From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution
Open accessAbstract
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic behavior, of the one-dimensional discrete time quantum walk is analytically shown. From the limit distribution of the discrete time quantum walk, the discrete time quantum walk can be taken as the quantum dynamical simulator of some physical systems.
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Convergence of the Dirac QW has been proved in (1+1)-dimensions in [13, 14, 16].
“It has been proved in + (1 1)-dimensions in [13, 14, 16].”
From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [16]
Section 4 (p. 10) derives dynamics of a discrete-time quantum walk that correspond to the Dirac equation in 1+1 dimensions, and Section 6 (p. 18) describes this as asymptotic behavior. The paper does not explicitly establish the claimed convergence of a Dirac quantum walk; its stated weak-convergence results concern quantum-walk limit distributions. (LLM, conf=0.80)
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- Authors
- Shikano, Y.
- Affiliations
- Tokyo Institute of Technology (JP)
- Corresponding author
- Shikano, Yutaka
- ORCID
- Shikano, Yutaka
- Venue
- Journal of Computational and Theoretical Nanoscience
- Publisher
- American Scientific Publishers
- Published
- 2013-07-01
- Volume
- 10
- Issue
- 7
- Pages
- 1558-1570
- ISSN
- 1546-1955 (ISSN-L)
- 1546-1963
- OpenAlex
- W1988534532
- Cited by
- 51
- References
- 0
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 2 · 2023: 2 · 2022: 3 · 2021: 1 · 2020: 5 · 2019: 7 · 2018: 2 · 2017: 4 · 2016: 6 · 2015: 5 · 2014: 7 · 2013: 2 · 2012: 1
- FWCI
- 7.37
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Computational and Theoretical Nanoscience (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- Massachusetts Institute of Technology
- Japan Society for the Promotion of Science
- 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, weak limit theorems, asymptotic distribution, asymptotic behavior, one-dimensional quantum walk
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