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arXiv:2606.11496

Logical error estimation from syndrome data of surface-code experiments

Evangelia Takou, Cesar Benito, Arian Vezvaee, Daniel A. Lidar, Kenneth R. Brown

quant-phSubmitted Jun 9, 2026• Announced Jun 11, 2026• 0 citations
v1 · Jun 9, 2026v2 · Jun 12, 2026
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Abstract

Decoders for quantum error correction (QEC) experiments rely on detector error models (DEMs), which encode, for each error, its probability and the detectors and logical observables it flips. Here we show that estimating DEM event probabilities from experimental syndromes is feasible, avoids independent device benchmarking, and produces useful decoder priors for estimating and reducing decoded logical error probabilities. We evaluate our methods using open-source data from surface-code memory experiments performed on Google's Willow chip, and we carry out analogous surface-code experiments on IBM's \texttt{ibm\_miami} processor. Despite the different physical error scales of the Google and IBM devices, in both cases our estimated DEMs improve logical error probabilities relative to baseline device-informed DEMs, typically at the $5\%-10\%$ level and with larger gains in some IBM cases, without additional calibration circuits, decoder fine-tuning, or supervised fitting to logical outcomes.

Comments
19 pages, 11 figures

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Decoders for quantum error correction (QEC) experiments rely on detector error models (DEMs), which encode, for each error, its probability and the detectors and logical observables it flips. Here we show that estimating DEM event probabilities from experimental syndromes is feasible, avoids independent device benchmarking, and produces useful decoder priors for estimating and reducing decoded logical error probabilities. We evaluate our methods using open-source data from surface-code memory experiments performed on Google's Willow chip, and we carry out analogous surface-code experiments on IBM's \texttt{ibm_miami} processor. Despite the different physical error scales of the Google and IBM devices, in both cases our estimated DEMs improve logical error probabilities relative to baseline device-informed DEMs, typically at the 5%−10%5\%-10\%5%−10% level and with larger gains in some IBM cases, without additional calibration circuits, decoder fine-tuning, or supervised fitting to logical outcomes.
We consolidate recent theoretical advances in Detector Error Model (DEM) estimation and formalize several algorithms to learn DEM parameters and structure from syndromes without using a decoder, demonstrating recovery of known DEMs from simulated syndromes with precision limited only by finite-sample effects. We then apply these algorithms to estimate DEMs from Google's 72- and 105-qubit chips. Using a likelihood function that is tractable for small DEMs, we show that DEMs estimated directly from syndromes agree more closely with unseen syndromes than DEMs trained to optimize logical performance, whereas the latter outperform the former as priors for decoders in logical memory experiments. We used a time-series of estimated DEMs to track both global error and specific local errors over the course of a QEC experiment, suggesting applications in online characterization. We employ a sequence of DEM estimation techniques to discover and quantify long-range detector correlations spanning the width of the 105-qubit chip, for which DEM analysis suggests correlated measurement errors rather than high-weight Pauli errors as the most likely explanation. Finally, we present two artifacts in repetition code syndromes that are \emph{not} well-modeled by a DEM: correlated flipping of pairs of adjacent detectors in many consecutive rounds of QEC, and signatures consistent with radiation events occurring more frequently than previously reported.
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Characterizing the error sources of quantum devices is essential for building reliable large-scale quantum architectures and tailoring error correction codes to the noise profile of the devices. Tomography techniques can provide detailed information on the noise or quality of quantum states but are typically both computationally and experimentally intensive with respect to the system's size. For QEC experiments, however, the information captured by a detector error model is sufficient for extracting the success rate of the experiment, as well as some information about the underlying noise. In this work, we estimate Pauli noise on detector error models, including hypergraphs, using only the syndrome statistics. We apply this method to well-known codes such as the repetition, surface, and 2D color codes. Under bare-ancilla syndrome extraction, two-point correlations are enough to reconstruct the detector error model for repetition or surface codes. For color codes or repetition codes under Steane-style syndrome extraction, we show how to extend the estimation method to multi-point correlators and extract the error rates of the hypergraphs. Finally, we find an increase in logical error suppression when we calibrate the decoder to noise fluctuations typically present in experiments.
Quantum computers could solve problems beyond the reach of classical devices, but this potential depends on quantum error correction (QEC) to protect fragile quantum states from noise. A central challenge in QEC is decoding: inferring likely physical errors from syndrome patterns generated by repeated stabilizer measurements. Existing decoders, including graph-based and neural approaches, typically return a single correction hypothesis and therefore discard the richer posterior structure of the error distribution conditioned on the observed syndrome. Here we recast QEC decoding as posterior inference using discrete denoising diffusion, exploiting the analogy between stochastic error accumulation and the forward diffusion process. We introduce DiffQEC, a generative decoder that combines a syndrome processor for multi-round spatial-temporal syndrome histories with syndrome feature modulation to condition denoising on the observed syndrome throughout inference. On experimental data from Google's superconducting quantum processor, DiffQEC reduces logical error rates by up to 10.2% relative to minimum-weight perfect matching and by about 5% relative to tensor-network decoding. These improvements persist for larger code distances up to 17 under depolarizing noise and for logical circuits of increasing depth. Beyond accuracy, the learned posterior provides confidence estimates for post-selection and reveals physically meaningful error structure, establishing posterior generative decoding as a practical framework for QEC.
Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.