A review of Quantum Cellular Automata

Terry Farrelly

doi:10.22331/q-2020-11-30-368

A review of Quantum Cellular Automata

Institut für Theoretische Physik, Leibniz Universität Hannover, 30167 Hannover, Germany
ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia

Published:	2020-11-30, volume 4, page 368
Eprint:	arXiv:1904.13318v2
Doi:	https://doi.org/10.22331/q-2020-11-30-368
Citation:	Quantum 4, 368 (2020).

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Abstract

Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally arose as an alternative paradigm for quantum computation, though more recently they have found application in understanding topological phases of matter and have} been proposed as models of periodically driven (Floquet) quantum systems, where QCA methods were used to classify their phases. QCAs have also been used as a natural discretization of quantum field theory, and some interesting examples of QCAs have been introduced that become interacting quantum field theories in the continuum limit. This review discusses all of these applications, as well as some other interesting results on the structure of quantum cellular automata, including the tensor-network unitary approach, the index theory and higher dimensional classifications of QCAs.

Featured image: Spacetime diagrams of the dynamics of some Clifford quantum cellular automata can have a fractal pattern.

► BibTeX data

@article{Farrelly2020reviewofquantum,
  doi = {10.22331/q-2020-11-30-368},
  url = {https://doi.org/10.22331/q-2020-11-30-368},
  title = {A review of {Q}uantum {C}ellular {A}utomata},
  author = {Farrelly, Terry},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {368},
  month = nov,
  year = {2020}
}

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