Promatch: Extending the Reach of Real-Time Quantum Error Correction with Adaptive Predecoding

TL;DR

Promatch addresses the challenge of extending real-time MWPM decoding to larger surface-code distances by introducing an adaptive syndromemodifying predecoder. It uses a locality-aware greedy approach that prioritizes matching patterns which avoid creating singletons and achieve sufficient coverage through multiple, simple steps, enabling the main RT-MWPM decoder to operate within the $1\mu s$ budget. When paired with Astrea-G, Promatch achieves MWPM-equivalent logical error rates for $d=13$ and, in isolation, delivers state-of-the-art real-time decoding LER values for $d=11$ and $d=13$ ($4.5\times 10^{-13}$ and $2.6\times 10^{-14}$, respectively), with $d=13$ reaching $3.4\times10^{-15}$ when combined. This framework advances practical fault-tolerant quantum computing by closing the gap between RT and non-RT MWPM at larger code distances and offering FPGA-friendly, deterministic predecoding suitable for real hardware. The approach broadens the applicability of real-time QEC, enabling larger-scale quantum processors to operate with MWPM-quality reliability in real time.

Abstract

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.

Figures (11)

• Figure 1: (a) The overview of QEC process in the presence of a predecoder. (b) The tradeoff between accuracy and coverage for Hierarchical predecoer delfosse2020hierarchical, Clique ravi2023better, and the greedy predecoder smith2023local. Existing predecoders either have low accuracy or low coverage. (c) The gap between current RT-MWPM and Non-RT MWPM decoders indicating a 43x higher LER (d) An overview of insights using in Promatch for the locality-aware greedy algorithm. Promatch checks the neighborhood of flipped parity bits and finds the correct matching (nodes 1 and 2), which enables additional correct prematching (nodes 3 and 4). These two prematchings result in a lower weight, having a higher probability ($P^2$ compared to at most $P^3$).
• Figure 2: (a) Illustration of a $d=5$ surface code logical qubit lattice, alongside the associated $Z$ and $X$ stabilizer extraction circuits. (b) Two-round decoding graph example for the $X$ stabilizer. (c) Real-time decoders, under $1\mu s$, exist for up to distance 9 while, for higher distances, 11 and 13, we need to rely on software-based decoders which have high latency.
• Figure 3: (a) NSM Predecoders attempt to decode the entire syndrome. If they fail, then the entire syndrome is sent to the main decoder. (b) SM Predecoders decode a subset of the syndrome and send the remainder to the main decoder.
• Figure 4: Logical error rate trends for MWPM, Astrea-G, Clique+MWPM, and AFS as code distance $d$ increases, considering a physical error rate of $10^{-4}$.
• Figure 5: More than $90\%$ of error chains, based on MWPM decoder, has length of 1. This means more than $90\%$ of flipped bits are matched to their neighbors. This plot is for distance 13 and physical error rate $10^{-4}$.