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2009

Fast Decoders for Topological Quantum Codes

Duclos-Cianci, Guillaume, Poulin, David

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We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects.

Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes.
For a system of linear size L, our algorithm runs in time log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.

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Then

Z. Nussinov and G. Ortiz, Phys. Rev. B 77
2008
Later among the works it cites.
A. Fowler, A. Stephens, and P. Groszkowski, (2008), eprint arXiv:0803.0272
Original
2008
Later among the works it cites.
M. Aguado and G. Vidal, Phys. Rev. Lett. 100
2008
Later among the works it cites.
D. Poulin and Y. Chung, Quant. Info. and Comp. 8
2008
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H. Bombin and M. Martin-Delgado, J. Phys. A 42
2009
Closest in time.
E. Bilgin and D. Poulin, (2009), eprint arXiv:0910.2299
Original
2009
Closest in time.

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