Improved single-shot decoding of higher dimensional hypergraph product codes

• URL: http://arxiv.org/abs/2206.03122v2
• Date: Tue, 27 Jun 2023 14:09:41 GMT
• Title: Improved single-shot decoding of higher dimensional hypergraph product codes
• Authors: Oscar Higgott and Nikolas P. Breuckmann
• Abstract summary: We study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics. We find that decoding data qubit and syndrome measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes.
• Score: 5.33024001730262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021]. We find that decoding data qubit and syndrome measurement errors together in a single stage leads to single-shot thresholds that greatly exceed all previously observed single-shot thresholds for these codes. For the 3D toric code and a phenomenological noise model, our results are consistent with a sustainable threshold of 7.1% for $Z$ errors, compared to the threshold of 2.90% previously found using a two-stage decoder~[Quintavalle et al., 2021]. For the 4D toric code, for which both $X$ and $Z$ error correction is single-shot, our results are consistent with a sustainable single-shot threshold of 4.3% which is even higher than the threshold of 2.93% for the 2D toric code for the same noise model but using $L$ rounds of stabiliser measurement. We also explore the performance of balanced product and 4D hypergraph product codes which we show lead to a reduction in qubit overhead compared the surface code for phenomenological error rates as high as 1%.

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