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Cited by 556Cellular Automata and ApplicationsQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

From quantum cellular automata to quantum lattice gases

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Meyer, David A.·1996·Journal of Statistical Physics
DOI 10.1007/bf02199356
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Crossref · 10.1007/bf02199356

Cites

34 of 34 references verified0 citation errors · 0 not checkable

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  • Both the collision and streaming operations are unitary and can be encoded in logical gates for quantum computing purposes.

    “Both operations are unitary and can be encoded in logical gates for quantum computing purposes [, ].”

    From Quantum lattice Boltzmann is a quantum walk (2015) · cites this paper as [34]

    Section 6 (pp. 13, 15) describes particle jumps followed by scattering and states that the scattering matrix must be unitary to ensure unitary evolution. The paper does not say that both operations can be encoded as logical gates; the Discussion (p. 18) treats local gates as a possibility for future investigation. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • The (2+1)-dimensional Dirac QW models the (2+1)-dimensional Dirac equation.

    “This Dirac QW [4-6] models the + (2 1)-dimensional Dirac equation.”

    From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [6]

    Section 4 (pp. 9, 11) says the quantum particle automaton approximates a Dirac particle and yields the Dirac propagator in the continuum limit. But the Introduction (p. 2) explicitly limits the paper to one dimension; it does not support the claim about a (2+1)-dimensional Dirac quantum walk. (LLM, conf=0.89)

    Experimental — accuracy not yet measured

  • The continuum limit of the DTQW mapping yields the one-dimensional Dirac equation.

    “where H D is the Hamiltonian for the one-dimensional Dirac equation (with ℏ = c = 1, p = -i∂ x ) [10]:”

    From Relativistic quantum walks (2006) · cites this paper as [9]

  • Consistency of the (1+1)-dimensional Dirac QW has been argued in [6], and for the (1+1)-dimensional massless case in [8].

    “Consistency of the + (1 1)-dimensional Dirac QW has been argued in [6], and for the + (1 1)-dimensional massless case in [8].”

    From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [6]

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Cites

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Research works printed but not linked: 8

  1. [12][12] S. Ulam, 'Random processes and transformations', in L. M. Graves, E. Hille, P. A. Smith and O. Zariski, eds., Proceedings of the International Congress of Mathematicians , Cambridge, MA, 30 August-6 September 1950 (Providence, RI: AMS 1952) II 264-275; - J. von Neumann, Theory of Self-reproducing Automata , edited and completed by A. W. Burks (Urbana, IL: University of Illinois Press 1966). -
  2. [15][15] K. Morita and M. Harao, 'Computation universality of one-dimensional reversible (injective) cellular automata', Trans. IEICE Japan E 72 (1989) 758-762. -
  3. [16][16] G. V. Riazanov, 'The Feynman path integral for the Dirac equation', JETP 6 (1958) 1107-1113; - R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals McGraw-Hill 1965) 34-36. 12. Sov. Phys. (New York: -
  4. [24][24] H. Weyl, The Theory of Groups and Quantum Mechanics , translated from the 2nd revised German edition by H. P. Robertson (New York: Dover 1950). -
  5. [28][28] Y. L. Luke, The Special Functions and Their Approximations , vol. I (NY: Academic Press 1969) 49. -
  6. [32][32] R. J. Baxter, Exactly Solved Models in Statistical Mechanics (New York: Academic Press 1982). -
  7. [35][35] M. H´ enon, 'On the relation between lattice gases and cellular automata', in R. Monaco, ed., Discrete Kinetic Theory, Lattice Gas Dynamics and Foundations of Hydrodynamics , proceedings of the workshop, Torino, Italy, 20-24 September 1988 (Singapore: World Scientific 1989) 160-161. -
  8. [41][41] L. Bombelli, J. Lee, D. A. Meyer and R. D. Sorkin, 'Spacetime as a causal set', Phys. Rev. Lett. 59 (1987) 521-524; - D. A. Meyer, 'Spacetime Ising models', UCSD preprint (1995); - D. A. Meyer, 'Induced actions for causal sets', UCSD preprint (1995).

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Authors
Meyer, D. A.
Affiliations
University of California San Diego (US)
Corresponding author
Meyer, David A.
Venue
Journal of Statistical Physics
Publisher
Springer Science and Business Media LLC
Published
1996-12
Volume
85
Issue
5-6
Pages
551-574
ISSN
  • 0022-4715 (ISSN-L)
  • 1572-9613
DOI
10.1007/bf02199356
OpenAlex
W2010265317
Cited by
556
References
34
Citations by year
2026: 10 · 2025: 18 · 2024: 13 · 2023: 17 · 2022: 21 · 2021: 27 · 2020: 33 · 2019: 38 · 2018: 27 · 2017: 21 · 2016: 45 · 2015: 27 · 2014: 26 · 2013: 21 · 2012: 17
FWCI
5.14
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Journal of Statistical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
  • 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
Keywords
quantum cellular automata, Dirac equation, interacting particles, exactly solvable models

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