Improved HDRG decoders for qudit and non-Abelian quantum error correction

Hutter, A. and Loss, D. and Wootton, J. R.. (2015) Improved HDRG decoders for qudit and non-Abelian quantum error correction. New journal of physics, 17 (3). 035017.

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Official URL: http://edoc.unibas.ch/40416/

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Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from Theta (L 2/3) to Omega (L 1-epsilon) for any epsilon > 0. We apply our algorithm to decoding D (Z d ) quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the D (Z d) quantum double models. The parallelized runtime of our algorithm is poly(log L)for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is O(1) for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.
Faculties and Departments:05 Faculty of Science > Departement Physik > Physik > Theoretische Physik Mesoscopics (Loss)
UniBasel Contributors:Loss, Daniel
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:IOP Publishing
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:30 Jun 2016 11:01
Deposited On:09 May 2016 11:09

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