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arXiv · 1708.09286

Renormalization group decoder for a four-dimensional toric code

Kasper Duivenvoorden·Nikolas P. Breuckmann·Barbara M. Terhal
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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 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 $4.35\pm0.1\%$. 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 $7.3\pm0.1\%$. For the gate-based depolarizing error model we find a threshold of $0.31\pm0.01\%$ which is below the threshold found for the two-dimensional toric code.

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Kasper Duivenvoorden, Nikolas P. Breuckmann, Barbara M. Terhal. 2017-08-30. Renormalization group decoder for a four-dimensional toric code. https://doi.org/10.1109/tit.2018.2879937

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