Source-linked AI summary
Fast and accurate neural triage decoding of ultra-high-rate quantum LDPC codes
Hong-Ye Hu, Zhenlai Wang, Binzhao Luo, Tao Xiang, Chen Zhao
TL;DR
High-rate qLDPC codes can reduce physical-qubit overhead, but practical decoding must combine accuracy with low latency, and neural decoding at ultra-high rates remains unestablished. Triage adaptively combines local neural message passing, residual-syndrome iteration, and diversification; on lifted-product and Kasai codes it reports state-of-the-art accuracy with substantially lower latency than tested algorithmic decoders.
Problem
High-rate qLDPC codes can reduce physical-qubit overhead, but their practical use requires accurate, low-latency decoders, and neural performance on ultra-high-rate codes encoding hundreds of logical qubits remains unestablished.
Source: §I · p. 1Method
Triage combines local graph-based neural message passing with repeated decoding of residual syndromes and conditional diversification to seek syndrome-consistent corrections.
Source: §I · p. 2Results
Triage achieves state-of-the-art accuracy comparable to or better than algorithmic decoders on lifted-product and Kasai codes while reducing decoding latency by factors of 10–100.
Source: §I · p. 2Takeaways & Limitations
Triage brings decoding accuracy, speed, and versatility together for ultra-high-rate qLDPC codes, with further hardware optimization offering a path toward real-time error correction of hundreds of logical qubits per block.
Source: §I · p. 2, §III · p. 5Complementary explanations can make exact bitwise marginal decisions violate syndrome constraints, including ambiguities from stabilizers whose weight does not grow with code distance.
Source: Local marginal decoder and iterative… · p. 3
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
High-rate qLDPC codes reduce physical-qubit overhead, but practical use requires accurate decoding with latency that keeps pace with quantum hardware. Triage combines local neural message passing, iteration, and adaptive diversification, and is reported to achieve strong accuracy with substantially lower latency on ultra-high-rate codes.
I. INTRODUCTION
- High-rate qLDPC codes can encode hundreds of logical qubits in blocks of approximately one thousand data qubits, with encoding rates exceeding one half.Sparse parity checks accompany this reduction in encoding overhead.Source: §I · p. 1
- Existing algorithmic decoders can approach near-optimal accuracy, but their computational cost, especially for most-likely-error search, limits throughput for real-time decoding.Belief propagation can also leave corrections that do not reproduce the measured syndrome.Source: §I · p. 1
- Whether neural decoders can match strong algorithmic decoders across code families remains unclear, particularly for ultra-high-rate blocks encoding hundreds of logical qubits.Prior neural qLDPC demonstrations covered blocks encoding tens of logical qubits.Source: §I · pp. 1–2
- Triage uses a graph-based local message-passing decoder, applies it iteratively to residual syndromes, and invokes diversification when a syndrome-compatible correction is still unavailable.Diversification reuses the trained network with syndrome flips, prior perturbations, and symmetric permutations.Source: §I · p. 2
- Triage achieves state-of-the-art accuracy comparable to or better than algorithmic decoders and reduces decoding latency by factors of 10–100 on lifted-product and Kasai codes.At p = 1.5% on the Kasai code, its per-qubit-per-round error rate is around 5 × 10^-10.Source: §I · p. 2
Local marginal decoder and iterative decoding
NeuralMP estimates fault marginals through sparse-graph message passing, but independent marginal decisions can violate syndrome constraints even when exact. Triage addresses residual violations by iterating the network and trains it with failure-focused examples and syndrome-consistency supervision.
