Quantum mechanics of lattice gas automata: One-particle plane waves and potentials
Open accessAbstract
Classical lattice gas automata effectively simulate physical processes, such as diffusion and fluid flow (in certain parameter regimes), despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one-dimensional quantum lattice gas we find discrete analogs of plane waves and wave packets, and then investigate their behavior in the presence of inhomogeneous potentials.
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The Dirac equation can be considered the quantization (by analytic continuation) of the two-velocity model for the telegrapher's equation.
“The Dirac equation can also be considered the quantization (by analytic continuation) of the two-velocity model for the telegrapher's equation [20].”
From Relativistic quantum walks (2006) · cites this paper as [20]
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Low-Depth Quantum Simulation of Materials
Babbush, R., Wiebe, N., McClean, J., McClain, J., Neven, H., & Chan, G. K.-L. (2018) · Physical Review X · doi:10.1103/physrevx.8.011044 · Cited by 335 · see citing works
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Discrete-time quantum walks: Continuous limit and symmetries
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- Authors
- Meyer, D. A.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Meyer, David A.
- ORCID
- Meyer, David A.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1997-05-01
- Volume
- 55
- Issue
- 5
- Pages
- 5261-5269
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2073914931
- Cited by
- 101
- References
- 5
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 2 · 2023: 1 · 2022: 2 · 2020: 2 · 2019: 2 · 2018: 4 · 2017: 1 · 2016: 6 · 2015: 4 · 2014: 7 · 2013: 3 · 2012: 4
- FWCI
- 7.09
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Institute for Scientific Interchange
- 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
- wave packets, inhomogeneous potentials, quantum simulation, quantum computing
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