Enhancing Fault-Tolerant Surface Code Decoding with Iterative Lattice Reweighting

2025-09-08

AI Summary

Recent quantum devices exhibit circuit-level noise inducing correlated X/Z errors, degrading surface code decoding performance. To address this, we propose a noise-aware iterative lattice reweighting decoder. Leveraging statistical correlations among fault detection events, the method dynamically adjusts dual-lattice edge weights via conditional probabilities, enabling hardware-agnostic suppression of correlated errors while preserving the minimum-weight perfect matching (MWPM) decoder’s theoretical distance guarantee. Experimental results demonstrate that, at physical error rates ≤ 0.001 and code distances ≥ 17, the logical error rate is reduced by over 20×; the accuracy threshold improves from 1.00% to 1.16%; and the code distance required to achieve a logical error rate of 10⁻¹⁶ decreases from 50 to 31—significantly reducing quantum resource overhead.

Technology Category

• Machine Learning: Hardware-aware ML
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Improving fault-tolerant quantum error correction decoding efficiency
• Addressing correlated X and Z errors in circuit-level noise
• Reducing qubit overhead for achieving low logical error rates

Innovation

• Iterative reweighting for correlated error handling
• Hardware-agnostic noise-aware decoding method
• Improves logical error rates with lattice updates