text: 55,127,1248599744747798528,1068545181576773632,Kenneth Brown,"New paper on a weighted Union-Find decoder for the toric code with @Huang_Shilin and Mike Newman (<LINK>). #DukeQuantum @DukeEngineering A weighted Union-Find decoder increases the threshold for the Union-Find decoder but at what cost? In previous work with @Huang_Shilin (<LINK>) on 2D compass codes, we predicted it should be quadratically slower. In this paper, we show that with truncated weights that the speed is comparable to unweighted Union-Find with negligible loss in performance. The truncated version can be readily implemented using a microarchitecture based on <LINK> by @krystasvore @mointweets, @nico_delf and co-workers.",http://arxiv.org/abs/2004.04693,"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. ",Fault-Tolerant Weighted Union-Find Decoding on the Toric Code,4,"['New paper on a weighted Union-Find decoder for the toric code with @Huang_Shilin and Mike Newman (<LINK>). #DukeQuantum @DukeEngineering', 'A weighted Union-Find decoder increases the threshold for the Union-Find decoder but at what cost? In previous work with @Huang_Shilin (https://t.co/rdqpuzwKfa) on 2D compass codes, we predicted it should be quadratically slower.', 'In this paper, we show that with truncated weights that the speed is comparable to unweighted Union-Find with negligible loss in performance.', 'The truncated version can be readily implemented using a microarchitecture based on https://t.co/P0WpSu6FZx by @krystasvore @mointweets, @nico_delf and co-workers.']",20,04,638