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Cited by 295Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum Mechanics and Applications

Implementing the quantum random walk

Open access
Travaglione, B. C., Milburn, G. J.·2002·Physical Review A
DOI 10.1103/physreva.65.032310
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Abstract

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains ``quantum,'' this algorithm could serve as an important benchmarking protocol for ion trap quantum computers.

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  • Random walks in random media, the Sinai walk, lead to ultra slow classical evolution σ2(t) proportional to ln t^4.

    “This is the so-called random random or Sinai walk[17, 18] which leads to ultra slow classical evolution σ 2 ( t ) ∝ ln t 4 , very close to a complete cease.”

    From Quantum walks on a random environment (2008) · cites this paper as [18]

  • Classical random walks in the presence of static disorder still propagate, albeit ultraslowly.

    “Surprisingly, classical random walks for static disorder are still propagating, although ultraslowly[17, 18].”

    From Quantum walks on a random environment (2008) · cites this paper as [18]

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Research works printed but not linked: 3

  1. [12]D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, Journal of Research of the National Institute of Standards and Technology 103 , 259 (1998).
  2. [14]C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Physical Review Letters 75 , 4011 (1995).
  3. [15]C. D'Helon and G. J. Milburn, Physical Review A 54 , 5141 (1996).

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Authors
Travaglione, B. C., & Milburn, G. J.
Affiliations
The University of Queensland (AU)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2002-02-20
Volume
65
Issue
3
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.65.032310
OpenAlex
W2070891810
Cited by
295
References
14
Citations by year
2026: 5 · 2025: 5 · 2024: 9 · 2023: 10 · 2022: 8 · 2021: 10 · 2020: 8 · 2019: 12 · 2018: 9 · 2017: 9 · 2016: 13 · 2015: 12 · 2014: 11 · 2013: 10 · 2012: 12
FWCI
21.12
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum walks, ion trap quantum computer, quadratic speedup, mixing time, decoherence, experimental implementation, one-dimensional walk

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