@book{tHooft2016,
  author    = {{'t Hooft}, Gerard},
  title     = {The Cellular Automaton Interpretation of Quantum Mechanics},
  publisher = {Springer},
  address   = {Cham},
  year      = {2016},
  doi       = {10.1007/978-3-319-41285-6}
}

@article{tHooft2013Duality,
  author        = {{'t Hooft}, Gerard},
  title         = {Duality Between a Deterministic Cellular Automaton and a Bosonic Quantum Field Theory in 1+1 Dimensions},
  journal       = {Foundations of Physics},
  volume        = {43},
  pages         = {597--614},
  year          = {2013},
  doi           = {10.1007/s10701-013-9702-z},
  eprint        = {1205.4107},
  archivePrefix = {arXiv},
  primaryClass  = {quant-ph},
  url           = {https://link.springer.com/article/10.1007/s10701-013-9702-z}
}

@article{ToffoliMargolus1990,
  author  = {Toffoli, Tommaso and Margolus, Norman},
  title   = {Invertible Cellular Automata: A Review},
  journal = {Physica D: Nonlinear Phenomena},
  volume  = {45},
  number  = {1--3},
  pages   = {229--253},
  year    = {1990},
  doi     = {10.1016/0167-2789(90)90185-R}
}

@article{Kari2018,
  author  = {Kari, Jarkko},
  title   = {Reversible Cellular Automata: From Fundamental Classical Results to Recent Developments},
  journal = {New Generation Computing},
  volume  = {36},
  pages   = {145--172},
  year    = {2018},
  doi     = {10.1007/s00354-018-0034-6}
}

@article{LevesqueVerlet1993,
  author  = {Levesque, Dominique and Verlet, Loup},
  title   = {Molecular Dynamics and Time Reversibility},
  journal = {Journal of Statistical Physics},
  volume  = {72},
  pages   = {519--537},
  year    = {1993},
  doi     = {10.1007/BF01048022},
  url     = {https://link.springer.com/article/10.1007/BF01048022}
}

@article{ReinTamayo2018,
  author        = {Rein, Hanno and Tamayo, Daniel},
  title         = {{JANUS}: A Bit-wise Reversible Integrator for {$N$}-body Dynamics},
  journal       = {Monthly Notices of the Royal Astronomical Society},
  volume        = {473},
  number        = {3},
  pages         = {3351--3357},
  year          = {2018},
  doi           = {10.1093/mnras/stx2479},
  eprint        = {1704.07715},
  archivePrefix = {arXiv},
  primaryClass  = {astro-ph.IM},
  url           = {https://academic.oup.com/mnras/article/473/3/3351/4243609}
}

@book{Strikwerda2004,
  author    = {Strikwerda, John C.},
  title     = {Finite Difference Schemes and Partial Differential Equations},
  edition   = {2},
  publisher = {SIAM},
  address   = {Philadelphia},
  year      = {2004}
}

@book{HairerLubichWanner2006,
  author    = {Hairer, Ernst and Lubich, Christian and Wanner, Gerhard},
  title     = {Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations},
  edition   = {2},
  publisher = {Springer},
  address   = {Berlin},
  year      = {2006}
}

@article{ArrighiNesmeWerner2017,
  author        = {Arrighi, Pablo and Nesme, Vincent and Werner, Reinhard F.},
  title         = {Bounds on the Speedup in Quantum Signaling},
  journal       = {Physical Review A},
  volume        = {95},
  number        = {1},
  pages         = {012331},
  year          = {2017},
  doi           = {10.1103/PhysRevA.95.012331},
  eprint        = {0910.4461},
  archivePrefix = {arXiv},
  primaryClass  = {quant-ph},
  url           = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.012331}
}

@article{SchumacherWerner2004,
  author       = {Schumacher, Benjamin and Werner, Reinhard F.},
  title        = {Reversible Quantum Cellular Automata},
  journal      = {arXiv preprint},
  year         = {2004},
  archivePrefix= {arXiv},
  doi          = {10.48550/arXiv.quant-ph/0405174}
}

@article{Arrighi2011,
  author  = {Arrighi, Pablo and Nesme, Vincent and Werner, Reinhard},
  title   = {Unitarity Plus Causality Implies Localizability},
  journal = {Journal of Computer and System Sciences},
  volume  = {77},
  number  = {2},
  pages   = {372--378},
  year    = {2011},
  doi     = {10.1016/j.jcss.2010.05.004}
}

@article{Farrelly2020,
  author  = {Farrelly, Terry},
  title   = {A Review of Quantum Cellular Automata},
  journal = {Quantum},
  volume  = {4},
  pages   = {368},
  year    = {2020},
  doi     = {10.22331/q-2020-11-30-368}
}

@book{ToffoliMargolus1987,
  author    = {Toffoli, Tommaso and Margolus, Norman},
  title     = {Cellular Automata Machines: A New Environment for Modeling},
  publisher = {The MIT Press},
  address   = {Cambridge, MA},
  year      = {1987},
  isbn      = {9780262200608}
}

@article{EarnTremaine1992,
  author  = {Earn, David J. D. and Tremaine, Scott},
  title   = {Exact Numerical Studies of Hamiltonian Maps: Iterating without Roundoff Error},
  journal = {Physica D: Nonlinear Phenomena},
  volume  = {56},
  number  = {1},
  pages   = {1--22},
  year    = {1992},
  doi     = {10.1016/0167-2789(92)90047-Q},
  url     = {https://davidearn.mcmaster.ca/publications/EarnTremaine1992}
}

@misc{NISTDLMF,
  author = {{National Institute of Standards and Technology}},
  title = {{NIST} Digital Library of Mathematical Functions},
  howpublished = {Online reference, Chapter 22, Sections 22.4 and 22.13},
  url = {https://dlmf.nist.gov/22.13},
  note = {Accessed 23 October 2026}
}