Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 140503 |
| Fachzeitschrift | Physical Review Letters |
| Jahrgang | 101 |
| Ausgabenummer | 14 |
| Publikationsstatus | Veröffentlicht - 3 Okt. 2008 |
| Extern publiziert | Ja |
Abstract
In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
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in: Physical Review Letters, Jahrgang 101, Nr. 14, 140503, 03.10.2008.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
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TY - JOUR
T1 - Approximate locality for quantum systems on graphs
AU - Osborne, Tobias J.
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/10/3
Y1 - 2008/10/3
N2 - In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.
AB - In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.
UR - http://www.scopus.com/inward/record.url?scp=53549085676&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.101.140503
DO - 10.1103/PhysRevLett.101.140503
M3 - Article
AN - SCOPUS:53549085676
VL - 101
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 14
M1 - 140503
ER -