Union-Intersection Union-Find for Decoding Depolarizing Errors in Topological Codes

• Published in: IEEE journal on selected areas in information theory Vol. 6; pp. 163 - 175
• Main Authors: Lin, Tzu-Hao, Lai, Ching-Yi
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Codes; Correlation; Decoding; Depolarization; Error analysis; Error correction; Error reduction; Iterative decoding; Iterative methods; Layout; Minimum weight; Noise; Performance enhancement; quantum error correction codes; Quantum information; Qubit; surface codes; topological codes; Topology; union-find decoder; X/Z correlation
• ISSN: 2641-8770; 2641-8770
• DOI: 10.1109/JSAIT.2025.3581810

In this paper, we introduce the Union-Intersection Union-Find (UIUF) algorithm for decoding depolarizing errors in topological codes, combining the strengths of iterative and standard Union-Find (UF) decoding. While iterative UF improves performance at moderate error rates, it lacks an error correction guarantee. To address this, we develop UIUF, which maintains the enhanced performance of iterative UF while ensuring error correction up to half the code distance. Through simulations under code capacity, phenomenological, and biased noise models, we show that UIUF significantly outperforms UF, reducing the logical error rate by over an order of magnitude (at around <inline-formula> <tex-math notation="LaTeX">10^{-5} </tex-math></inline-formula>). Moreover, UIUF achieves lower logical error rates than the Minimum Weight Perfect Matching (MWPM) decoder on rotated surface codes under both the code capacity and phenomenological noise models, while preserving efficient linear-time complexity.