Coined quantum walks on weighted graphs

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.

Original languageEnglish (US)
Article number475301
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number47
DOIs
StatePublished - Oct 25 2017

Fingerprint

Quantum Walk
Weighted Graph
Ballistics
apexes
Vertex of a graph
ballistics
integers
Walk
Complete Graph
Discrete-time
Generalise
Integer
Line

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Coined quantum walks on weighted graphs. / Wong, Thomas.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 47, 475301, 25.10.2017.

Research output: Contribution to journalArticle

@article{62191dce6a3446e4912c2c10e605968a,
title = "Coined quantum walks on weighted graphs",
abstract = "We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.",
author = "Thomas Wong",
year = "2017",
month = "10",
day = "25",
doi = "10.1088/1751-8121/aa8c17",
language = "English (US)",
volume = "50",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "47",

}

TY - JOUR

T1 - Coined quantum walks on weighted graphs

AU - Wong, Thomas

PY - 2017/10/25

Y1 - 2017/10/25

N2 - We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.

AB - We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.

UR - http://www.scopus.com/inward/record.url?scp=85034219808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034219808&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aa8c17

DO - 10.1088/1751-8121/aa8c17

M3 - Article

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 47

M1 - 475301

ER -