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Time asymptotics and entanglement generation of Clifford quantum cellular automata

Source: J. Math. Phys. 51, 015203 (2010); doi:10.1063/1.3278513

Published 29 January 2010

KEYWORDS and PACS
Keywords
PACS
  • 03.65.Ud
    Entanglement and quantum nonlocality
  • 03.67.Lx
    Quantum computation architectures and implementations
  • 02.60.-x
    Numerical approximation and analysis
  • 05.45.Df
    Fractals
  • YEAR: 2010
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PUBLICATION DATA
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Johannes Gütschow,1,2 Sonja Uphoff,1,3 Reinhard F. Werner,1,2 and Zoltán Zimborás4,5
1Institut für Mathematische Physik, Technische Universität Braunschweig, Mendelssohnstraße 3, 38106 Braunschweig, Germany
2Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
3Institut für Rechnergestützte Modellierung im Bauingenieurwesen, Technische Universität Braunschweig, Pockelsstraße 3, 38106 Braunschweig, Germany
4Institut für Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
5Quantum Information Theory Unit, ISI Foundation, Viale S. Severo 65, 10133 Torino, Italy
We consider Clifford quantum cellular automata (CQCAs) and their time-evolution. CQCAs are an especially simple type of quantum cellular automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs, and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, such as quasifree and stabilizer states. Finally, we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states. ©2010 American Institute of Physics
History: Received 25 June 2009; accepted 4 December 2009; published 29 January 2010
Permalink: http://link.aip.org/link/?JMAPAQ/51/015203/1

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