Researchers have built a neural network-assisted decoder that nearly matches the best possible performance for correcting errors in quantum computers.
The system, called Neural Minimum Weight Perfect Matching (NMWPM), pairs a graph neural network with a Transformer to improve a standard quantum error correction algorithm. The classic approach — Minimum Weight Perfect Matching — uses fixed edge weights on a graph to find the most probable error chains in a qubit array. NMWPM learns to predict those weights dynamically from the data instead, letting the underlying algorithm stay intact while the neural layer adapts to actual noise patterns. Testing on the toric code under depolarizing noise, the decoder reached thresholds of 17.9% and 10.95%, compared to theoretical maximums of 18.9% and 11.0%.
Getting close to maximum likelihood bounds matters because error correction is the gating factor for practical quantum computing — without it, noise accumulates faster than any computation can outrun it. Most learned decoders sacrifice the structural guarantees of classical algorithms for flexibility; this hybrid approach keeps both, which is why the numbers land so close to the ceiling.
One open question is whether these thresholds hold at the scale and noise profiles of real hardware, where depolarizing noise is a convenient model but not the whole story.