Measurement Based Quantum Computation on Fractal Lattices

Damian Markham
Janet Anders
Michal Hajdušek
Vlatko Vedral

In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.

In S. Barry Cooper, Prakash Panangaden and Elham Kashefi: Proceedings Sixth Workshop on Developments in Computational Models: Causality, Computation, and Physics (DCM 2010), Edinburgh, Scotland, 9-10th July 2010, Electronic Proceedings in Theoretical Computer Science 26, pp. 109–115.
Published: 9th June 2010.

ArXived at: bibtex PDF

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