Local marginal decoder and iterative decoding
- NeuralMP passes messages between fault-mechanism and detector nodes on a sparse Tanner graph, using mechanism priors and syndrome values as node inputs.Its output is a marginal likelihood estimate for each error mechanism.Source: Local marginal decoder and iterative… · p. 2, Figure 2 · p. 3
- At fixed R and χ, one NeuralMP evaluation costs O(R[Eχ + Nχ^2]), linear in N when E = O(N), unlike attention-based global decoders’ O(N^2) scaling.Here N = m + F counts detector and fault nodes, while E is the number of graph edges.Source: Local marginal decoder and iterative… · p. 3
- Training targets rare difficult cases with error-weight-conditioned online simulations and a mistake bank that stores hard examples and removes them after repeated successes.Replay examples are augmented by code symmetries, and supervision covers fault predictions, logical observables, and syndrome consistency.Source: Local marginal decoder and iterative… · p. 3, Figure 2 · p. 3
- Complementary minimum-weight explanations can make supported-bit marginals approach 1/2, so independent hard decisions may violate syndrome constraints even with exact marginals.The ambiguity can arise from stabilizers whose weight does not grow with code distance; phenomenological space-time degeneracies may be lower weight than purely spatial stabilizers.Source: Local marginal decoder and iterative… · p. 3
- For LP and Kasai code shots with ν = 3, exact marginal MAP has Pinc(p) = Ω(p^4), and single-pass NeuralMP results are consistent with this mechanism.The theorem’s scope includes independent X/Z phenomenological models; its bound follows under the stated code and noise assumptions.Source: Local marginal decoder and iterative… · pp. 3–4
- Triage repeatedly applies the same trained network to the current residual syndrome and stops when the residual vanishes or Kmax iterations are reached.The practical setting is Kmax = 4; unresolved shots proceed to diversification.Source: Local marginal decoder and iterative… · p. 4
Improved convergence with diversification
Diversification searches alternative correction trajectories for shots that remain unresolved after iterative decoding. It modifies inference conditions while reusing the trained network, then checks candidates against the original syndrome and ranks consistent ones by likelihood.
Improved convergence with diversification
- Diversification generates alternative candidates using prior perturbations, symmetry-preserving coordinate permutations, and syndrome flips guided by uncertain or repeatedly corrected mechanisms.Each trajectory starts from the original syndrome and reuses the iterative decoder under modified inference conditions.Source: Improved convergence with… · p. 4
- Figure 3 compares logical error rate against physical error rate and amortized decoding latency, including Triage’s full-decoder cost at batch size 64.The latency panel distinguishes the NeuralMP frontend from the composed Triage decoder, including handoff and diversification.Source: Figure 3 · p. 4
- A syndrome flip modifies the search preference between complementary corrections while preserving the original decoding problem’s relative likelihoods.For a half-support pair, flipping one supported qubit makes the two modified candidates differ in weight by two, favoring the lighter one under p < 1/2.Source: Improved convergence with… · p. 4
- Triage sends only unresolved shots to diversification, returns the best syndrome-consistent candidate when found, and retains the initial iterative correction if the search budget is exhausted.The supplementary stage combines further sign flips, symmetric permutations, and prior perturbations.Source: Improved convergence with… · pp. 4–5
Decoding high-rate qLDPC codes
Triage is evaluated on two high-rate qLDPC codes under phenomenological noise, with accuracy, decoding cost, and sensitivity to prior mismatch assessed. It achieves low logical error rates with faster decoding than the cited algorithmic baselines and near-unity block-LER ratios under the tested prior perturbations.
Decoding high-rate qLDPC codes
- The benchmarks use phenomenological noise on LP20 with five noisy measurement rounds and Kasai with eight, each followed by a final perfect syndrome extraction.LP20 uses independent X and Z errors; Kasai uses depolarizing noise, and both are trained at p = 2% and evaluated at unseen error rates.Source: Decoding high-rate qLDPC codes · p. 5
- At p = 0.015, estimated per-qubit-per-round LER is 9.33×10−11 on LP20 and 5.08×10−10 on Kasai, compared with 4.43×10−10 for BP-OSD and 1.76×10−9 for BP-relay-MLE Tiered, respectively.The reported comparisons are for Triage with iterative NeuralMP decoding and diversification.Source: Decoding high-rate qLDPC codes · p. 5
- At batch size 64, full-decoder costs are 2.37 ms per shot on LP20 and 12.3 ms on Kasai, yielding 343× and 28× speedups over the CPU baselines, respectively.The CPU baseline means are 815 ms for BP-OSD and 349 ms for the Tiered decoder.Source: Decoding high-rate qLDPC codes · p. 5
- At σr = 0.5, four-iteration NeuralMP has block-LER ratios of approximately 1.01 for LP20 and 0.98 for Kasai, while algorithmic baselines increase approximately 1.6–2.1 times.Figure 4 compares block-LER ratios against nominal mismatch strength for LP20 at p = 0.024 and Kasai at p = 0.0175.Source: Decoding high-rate qLDPC codes · p. 5, Figure 4 · p. 5
III. DISCUSSION
The discussion frames Triage as an adaptive decoder whose accuracy is comparable to or better than tested algorithmic decoders, with lower amortized decoding costs. It identifies symmetry integration, failure analysis, hardware feedback, broader evaluation, and deployment measurements as directions for further work.
