Fractional scaling of quantum walks on two-dimensional percolation lattices

Viv Kendon; Godfrey Leung; Paul Knott; Joe Bailey

doi:10.1063/1.3630171

Fractional scaling of quantum walks on two-dimensional percolation lattices

Viv Kendon
, Godfrey Leung
, Paul Knott
, Joe Bailey

Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

Abstract

We study the spreading behaviour of coined quantum walks on percolation lattices for both bond and site percolation on two-dimensional Cartesian lattices. Using numerical simulation, we observe fractional scaling of the spreading with the number of steps of the walk. The exponent varies from zero at the critical percolation probability through to unity for the full lattice. For the lattices we simulate, up to 140x140, we observe faster than classical scaling for percolation probabilities above about 0.85.

Original language	English
Title of host publication	Quantum Communication, Measurement and Computing (QCMC)
Subtitle of host publication	The Tenth International Conference
Editors	Timothy Ralph, Ping Koy Lam
Place of Publication	Melville, NY
Pages	159-162
Number of pages	4
DOIs	https://doi.org/10.1063/1.3630171
Publication status	Published - 17 Oct 2011
Event	Quantum Communication, Measurement and Computing (QCMC): The Tenth International Conference - Brisbane, Australia Duration: 19 Jul 2010 → 23 Jul 2010

Conference

Conference	Quantum Communication, Measurement and Computing (QCMC)
Country/Territory	Australia
City	Brisbane
Period	19/07/10 → 23/07/10

Keywords

percolation lattices
quantum walks

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10.1063/1.3630171

Cite this

@inproceedings{25e7884f1338476db5b4703a9bb2fb92,

title = "Fractional scaling of quantum walks on two-dimensional percolation lattices",

abstract = "We study the spreading behaviour of coined quantum walks on percolation lattices for both bond and site percolation on two-dimensional Cartesian lattices. Using numerical simulation, we observe fractional scaling of the spreading with the number of steps of the walk. The exponent varies from zero at the critical percolation probability through to unity for the full lattice. For the lattices we simulate, up to 140x140, we observe faster than classical scaling for percolation probabilities above about 0.85.",

keywords = "percolation lattices, quantum walks",

author = "Viv Kendon and Godfrey Leung and Paul Knott and Joe Bailey",

year = "2011",

month = oct,

day = "17",

doi = "10.1063/1.3630171",

language = "English",

isbn = "9780735409217",

pages = "159--162",

editor = "Timothy Ralph and Lam, \{Ping Koy\}",

booktitle = "Quantum Communication, Measurement and Computing (QCMC)",

note = "Quantum Communication, Measurement and Computing (QCMC) : The Tenth International Conference ; Conference date: 19-07-2010 Through 23-07-2010",

}

Kendon, V, Leung, G, Knott, P & Bailey, J 2011, Fractional scaling of quantum walks on two-dimensional percolation lattices. in T Ralph & PK Lam (eds), Quantum Communication, Measurement and Computing (QCMC): The Tenth International Conference. Melville, NY, pp. 159-162, Quantum Communication, Measurement and Computing (QCMC), Brisbane, Australia, 19/07/10. https://doi.org/10.1063/1.3630171

Fractional scaling of quantum walks on two-dimensional percolation lattices. / Kendon, Viv; Leung, Godfrey; Knott, Paul et al.
Quantum Communication, Measurement and Computing (QCMC): The Tenth International Conference. ed. / Timothy Ralph; Ping Koy Lam. Melville, NY, 2011. p. 159-162.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Fractional scaling of quantum walks on two-dimensional percolation lattices

AU - Kendon, Viv

AU - Leung, Godfrey

AU - Knott, Paul

AU - Bailey, Joe

PY - 2011/10/17

Y1 - 2011/10/17

N2 - We study the spreading behaviour of coined quantum walks on percolation lattices for both bond and site percolation on two-dimensional Cartesian lattices. Using numerical simulation, we observe fractional scaling of the spreading with the number of steps of the walk. The exponent varies from zero at the critical percolation probability through to unity for the full lattice. For the lattices we simulate, up to 140x140, we observe faster than classical scaling for percolation probabilities above about 0.85.

AB - We study the spreading behaviour of coined quantum walks on percolation lattices for both bond and site percolation on two-dimensional Cartesian lattices. Using numerical simulation, we observe fractional scaling of the spreading with the number of steps of the walk. The exponent varies from zero at the critical percolation probability through to unity for the full lattice. For the lattices we simulate, up to 140x140, we observe faster than classical scaling for percolation probabilities above about 0.85.

KW - percolation lattices

KW - quantum walks

U2 - 10.1063/1.3630171

DO - 10.1063/1.3630171

M3 - Conference contribution book

SN - 9780735409217

SP - 159

EP - 162

BT - Quantum Communication, Measurement and Computing (QCMC)

A2 - Ralph, Timothy

A2 - Lam, Ping Koy

CY - Melville, NY

T2 - Quantum Communication, Measurement and Computing (QCMC)

Y2 - 19 July 2010 through 23 July 2010

ER -

Fractional scaling of quantum walks on two-dimensional percolation lattices

Abstract

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Keywords

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