Renormalization Group Decoder for a Four-Dimensional Toric Code

Journal article (2019)

Authors

Nikolas P. Breuckmann Rheinisch-Westfälische Technische Hochschule, University College London
B.M. Terhal , Forschungszentrum Jülich, QuTech Advanced Research Centre
K. Duivenvoorden Rheinisch-Westfälische Technische Hochschule
Copyright: © 2019 N.P. Breuckmann, B.M. Terhal, K. Duivenvoorden
DOI
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https://doi.org/10.1109/TIT.2018.2879937
Quantum computing Error correcting codes Smoothing method
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Published Date

2019

Language

English

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Abstract

We describe a computationally efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding a minimal surface given its boundary (curve) in any hypercubic lattice of dimension D > 2. We use this algorithm to correct errors occurring in a four-dimensional variant of the toric code, having open as opposed to periodic boundaries. For a phenomenological error model which includes measurement errors we use a five-dimensional version of our algorithm, achieving a threshold of 4.35?0.1%. For this error model, this is the highest known threshold of any topological code. Without measurement errors, a four-dimensional version of our algorithm can be used and we find a threshold of 7.3?0.1%. For the gate-based depolarizing error model we find a threshold of 0.31?0.01% which is below the threshold found for the twodimensional toric code.

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