Fault-Tolerant Weighted Union-Find Decoding on the Toric Code

• URL: http://arxiv.org/abs/2004.04693v1
• Date: Thu, 9 Apr 2020 17:24:30 GMT
• Title: Fault-Tolerant Weighted Union-Find Decoding on the Toric Code
• Authors: Shilin Huang, Michael Newman, Kenneth R. Brown
• Abstract summary: We benchmark a weighted variant of the union-find decoder on the toric code under circuit-level depolarizing noise. This variant preserves the almost-linear time complexity of the original while significantly increasing the performance in the fault-tolerance setting.
• Score: 2.492300648514129
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction requires decoders that are both accurate and efficient. To this end, union-find decoding has emerged as a promising candidate for error correction on the surface code. In this work, we benchmark a weighted variant of the union-find decoder on the toric code under circuit-level depolarizing noise. This variant preserves the almost-linear time complexity of the original while significantly increasing the performance in the fault-tolerance setting. In this noise model, weighting the union-find decoder increases the threshold from 0.38% to 0.62%, compared to an increase from 0.65% to 0.72% when weighting a matching decoder. Further assuming quantum non-demolition measurements, weighted union-find decoding achieves a threshold of 0.76% compared to the 0.90% threshold when matching. We additionally provide comparisons of timing as well as low error rate behavior.

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