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Cited by 180Quantum Computing Algorithms and ArchitectureQuantum Mechanics and ApplicationsQuantum Information and Cryptography

Connecting the discrete- and continuous-time quantum walks

Open access
Strauch, Frederick W.·2006·Physical Review A
DOI 10.1103/physreva.74.030301
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Abstract

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time quantum walk. Though the properties of these two walks have shown similarities, it has remained an open problem to find the exact relation between the two. The precise connection of these two processes, both quantally and classically, is presented. Extension to higher dimensions is also discussed.

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Crossref · 10.1103/physreva.74.030301

Cites

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  • The difficulty to analyse the (3+1)-dimensional Dirac QW is mentioned in [14, 17-19].

    “The difficulty to analyse the + (3 1)-dimensional Dirac QW is mentioned in [14, 17-19].”

    From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [17]

    On p. 4, Strauch says a calculation for a four-component quantum walk on a three-dimensional lattice breaks down because its operators do not commute. This supports a difficulty in analyzing a related higher-dimensional walk, but the passage concerns a particular continuous-time limit and does not identify the example as a (3+1)-dimensional Dirac quantum walk or claim that analyzing it generally is difficult. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

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Cites

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Research works printed but not linked: 1

  1. [22]A. Ambainis, J. Kempe, and A. Rivosh, Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SIAM Press, Philadelphia, 2005), p. 1099.

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Authors
Strauch, F. W.
Affiliations
National Institute of Standards and Technology (US)
Corresponding author
Strauch, Frederick W.
ORCID
Strauch, Frederick W.
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2006-09-07
Volume
74
Issue
3
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.74.030301
OpenAlex
W2147228721
Cited by
180
References
27
Citations by year
2026: 7 · 2025: 3 · 2024: 5 · 2023: 6 · 2022: 4 · 2021: 5 · 2020: 7 · 2019: 14 · 2018: 5 · 2017: 9 · 2016: 13 · 2015: 9 · 2014: 13 · 2013: 11 · 2012: 12
FWCI
11.41
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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
discrete-time quantum walks, continuous-time quantum walks, quantum walks, quantum algorithms, classical random walks

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