Abstract
We explore a quantum version of Janzing’s “physical universality”, a notion of computational universality for cellular automata which requires computations to be done directly on the cells. We discuss physical universality in general, the issues specific to the quantum setting, and give an example of a quantum cellular automaton achieving a quantum definition of physical universality.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Dawson, C.M., Nielsen, M.A.: The Solovay-Kitaev algorithm. Quantum Info. Comput. 6(1), 81–95 (2006)
Janzing, D.: Is there a physically universal cellular automaton or Hamiltonian? (2010). http://arxiv.org/abs/1009.1720
Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321 (1997)
Raussendorf, R.: Quantum cellular automaton for universal quantum computation. Phys. Rev. A 72, 022301 (2005)
Salo, V., Törmä, I.: A one-dimensional physically universal cellular automaton. Personal Communication (2014)
Schaeffer, L.: A physically universal cellular automaton. In: Roughgarden, T. (ed.) Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, pp. 237–246. ACM, Rehovot (2015)
van Dam, W.: A universal quantum cellular automaton. In: Proceedings of PhysComp96, pp. 323–331. InterJournal (1996)
Watrous, J.: On one-dimensional quantum cellular automata. In: 36th Annual Symposium on Foundations of Computer Science, pp. 528–537. Society Press (1995)
Youssef, S.: Quantum Mechanics as Bayesian Complex Probability Theory. Modern Physics Letters A 9, 2571–2586 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 IFIP International Federation for Information Processing
About this paper
Cite this paper
Schaeffer, L. (2015). A Physically Universal Quantum Cellular Automaton. In: Kari, J. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2015. Lecture Notes in Computer Science(), vol 9099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47221-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-47221-7_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-47220-0
Online ISBN: 978-3-662-47221-7
eBook Packages: Computer ScienceComputer Science (R0)