Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation

Fault-tolerant quantum computing, the prerequisite for every scalable quantum algorithm, hinges on a classical decoder that is simultaneously fast and accurate. Existing decoders face a sharp accuracy–latency trade-off: iterative decoders are fast but too inaccurate on high-rate codes, while near-optimal combinatorial-search decoders are far too slow for real-time use. We treat decoding as a structured inference problem on a spatiotemporal graph with known symmetry, and introduce Cascade: a translation-equivariant convolutional decoder that applies the same architectural template to both surface codes and high-rate quantum LDPC codes, adapting only the convolution to the code's lattice symmetry. A single model trained at one high physical error rate generalizes across seven orders of magnitude in logical error rate with well-calibrated uncertainty, and error suppression improves continuously with model capacity. On the $[[144,12,12]]$ Gross code at $p = 0.1$%, Cascade reaches a logical error rate of $\sim 10^{-10}$, up to $\sim 4000\times$ lower than widely-used iterative decoders and $\sim 17\times$ lower than the strongest iterative variant, while matching the accuracy of a near-optimal combinatorial decoder at 3–5 orders of magnitude lower latency. This accuracy reveals a previously inaccessible 'waterfall' regime of error suppression, substantially steeper than the scaling assumptions underlying current resource estimates for fault-tolerant quantum algorithms, and implying substantially lower physical-qubit and runtime overhead than currently anticipated.