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Paper 1

Efficient Decoders for Qudit Topological Codes

Hussain Anwar, Benjamin J. Brown, Earl T. Campbell, Dan E. Browne

Year

2013

Journal

arXiv preprint

DOI

arXiv:1311.4895

arXiv

1311.4895

Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this paper we introduce two renormalization group decoders for qudit codes and analyze their error correction thresholds and efficiency. The first decoder is a generalization of a "hard-decisions" decoder due to Bravyi and Haah [arXiv:1112.3252]. We modify this decoder to overcome a percolation effect which limits its threshold performance for high dimensions. The second decoder is a generalization of a "soft-decisions" decoder due to Poulin and Duclos-Cianci [Phys. Rev. Lett. 104, 050504 (2010)], with a small cell size to optimize the efficiency of implementation in the high dimensional case. In each case, we estimate thresholds for the uncorrelated bit-flip error model and provide a comparative analysis of the performance of both these approaches to error correction of qudit toric codes.

Open paper

Paper 2

Topological quantum hashing with the icosahedral group.

Burrello M, Xu H, Mussardo G, Wan X.

Year

2010

Journal

Phys Rev Lett

DOI

10.1103/physrevlett.104.160502

arXiv

-

No abstract.

Open paper