III. DISCUSSION
- Triage combines local neural message passing, iterative decoding, and rarely invoked diversification to allocate computation by decoding difficulty.The discussion reports accuracy comparable to or better than tested algorithmic decoders, with substantially lower amortized decoding costs.Source: §III · p. 5
- Symmetric permutations currently enter only through diversification; integrating them into NeuralMP could reduce network size and inference cost, but remains a proposed direction.The discussion also calls for systematic analysis of how diversification proposals address decoding failures.Source: §III · p. 6
- AI-agent feedback is proposed as a way to analyze failures, propose decoder revisions, and evaluate them against logical error rates and total decoding costs.The proposed loop aims to reduce manual tuning while retaining explicit accuracy and runtime criteria.Source: §III · p. 6
- The proposed decoding and hardware self-calibration loop has not yet been evaluated together for physical-drift tracking, online-update cost, or stability.The four-iteration frontend’s resilience to tested prior perturbations motivates studying this integration.Source: §III · p. 6
- Further evaluation is needed on circuit-level gadgets, algorithms, and experimental data, as well as single-shot latency, sustained throughput, and GPU or FPGA deployment.The reported GPU and CPU comparisons quantify amortized costs under specified batching and hardware conditions.Source: §III · p. 6
A. NeuralMP architecture
NeuralMP represents a detector error model as a bipartite Tanner graph and performs parallel message-passing updates to predict fault scores. Inference repeats fresh forward passes using the residual syndrome, with a bounded number of network evaluations before diversification.
A. NeuralMP architecture
- The detector error model has F fault mechanisms, m detectors, and k logical observables represented by H and L; configurations differing by a vector in ker H ∩ ker L share syndrome and logical labels.The graph has N = m + F nodes, and fault and detector states are initialized from priors, outcomes, and learned coordinate features.Source: A. NeuralMP architecture · p. 6
- Each directional update aggregates incoming messages and applies a two-layer MLP with a ReLU hidden activation, residual addition, and layer normalization.Distinct modules are used for the two directions and successive MP-rounds, while updates run in parallel across each node family.Source: A. NeuralMP architecture · p. 6
- The deployed Kasai network uses hidden dimension χ = 64 and R = 80 MP-rounds with distinct round-specific parameters.Training uses replayed thresholded predictions with incorrect logical observables and verified symmetries; its scores are not assumed to be calibrated deployment posteriors.Source: A. NeuralMP architecture · p. 6
- Each outer iteration reinitializes hidden states from the current residual syndrome and original priors, carrying no hidden state or logits from the previous pass.Information passes between iterations only through the residual syndrome.Source: A. NeuralMP architecture · p. 6
- Proposal bits are sampled using temperature T, with the deployed configuration set to T = 1; inference allows at most K = 4 network evaluations per shot before diversification.Network parameters remain fixed throughout inference.Source: A. NeuralMP architecture · p. 6
B. Training objective
NeuralMP is trained with physical-error-level, logical, and syndrome supervision. The three loss terms target fault predictions, logical outcomes, and syndrome consistency, while exact consistency is checked separately during decoding.
B. Training objective
- NeuralMP training combines physical-error-level, logical, and syndrome supervision, with unit coefficients for all three loss terms.The terms encourage accurate fault predictions, correct logical outcomes, and syndrome consistency; exact consistency is checked separately during decoding.Source: B. Training objective · pp. 6–7
- The fault loss is binary cross-entropy with positive-class weight eight to compensate for sparse faults.Source: B. Training objective · p. 7
- Logical supervision uses a differentiable parity estimate under a factorized Bernoulli approximation, while the syndrome penalty compares predicted fault parities with measured detectors.Source: B. Training objective · p. 7
C. Marginal decoding and syndrome inconsistency
This section shows that exact bitwise marginal MAP can produce syndrome-inconsistent corrections, then constructs witnesses proving a nonzero asymptotic inconsistency rate under stated code and noise conditions.
