Natural Computing

, Volume 11, Issue 1, pp 13–22 | Cite as

Partitioned quantum cellular automata are intrinsically universal

  • Pablo Arrighi
  • Jonathan Grattage


There have been several non-axiomatic approaches taken to define quantum cellular automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we show that any QCA can be put into the form of a PQCA. Our construction reconciles all the non-axiomatic definitions of QCA, showing that they can all simulate one another, and hence that they are all equivalent to the axiomatic definition. This is achieved by defining generalised n-dimensional intrinsic simulation, which brings the computer science based concepts of simulation and universality closer to theoretical physics. The result is not only an important simplification of the QCA model, it also plays a key role in the identification of a minimal n-dimensional intrinsically universal QCA.


Quantum computing Cellular automata Intrinsic universality 



The authors would like to thank Jérôme Durand-Lose, Jacques Mazoyer, Nicolas Ollinger, Guillaume Theyssier and Philippe Jorrand.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Laboratoire LIG, Bâtiment IMAG C University of GrenobleSaint-Martin-d’HèresFrance
  2. 2.Laboratoire LIP, Ecole Normale Supérieure de LyonLyon cedex 07France

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