Fault-tolerant quantum computing relies on Quantum Error Correction, which encodes logical qubits into data and parity qubits. Error decoding is the process of translating the measured parity bits into types and locations of errors. To prevent a backlog of errors, error decoding must be performed in real-time. Minimum Weight Perfect Matching (MWPM) is an accurate decoding algorithm for surface code, and recent research has demonstrated real-time implementations of MWPM (RT-MWPM) for a distance of up to 9. Unfortunately, beyond d=9, the number of flipped parity bits in the syndrome, referred to as the Hamming weight of the syndrome, exceeds the capabilities of existing RT-MWPM decoders. In this work, our goal is to enable larger distance RT-MWPM decoders by using adaptive predecoding that converts high Hamming weight syndromes into low Hamming weight syndromes, which are accurately decoded by the RT-MWPM decoder. An effective predecoder must balance both accuracy and coverage. In this paper, we propose Promatch, a real-time adaptive predecoder that predecodes both simple and complex patterns using a locality-aware, greedy approach. Our approach ensures two crucial factors: 1) high accuracy in prematching flipped bits, ensuring that the decoding accuracy is not hampered by the predecoder, and 2) enough coverage adjusted based on the main decoder's capability given the time constraints. Promatch represents the first real-time decoding framework capable of decoding surface codes of distances 11 and 13, achieving an LER of $2.6\times 10^{-14}$ for distance 13. Moreover, we demonstrate that running Promatch concurrently with the recently proposed Astrea-G achieves LER equivalent to MWPM LER, $3.4\times10^{-15}$, for distance 13, representing the first real-time accurate decoder for up-to a distance of 13.

翻译：容错量子计算依赖于量子纠错，该技术将逻辑量子比特编码为数据和校验量子比特。错误解码是将测量的校验比特转换为错误类型和位置的过程。为避免错误积压，错误解码必须实时完成。最小权重完美匹配（MWPM）是表面码的精确解码算法，近期研究已实现距离最高达9的MWPM实时解码（RT-MWPM）。遗憾的是，当距离d超过9时，综合征中翻转校验比特的数量（即综合征的汉明重量）超出了现有RT-MWPM解码器的处理能力。本研究旨在通过自适应预解码实现更大距离的RT-MWPM解码器，将高汉明重量综合征转换为低汉明重量综合征，再由RT-MWPM解码器精确解码。有效的预解码器需同时兼顾准确性与覆盖范围。本文提出Promatch——一种实时自适应预解码器，采用局部感知的贪心方法预解码简单与复杂模式。该方法确保两个关键因素：1）预匹配翻转比特的高准确性，避免预解码影响解码精度；2）基于时间约束下主解码器能力动态调整的充分覆盖范围。Promatch是首个能解码距离11和13的表面码的实时解码框架，距离13时逻辑错误率（LER）达到$2.6\times 10^{-14}$。此外，我们证明Promatch与近期提出的Astrea-G并发运行时，距离13的LER等效于MWPM的LER（$3.4\times10^{-15}$），这是首个支持距离最高达13的实时精确解码器。