Post date: Jan 09, 2014 3:12:48 PM
In collaboration with Ben Brown (Imperial College) and Earl Campbell (Berlin), Dan Browne and Hussain Anwar have posted a new paper to the pre-print archive arxiv.org developing new error correction procedures for topological codes, and important class of error correcting codes for fault tolerant quantum computation.
Abstract: 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.
Link to pre-print: http://arxiv.org/abs/1311.4895