Please use this identifier to cite or link to this item: https://doi.org/10.1017/S0960129512000175
Title: Topological features of good resources for measurement-based quantum computation
Authors: Markham, D.
Anders, J.
Hajdušek, M.
Vedral, V. 
Issue Date: Feb-2013
Citation: Markham, D., Anders, J., Hajdušek, M., Vedral, V. (2013-02). Topological features of good resources for measurement-based quantum computation. Mathematical Structures in Computer Science 23 (2) : 441-453. ScholarBank@NUS Repository. https://doi.org/10.1017/S0960129512000175
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. © 2013 Cambridge University Press.
Source Title: Mathematical Structures in Computer Science
URI: http://scholarbank.nus.edu.sg/handle/10635/98941
ISSN: 09601295
DOI: 10.1017/S0960129512000175
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