Enhancing Fault-Tolerant Surface Code Decoding with Iterative Lattice Reweighting

• URL: http://arxiv.org/abs/2509.06756v2
• Date: Tue, 09 Sep 2025 05:18:35 GMT
• Title: Enhancing Fault-Tolerant Surface Code Decoding with Iterative Lattice Reweighting
• Authors: Yi Tian, Y. Zheng, Xiaoting Wang, Ching-Yi Lai,
• Abstract summary: We introduce the Iterative Reweighting Minimum-Weight Perfect Matching (IRMWPM) decoder.<n>We show that IRMWPM reduces logical error rates by over 20x with only a few distances.<n>It also raises the accuracy threshold from 1% to 1.16%, making it practical for near-term real-time decoding.
• Score: 12.330043396100635
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficient and realistic error decoding is crucial for fault-tolerant quantum computation (FTQC) on near-term devices. While decoding is a classical post-processing task, its effectiveness depends on accurately modeling quantum noise, which is hardware-dependent. In particular, correlated bit-flip ($X$) and phase-flip ($Z$) errors often arise under circuit-level noise. We introduce the Iterative Reweighting Minimum-Weight Perfect Matching (IRMWPM) decoder, which systematically incorporates such correlations to enhance quantum error correction. Our method leverages fault-detection patterns to guide reweighting: correlated $X$ and $Z$ detection events are identified, and their conditional probabilities update weights on the primal and dual lattices. This iterative procedure improves handling of realistic error propagation in a hardware-agnostic yet noise-aware manner. We prove that IRMWPM converges in finite time while preserving the distance guarantee of MWPM. Numerical results under circuit-level noise show substantial improvements. For distances $\geq 17$ and physical error rates $\leq 0.001$, IRMWPM reduces logical error rates by over 20x with only a few iterations. It also raises the accuracy threshold from 1% to 1.16%, making it practical for near-term real-time decoding. Extrapolated estimates suggest that to reach logical error rate $10^{-16}$, IRMWPM requires distance $d=31$, while standard MWPM needs $d=50$, implying a major reduction in qubit overhead.

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