Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2504.20212

Estimating decoding graphs and hypergraphs of memory QEC experiments

Evangelia Takou, Kenneth R. Brown

Published Apr 28, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2504.20212

Related papers

Reconstruction of detector error model for quantum error correction

Cheng Ye, Pan Zhang

Fault-tolerant quantum computing fundamentally relies on the accurate characterization of circuit-level noise to optimize decoding algorithms. However, extracting complex multi-body error correlations remains challenging. Contemporary greedy inference algorithms can suffer from statistical distortion, discarding true physical mechanisms while introducing many unphysical false positives. Here, we introduce the Correlation-Analysis-based Hypergraph Reconstruction (CAHR) algorithm, a globally consistent framework to invert experimental syndrome statistics directly into discrete physical hypergraphs. By coupling exact algebraic correlation equations with a top-down concurrent-pruning strategy, CAHR recovers the fault topology without false positives for both $d=5$ rotated surface codes and dense 8-body 2D color codes in our benchmark settings. Furthermore, we show that exact continuous parameter extraction in dense codes is limited by a \textit{variance cascade}, where absolute statistical variance accumulates linearly from high- to low-degree mechanisms. This motivates a two-stage inference paradigm: utilizing CAHR to extract the fault topology, followed by continuous probability optimization. This provides a practical approach for characterizing and decoding highly correlated noise in realistic quantum hardware.

quant-pharXiv:2606.16288•Chinese Physics B•Jun 16, 2026•0 citations

Logical error estimation from syndrome data of surface-code experiments

Evangelia Takou, Cesar Benito, Arian Vezvaee +2 more

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.

quant-pharXiv:2606.11496•Jun 11, 2026•0 citations

What Must a Quantum-Memory Decoder Know About Temporally Correlated Noise?

Danesh Morales-Hashemi, Graeme Smith, Ningping Cao

What must a quantum error-correction decoder know about temporally correlated noise, and what does it cost to learn? We study this question for fixed stabilizer memory experiments with known system-environment interactions. We formulate calibration in terms of the fidelity differences that select a Pauli recovery and relate missing information to the resulting fidelity loss. Our main example uses weak coherent $X$ rotations in a class of CSS codes including Shor, Steane, and odd-distance rotated surface codes. All physical qubits share a sign either fixed throughout a run or independently redrawn each interval. The two models have identical syndrome statistics and the same spatiotemporal Pauli process (SPP), obtained by Pauli-twirling every noise interval. Yet at suitable storage times, they require different logical corrections. In the weak-noise limit, each model is almost perfectly correctable when known. Without model information, even the best final recovery has a worst-case fidelity loss approaching $1/2$ relative to the noise-aware optimum, despite access to the full syndrome record. For this pair of models, at fixed code and fixed positive target loss below $1/2$, we prove matching calibration bounds. With logical preparation and final readout, complete QEC cycles require a number of noise intervals scaling as the inverse rotation angle raised to the code's $X$ distance. Allowing two uninterrupted intervals before one extraction reduces the optimal cost to inverse-square scaling. Physical Pauli twirling of every noise interval changes both recovery performance and its information requirements. Discarding the record of applied random Pauli operations makes the SPP sufficient for optimal recovery. Keeping this record can improve the attainable fidelity, but reaching that optimum may require additional noise information.

quant-pharXiv:2610.03545•Oct 5, 2026•0 citations

Estimating Detector Error Models on Google's Willow

Kregg Elliot Arms, Martin James McHugh, Joseph Edward Nyhan +2 more

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.

quant-pharXiv:2512.10814•Dec 12, 2025•1 citation

Simulating Quantum Error Correction beyond Pauli Stochastic Errors

Jordan Hines, Corey Ostrove, Kenneth Rudinger +4 more

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.

quant-pharXiv:2603.18457•Mar 20, 2026•0 citations

Learning Correlated Noise in a 39-Qubit Quantum Processor

Robin Harper, Steven T. Flammia

Building error-corrected quantum computers relies crucially on measuring and modeling noise on candidate devices.In particular, optimal error correction requires knowing the noise that occurs in the device as it executes the circuits required for error correction.As devices increase in size, we will become more reliant on efficient models of this noise.However, such models must still retain the information required to optimize the algorithms used for error correction.Here, we propose a method of extracting detailed information of the noise in a device running syndrome extraction circuits.We introduce and execute an experiment on a superconducting device using 39 of its qubits in a surface code doing repeated rounds of syndrome extraction but omitting the midcircuit measurement and reset.We show how to extract from the 20 data qubits the information needed to build noise models of various sophistication in the form of graphical models.These models give efficient descriptions of noise in large-scale devices and are designed to illuminate the effectiveness of error correction against correlated noise.Our estimates are furthermore precise: we learn a consistent global distribution where all one-and two-qubit error rates are known to a relative error of 0.1%.By extrapolating our experimentally learned noise models toward lower error rates, we demonstrate that accurate correlated noise models are increasingly important for successfully predicting subthreshold behavior in quantum error-correction experiments.

