Quantum error correction is indispensable for scalable quantum computation. Although encoding logical qubits substantially enhances noise resilience, achieving logical error rates low enough for practical algorithms remains challenging on existing hardware. Here we introduce argument reweighting, a simple and broadly applicable post-selection decoding strategy that boosts the performance of maximum-likelihood-type decoders, including minimum-weight perfect matching and belief-propagation families. The method suppresses logical errors by performing additional decoding rounds under reweighted error models, enabling acceptance of high-confidence syndrome outcomes. Circuit-level simulations across multiple decoders and qLDPC codes show that argument reweighting substantially suppresses logical errors, requiring a rejection rate of only $1.44\times10^{-5}$ to reduce the logical error rate by almost two orders of magnitude for the $[[144,12,12]]$ bivariate bicycle code. These results establish argument reweighting as a practical and resource-efficient approach for enhancing quantum fault tolerance.
Quantum error correction is indispensable for scalable quantum computation. Although encoding logical qubits substantially enhances noise resilience, achieving logical error rates low enough for practical algorithms remains challenging on existing hardware. Here we introduce argument reweighting, a simple and broadly applicable post-selection decoding strategy that boosts the performance of maximum-likelihood-type decoders, including minimum-weight perfect matching and belief-propagation families. The method suppresses logical errors by performing additional decoding rounds under reweighted error models, enabling acceptance of high-confidence syndrome outcomes. Circuit-level simulations across multiple decoders and qLDPC codes show that argument reweighting substantially suppresses logical errors, requiring a rejection rate of only 1.44×10−5 to reduce the logical error rate by almost two orders of magnitude for the [[144,12,12]] bivariate bicycle code. These results establish argument reweighting as a practical and resource-efficient approach for enhancing quantum fault tolerance.
Post-selection improves the logical reliability of quantum computation by rejecting shots which are likely to result in logical failure. We introduce graph neural networks that predict decoder failure without additional decoder executions, using only syndromes, and for high-rate quantum low-density parity-check (qLDPC) codes, existing belief-propagation posteriors. We evaluate rotated surface and bivariate bicycle (BB) code memories under uniform depolarising circuit-level noise. Retaining 90% of shots gives approximately 3700x and 740x reductions in logical error rates for [[72,12,6]] and [[144,12,12]] BB codes at realistic physical error rates. For the distance 5 surface code at physical noise p=0.003, our neural post-selector achieves logical error suppression comparable to the leading complementary gap method without running the decoder.
Abstract Post-selection strategies that discard low-confidence results can significantly improve the effective fidelity of quantum computing at the cost of reduced acceptance rates, particularly useful for offline resource state generation and moderate-depth fault-tolerant circuits. Prior work has primarily relied on the “logical gap” metric, which faces fundamental limitations including computational overhead that scales exponentially with the number of logical qubits and poor generalizability beyond surface codes. We develop post-selection strategies based on computationally efficient heuristic metrics that leverage error cluster statistics from clustering-based decoders, which are applicable to arbitrary quantum low-density parity check (QLDPC) codes. We validate our method through extensive numerical simulations on surface codes, bivariate bicycle codes, and hypergraph product codes, demonstrating orders of magnitude reductions in logical error rates with moderate abort rates. For instance, applying our strategy to the [[144, 12, 12]] bivariate bicycle code achieves ~ 1000 × reduction in the logical error rate with an abort rate of only 1% at a physical error rate of 0.1%. Additionally, we integrate our approach with the sliding-window framework for real-time decoding, featuring mid-circuit abort decisions that eliminate unnecessary overheads. Notably, its performance matches or even surpasses the original strategy, while exhibiting favorable scaling in the number of rounds.
We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to provide a solution where the given observable has the complementary outcome. Shots are rejected that find logically complementary solutions with similar likelihoods compared to the baseline. Using the Relay-BP decoder, we benchmark the strategy on the 72-qubit and 144-qubit bivariate bicycle codes, as well as surgery gadgets for the latter. In comparison to previous post-selection strategies, our results offer an improved logical error rate by over a factor of 4 on the same circuit and physical error rate, and at the same rate of post-selection. Our strategies are also lightweight, relying only on FPGA-friendly belief propagation, whereas the previous best used repeated rounds of a high-latency BP-OSD decoder.
