
Vorheriger Artikel Learning bounds for quantum circuits in the agnostic setting
Nächster Artikel A novel quantum (t, n) threshold group signature based on d-dimensional quantum system

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Metadaten
Titel
An index theorem for one-dimensional gapless non-unitary quantum walks
verfasst von
Keisuke Asahara
Daiju Funakawa
Motoki Seki
Yohei Tanaka
Publikationsdatum
01.09.2021
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 9/2021
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-03212-y

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