arXiv:2303.00780•PRX Quantum•Oct 17, 2023•28 citations
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.
Fault-tolerant quantum computing fundamentally relies on the accurate characterization of circuit-level noise to optimize decoding algorithms. However, extracting complex multi-body error correlations remains challenging. Contemporary greedy inference algorithms can suffer from statistical distortion, discarding true physical mechanisms while introducing many unphysical false positives. Here, we introduce the Correlation-Analysis-based Hypergraph Reconstruction (CAHR) algorithm, a globally consistent framework to invert experimental syndrome statistics directly into discrete physical hypergraphs. By coupling exact algebraic correlation equations with a top-down concurrent-pruning strategy, CAHR recovers the fault topology without false positives for both d=5d=5d=5 rotated surface codes and dense 8-body 2D color codes in our benchmark settings. Furthermore, we show that exact continuous parameter extraction in dense codes is limited by a \textit{variance cascade}, where absolute statistical variance accumulates linearly from high- to low-degree mechanisms. This motivates a two-stage inference paradigm: utilizing CAHR to extract the fault topology, followed by continuous probability optimization. This provides a practical approach for characterizing and decoding highly correlated noise in realistic quantum hardware.
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.
What must a quantum error-correction decoder know about temporally correlated noise, and what does it cost to learn? We study this question for fixed stabilizer memory experiments with known system-environment interactions. We formulate calibration in terms of the fidelity differences that select a Pauli recovery and relate missing information to the resulting fidelity loss. Our main example uses weak coherent XXX rotations in a class of CSS codes including Shor, Steane, and odd-distance rotated surface codes. All physical qubits share a sign either fixed throughout a run or independently redrawn each interval. The two models have identical syndrome statistics and the same spatiotemporal Pauli process (SPP), obtained by Pauli-twirling every noise interval. Yet at suitable storage times, they require different logical corrections. In the weak-noise limit, each model is almost perfectly correctable when known. Without model information, even the best final recovery has a worst-case fidelity loss approaching 1/21/21/2 relative to the noise-aware optimum, despite access to the full syndrome record. For this pair of models, at fixed code and fixed positive target loss below 1/21/21/2, we prove matching calibration bounds. With logical preparation and final readout, complete QEC cycles require a number of noise intervals scaling as the inverse rotation angle raised to the code's XXX distance. Allowing two uninterrupted intervals before one extraction reduces the optimal cost to inverse-square scaling. Physical Pauli twirling of every noise interval changes both recovery performance and its information requirements. Discarding the record of applied random Pauli operations makes the SPP sufficient for optimal recovery. Keeping this record can improve the attainable fidelity, but reaching that optimum may require additional noise information.
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.
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.
Building error-corrected quantum computers relies crucially on measuring and modeling noise on candidate devices.In particular, optimal error correction requires knowing the noise that occurs in the device as it executes the circuits required for error correction.As devices increase in size, we will become more reliant on efficient models of this noise.However, such models must still retain the information required to optimize the algorithms used for error correction.Here, we propose a method of extracting detailed information of the noise in a device running syndrome extraction circuits.We introduce and execute an experiment on a superconducting device using 39 of its qubits in a surface code doing repeated rounds of syndrome extraction but omitting the midcircuit measurement and reset.We show how to extract from the 20 data qubits the information needed to build noise models of various sophistication in the form of graphical models.These models give efficient descriptions of noise in large-scale devices and are designed to illuminate the effectiveness of error correction against correlated noise.Our estimates are furthermore precise: we learn a consistent global distribution where all one-and two-qubit error rates are known to a relative error of 0.1%.By extrapolating our experimentally learned noise models toward lower error rates, we demonstrate that accurate correlated noise models are increasingly important for successfully predicting subthreshold behavior in quantum error-correction experiments.