Reconstruction of detector error model for quantum error correction

• URL: http://arxiv.org/abs/2606.16288v2
• Date: Wed, 17 Jun 2026 15:05:41 GMT
• Title: Reconstruction of detector error model for quantum error correction
• Abstract summary: We introduce a globally consistent framework to invert experimental syndrome statistics directly into discrete physical hypergraphs.<n>We show that exact continuous parameter extraction in dense codes is limited by a textitvariance cascade, where absolute statistical variance accumulates linearly from high to low-degree mechanisms.<n>This provides a practical approach for characterizing and decoding highly correlated noise in realistic quantum hardware.
• Score: 6.505803823301456
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fault-tolerant quantum computing fundamentally relies on the accurate characterization of circuit-level noise to optimize decoding algorithms. However, extracting complex multi-body error correlations remains challenging. Contemporary greedy inference algorithms can suffer from statistical distortion, discarding true physical mechanisms while introducing many unphysical false positives. Here, we introduce the Correlation-Analysis-based Hypergraph Reconstruction (CAHR) algorithm, a globally consistent framework to invert experimental syndrome statistics directly into discrete physical hypergraphs. By coupling exact algebraic correlation equations with a top-down concurrent-pruning strategy, CAHR recovers the fault topology without false positives for both $d=5$ rotated surface codes and dense 8-body 2D color codes in our benchmark settings. Furthermore, we show that exact continuous parameter extraction in dense codes is limited by a \textit{variance cascade}, where absolute statistical variance accumulates linearly from high- to low-degree mechanisms. This motivates a two-stage inference paradigm: utilizing CAHR to extract the fault topology, followed by continuous probability optimization. This provides a practical approach for characterizing and decoding highly correlated noise in realistic quantum hardware.

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