Quantum error correction (QEC) enables fault-tolerant quantum computation but requires operating quantum hardware at physical error rates below code-dependent thresholds, which remains challenging for current devices. We introduce syndrome resampling, a general method that increases QEC thresholds of any decoder and suppresses logical errors without additional hardware, decoding modifications, or code-specific assumptions beyond syndrome statistics. The method exploits the fact that syndromes with low probability are likely to lead to logical failure, therefore biasing syndrome averages towards most likely syndromes effectively increases logical fidelities. We establish a direct connection between the Rényi coherent information (RCI) and powers of the syndrome probability distribution, showing that resampling syndromes according to these powers combined with maximum likelihood decoding (MLD) realizes a family of optimal thresholds associated with phase transitions in the RCI. Numerical simulations of surface codes demonstrate that syndrome resampling substantially increases thresholds for both optimal and suboptimal decoders and reduces logical error rates by up to four orders of magnitude in experimentally relevant regimes. We further show that syndrome resampling can be effectively implemented from finite data and combined with decoding-based post-selection to achieve additional gains. Finally, applying the method to existing experimental QEC data yields up to two orders of magnitude reduction in logical error rates without requiring additional measurements. Our results provide a practical and decoder-agnostic route to improved logical fidelities in near-term QEC experiments.
Quantum error correction can be enhanced by post-selecting out runs that are likely to produce a logical failure, but the most accurate measures for that require costly decoder-level information. We introduce a practical, decoder-agnostic post-selection method that learns directly from syndrome data. The method trains a supervised classifier to distinguish between syndromes from low- and high-noise regimes, and then uses the classifier's output as an abort score for new runs, without requiring logical-error labels, correction operators, or code-specific likelihood calculations. We validate the approach in three complementary settings: circuit-level simulations of the Gross bivariate-bicycle code, code-capacity simulations of the surface code, and experimental logical magic-state distillation data from the QuEra neutral-atom processor. In the Gross and surface codes, learned syndrome post-selection reduces the conditional logical error rate at a fixed acceptance rate, with performance comparable to syndrome-weight filtering. For the surface code, the learned classifier reveals a post-selection transition distinct from the conventional decoding threshold. In the experimental data, the machine-learning score outperforms syndrome-weight post-selection and, when combined with logical-gap filtering, improves the output fidelity beyond using the logical gap alone. These results show that syndrome-only learning provides a scalable and hardware-compatible route to improving the reliability of quantum error correction.
Accurate decoding of quantum low-density parity-check (qLDPC) codes often relies on expensive post-processing search, although decoding difficulty varies strongly between syndromes. We find that the benefit of deeper post-processing search is highly concentrated in a small subset of decoding instances, and that these instances can be identified directly from the decoder itself. To this end, we introduce an adaptive decoder based on belief propagation (BP) and ordered-statistics decoding (OSD), using the disagreement between the BP hard decision and the syndrome-consistent order-zero OSD solution as an internal risk signal to determine where deeper search is required. On a [[144,12,12]] bivariate bicycle code under circuit-level depolarising noise, encoding 12 logical qubits in 144 data qubits with distance 12, escalating only the highest-risk 20% of instances recovers 85% to 92% of the improvement in logical error rate available from a full one-free-variable sweep, while reducing the mean serial decoding cost by a factor of 3.6 relative to applying the same truncated search to every instance. At matched budget, disagreement-guided routing also outperforms routing based on the BP syndrome residual, syndrome weight and random selection. The same behaviour reappears on a structurally distinct radial qLDPC code obtained from a lifted-product construction, where escalating 20% of instances recovers 87% to 94% of the available gain. A Z-memory experiment on the Quantinuum H2 trapped-ion processor, implementing both X-type and Z-type checks, further shows that the signal remains predictive under device noise. These results show that decoder-internal disagreement can expose where additional decoding effort is valuable, allowing classical computation to be concentrated on the instances most likely to benefit from it.