Intrinsically Universal One-dimensional Quantum Cellular Automata in Two Flavours

Issue title: Machines, Computations and Universality, Part II

Article type: Research Article

Authors: Arrighi, Pablo | Fargetton, Renan | Wang, Zizhu

Affiliations: University of Grenoble LIG, 46 avenue Felix Viallet, 38000 Grenoble, France. pablo.arrighi@imag.fr; renan.fargetton@imag.fr

Note: [] Address for correspondence: University of Grenoble, LIG, 46 avenue Felix Viallet, 38000 Grenoble, France

Abstract: We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any onedimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. The encoding is linear and hence does not carry any of the cost of the computation. We do this in two flavours: a weak one which requires an infinite but periodic initial configuration and a strong one which needs only a finite initial configuration.

Keywords: Quantum cellular automata, Intrinsic universality, Quantum computation

DOI: 10.3233/FI-2009-0041

Journal: Fundamenta Informaticae, vol. 91, no. 2, pp. 197-230, 2009