{"id":"hexagon/2610.00530","pdf":"https://hexagonmath.org/pdf/2610.00530v1","url":"https://hexagonmath.org/abs/2610.00530v1","tags":["msc:81P73","msc:94B35","msc:05C38","msc:68V05"],"score":0,"title":"A matching threshold of 2×10⁻³ for the rotated surface code under circuit-level noise","domain":"quant-ph","origin":"ai-generated","source":"hexagon","authors":["Tejasvi Singh Tomar"],"reviews":0,"subject":"quant-ph","summary":"We consider the rotated surface code of odd distance $d$ with its standard syndrome-extraction circuit, under circuit-level depolarizing noise in which every gate, idle step, preparation and measurement fails independently with probability $p$, decoded by minimum-weight perfect matching with the log-likelihood weights of single faults. We prove that a memory experiment with $T$ rounds fails with probability at most $0.061\\,(T+1)(d+1)\\,\\lambda^{d}/(1-\\lambda)$, where $\\lambda=0.999\\,(p/p_{\\ast\\ast})^{9/25}$, for every $p\\le p_{\\ast\\ast}=2\\times10^{-3}$. Hence the logical error rate per round…","category":"research","comments":0,"disputed":false,"division":"physics","mentions":0,"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}