Fast and accurate neural triage decoding of ultra-high-rate quantum LDPC codes

Abstract

Quantum error correction is essential for fault-tolerant quantum computing. High-rate quantum low-density parity-check (qLDPC) codes have emerged as a promising approach to reducing the substantial physical qubit overhead of quantum error correction, enabling encoding rates exceeding $1/2$ in blocks of approximately one thousand physical data qubits. However, their practical implementation requires decoders that combine high accuracy with low latency to keep pace with quantum hardware. Existing decoders of high-rate qLDPC codes can achieve high accuracy but often incur substantial computational latency, whereas neural network decoders have yet to be demonstrated for high-rate qLDPC codes. Here, we introduce \emph{neural triage decoding}, a framework that uses syndrome consistency to adaptively allocate neural computation. A local neural message-passing network rapidly predicts error corrections, additional iterations reduce residual syndrome violations, and a rarely invoked diversification stage searches for consistent corrections to the remaining shots. We demonstrate that the \texttt{Triage} decoder can decode ultra-high-rate qLDPC codes encoding a few hundred logical qubits, including lifted-product and Kasai codes, achieving state-of-the-art accuracy comparable to the near optimal algorithmic decoders while reducing decoding latency by approximately one to two orders of magnitude. Our framework is inspired by a rigorous analysis of the exact bitwise marginal decoder, revealing a distance-independent syndrome-inconsistent error floor. In addition, we show the robustness of neural network decoders to mismatched error priors. Our results establish adaptive neural decoding as a promising route towards fast, accurate, and scalable quantum error correction in the near term.

The paper addresses whether neural decoders can combine low logical error rates with manageable computational cost for high-rate qLDPC quantum memories. Its **Triage** framework applies a Tanner-graph neural message-passing decoder to the residual syndrome for up to four iterations, then escalates unresolved shots to searches using syndrome flips, prior perturbations and code symmetries. Syndrome-consistent candidates are ranked by likelihood under the original priors. A theoretical analysis shows that exact bitwise MAP decisions can remain syndrome-inconsistent despite using exact marginals. Under specified graph assumptions and independent phenomenological noise, it proves $P_{\mathrm{inc}}=\Omega(p^{\kappa(\nu)})$, where $\kappa(\nu)=\nu/2+1$ for even minimum qubit degree $\nu$ and $\nu+1$ for odd $\nu$. Both benchmark matrices have $\nu=3$, yielding a quartic lower bound at fixed code size. Monte Carlo benchmarks use the $[[1122,148,d\leq20]]$ lifted-product code and $[[1152,580,d\leq12]]$ Kasai code, with five and eight noisy measurement rounds respectively. At $p=1.5\%$, reported per-qubit-per-round logical error rates are $9.33\times10^{-11}$ and $5.08\times10^{-10}$. Full-decoder amortized costs are $2.37$ and $12.3$ ms per shot, versus $815$ and $349$ ms for the selected algorithmic baselines. Networks trained at $p=2\%$ are evaluated across other error rates; separate frontend tests examine robustness to perturbed priors. The timing comparison uses GPU batches of 64 versus CPU baselines, not matched-hardware single-shot latency. Benchmarks use phenomenological noise with perfect final extraction; circuit-level decoding, experimental validation, latency distributions, sustained real-time operation and online calibration remain untested.