A Review Of Quantum Cellular Automata

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}<br /> }

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[2] P. Arrighi, “An overview of quantum cellular automata”, Natural Computing 18 4, 885 (2019).

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[5] Logan E. Hillberry, Matthew T. Jones, David L. Vargas, Patrick Rall, Nicole Yunger Halpern, Ning Bao, Simone Notarnicola, Simone Montangero, and Lincoln D. Carr, “Entangled quantum cellular automata, physical complexity, and Goldilocks rules”, arXiv:2005.01763.

[6] Lorenzo Piroli and J. Ignacio Cirac, “Quantum Cellular Automata, Tensor Networks, and Area Laws”, Physical Review Letters 125 19, 190402 (2020).

[7] Edward Gillman, Federico Carollo, and Igor Lesanovsky, “Nonequilibrium Phase Transitions in (1 +1 )-Dimensional Quantum Cellular Automata with Controllable Quantum Correlations”, Physical Review Letters 125 10, 100403 (2020).

[8] Terry Farrelly and Julien Streich, “Discretizing quantum field theories for quantum simulation”, arXiv:2002.02643.

[9] Lorenzo Piroli, Alex Turzillo, Sujeet K. Shukla, and J. Ignacio Cirac, “Fermionic quantum cellular automata and generalized matrix product unitaries”, arXiv:2007.11905.

[10] Zoltán Zimborás, Terry Farrelly, Szilárd Farkas, and Lluis Masanes, “Does causal dynamics imply local interactions?”, arXiv:2006.10707.

[11] Leonard Mlodinow and Todd A. Brun, “Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions”, Physical Review A 102 4, 042211 (2020).

[12] Ruhi Shah and Jonathan Gorard, “Quantum Cellular Automata, Black Hole Thermodynamics, and the Laws of Quantum Complexity”, arXiv:1910.00578.

[13] Paolo Perinotti, “Cellular automata in operational probabilistic theories”, arXiv:1911.11216.

[14] Tom Farshi, Daniele Toniolo, Carlos E. González-Guillén, Álvaro M. Alhambra, and Lluis Masanes, “Time-periodic dynamics generates pseudo-random unitaries”, arXiv:2007.03339.

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[17] Luca Apadula, Alessandro Bisio, Giacomo Mauro D’Ariano, and Paolo Perinotti, “Symmetries of the Dirac quantum walk and emergence of the de Sitter group”, Journal of Mathematical Physics 61 8, 082202 (2020).

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[19] Edward Gillman, Federico Carollo, and Igor Lesanovsky, “Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects”, arXiv:2010.10954.

[20] Leonard Mlodinow and Todd A. Brun, “Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions”, arXiv:2011.05597.

[21] David Berenstein and Jiayao Zhao, “Exotic equilibration dynamics on a 1-D quantum CNOT gate lattice”, arXiv:2102.05745.

[22] Zongping Gong, Lorenzo Piroli, and J. Ignacio Cirac, “Topological lower bound on quantum chaos by entanglement growth”, arXiv:2012.02772.

The above citations are from Crossref’s cited-by service (last updated successfully 2021-02-15 02:01:28) and SAO/NASA ADS (last updated successfully 2021-02-15 02:01:29). The list may be incomplete as not all publishers provide suitable and complete citation data.

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