C. Marginal decoding and syndrome inconsistency
- When |∆|>|δ|, two endpoint marginals fall on the same side of 1/2, so their MAP decisions violate the required odd parity.The criterion applies to two disjoint minimum-weight explanations whose compatible corrections on their union require ei ⊕ ej=1.Source: C. Marginal decoding and syndrome… · pp. 7–8
- The witness uses two equal-prior minimum explanations that move one qubit’s data fault across τ measurement rounds, joined by measurement-fault strings.The explanations have weight κ(ν)=1+τν/2, with τ=1 for even ν and τ=2 for odd ν.Source: C. Marginal decoding and syndrome… · p. 8
- Pinc(p)=Ω(p^κ) for exact bitwise MAP under the theorem’s fixed-code, phenomenological-noise, and spatial assumptions.Each constructed syndrome has probability Θ(p^κ) and forces an inconsistent MAP correction.Source: C. Marginal decoding and syndrome… · pp. 7–9
- For the LP matrix with n=1122 and five noisy rounds, and the Kasai matrix with n=1152 and eight rounds, exact marginal MAP has Pinc(p)=Ω(p^4) when q=Θ(p).Both matrices have minimum column degree ν=3.Source: C. Marginal decoding and syndrome… · p. 9
D. Diversification
Diversification applies additional NeuralMP decoding attempts to shots with nonzero residual syndrome, seeking a consistent correction while retaining the original noise model for candidate selection.
D. Diversification
- Syndrome-flip search changes the syndrome by hypothesized mechanisms, re-decodes it, and maps each resulting correction back to the original problem.It ranks mechanisms using locally ambiguous first-iteration logits or repeated corrections, then tests 192 single, pair, and triple hypotheses per shot.Source: D. Diversification · p. 9
- For LP20, a further stage uses equivalent code-automorphism representations and prior perturbations to generate different decoding trajectories.Candidates are mapped back and ranked by their likelihood under the original noise model; if none is syndrome-consistent, the fourth iterative output is retained.Source: D. Diversification · p. 9
- At p=1.5% on Kasai, search resolves 99.6% of shots left unresolved by iterative decoding, reducing the unresolved fraction from 2.6 × 10^-4 to 1.0 × 10^-6 per shot.Candidate batches allow search latency to be amortized.Source: D. Diversification · p. 9
E. Quantum memory benchmarks
The benchmark section specifies the simulated noise settings, decoder configurations, and evaluation conventions for the lifted-product and Kasai codes.
E. Quantum memory benchmarks
- LP20 is simulated for r=5 measurement rounds with independent X and Z data errors, each probability p, and measurement-error probability q=p; Kasai uses r=8 rounds, depolarizing data-error probability p, and q=4p/3.Source: E. Quantum memory benchmarks · p. 9
- Triage uses at most four outer iterations and sends shots with nonzero residual syndrome to syndrome-flip search, with an additional diversification stage for LP20 but none for Kasai.The search tests 192 iterative-decoding candidates; LP20 also tests prior-perturbed and symmetry-transformed candidates.Source: E. Quantum memory benchmarks · pp. 9–10
- The LP20 BP-OSD baseline uses 100 min-sum iterations and order-10 combination-sweep OSD, while its relay-BP baseline permits up to 300 relay stages.For Kasai, the two-stage baseline permits up to 300 relay stages, and Tiered adds a COPT-based search capped at 120 seconds per side with eight solver threads.Source: E. Quantum memory benchmarks · p. 10
- The per-qubit-per-round LER is computed as [1 − (1 − P̄)^(1/r)]/k from mean block failure probability P̄, measurement rounds r, and logical-qubit count k.The reported error-bar calculation treats sector counts as independent, an approximation.Source: E. Quantum memory benchmarks · p. 10
- Triage’s amortized time combines measured front-end and search costs with observed search frequencies at batch size 64, while the algorithmic baselines use CPU measurements.The neural decoder runs on one NVIDIA H-series GPU; BP and relay-BP are single-threaded, and the Tiered solver uses eight threads.Source: E. Quantum memory benchmarks · p. 10