A matching threshold of 2×10⁻³ for the rotated surface code under circuit-level noise
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…
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