Faster quantum walk search on a weighted graph

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

Original languageEnglish (US)
Article number032320
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume92
Issue number3
DOIs
StatePublished - Sep 21 2015
Externally publishedYes

Fingerprint

apexes
walking
perturbation theory
adjusting

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

Faster quantum walk search on a weighted graph. / Wong, Thomas.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, No. 3, 032320, 21.09.2015.

Research output: Contribution to journalArticle

@article{e35cb6c47ecc43619b06d475ff79a96d,
title = "Faster quantum walk search on a weighted graph",
abstract = "A randomly walking quantum particle evolving by Schr{\"o}dinger's equation searches for a unique marked vertex on the {"}simplex of complete graphs{"} in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.",
author = "Thomas Wong",
year = "2015",
month = "9",
day = "21",
doi = "10.1103/PhysRevA.92.032320",
language = "English (US)",
volume = "92",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1050-2947",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Faster quantum walk search on a weighted graph

AU - Wong, Thomas

PY - 2015/9/21

Y1 - 2015/9/21

N2 - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

AB - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

UR - http://www.scopus.com/inward/record.url?scp=84943167511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943167511&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.92.032320

DO - 10.1103/PhysRevA.92.032320

M3 - Article

VL - 92

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032320

ER -