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Topological features of good resources for measurement-based quantum computation

Published online by Cambridge University Press:  28 February 2013

DAMIAM MARKHAM ,
JANET ANDERS ,
MICHAL HAJDUŠEK  and
VLATKO VEDRAL
DAMIAM MARKHAM
Affiliation:
CNRS, LTCI, Telecom ParisTech, 37/39 rue Dareau, 75014 Paris, France Email: markham@telecom-paristech.fr
JANET ANDERS
Affiliation:
Department of Physics & Astronomy, University College London, London WC1E 6BT, United Kingdom Email: janet@qipc.org
MICHAL HAJDUŠEK
Affiliation:
The School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom, and Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan, 113-0033 Email: michal@eve.phys.s.u-tokyo.ac.jp
VLATKO VEDRAL
Affiliation:
Centre for Quantum Technologies, National University of Singapore, Singapore, and Department of Physics, National University of Singapore, Singapore, and Clarendon Laboratory, University of Oxford, Oxford, United Kingdom Email: vlatko.vedral@qubit.org
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Abstract

We study how graph states on fractal lattices can be used to perform measurement-based quantum computation, and investigate which topological features allow this application. We find fractal lattices of arbitrary dimension greater than one that all act as good resources for measurement-based quantum computation, and sets of fractal lattices with dimension greater than one that do not. The difference is put down to other topological factors such as ramification and connectivity. This is in direct analogy to the tendency of lattices to observe criticality in spin systems. We also discuss the analogy between thermodynamics and one-way computation in this context. This work adds confidence to the analogy and highlights new features of what we require for universal resources for measurement-based quantum computation. This paper is an extended version of Markham et al. (2010), which appeared in the proceedings of DCM 2010.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 441 - 453
Copyright
Copyright © Cambridge University Press 2013

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