  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.
