Details
| Original language | English |
|---|---|
| Article number | 140503 |
| Journal | Physical Review Letters |
| Volume | 101 |
| Issue number | 14 |
| Publication status | Published - 3 Oct 2008 |
| Externally published | Yes |
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 subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Physical Review Letters, Vol. 101, No. 14, 140503, 03.10.2008.
Research output: Contribution to journal › Article › Research › peer review
}
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 -