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:2601.22286

Efficient learning of logical noise from syndrome data

Han Zheng, Chia-Tung Chu, Senrui Chen, Argyris Giannisis Manes, Su-un Lee, Sisi Zhou, Liang Jiang

quant-phmath-phSubmitted Jan 29, 2026• Announced Feb 2, 2026• 0 citations
v1 · Jan 29, 2026v2 · Feb 10, 2026
arXivHTMLPDF

Abstract

Characterizing errors in quantum circuits is essential for device calibration, yet detecting rare error events requires a large number of samples. This challenge is particularly severe in calibrating fault-tolerant, error-corrected circuits, where logical error probabilities are suppressed to higher order relative to physical noise and are therefore difficult to calibrate through direct logical measurements. Recently, Wagner et al. [PRL 130, 200601 (2023)] showed that, for phenomenological Pauli noise models, the logical channel can instead be inferred from syndrome measurement data generated during error correction. Here, we extend this framework to realistic circuit-level noise models. From a unified code-theoretic perspective and spacetime code formalism, we derive necessary and sufficient conditions for learning the logical channel from syndrome data alone and explicitly characterize the learnable degrees of freedom of circuit-level Pauli faults. Using Fourier analysis and compressed sensing, we develop efficient estimators with provable guarantees on sample complexity and computational cost. We further present an end-to-end protocol and demonstrate its performance on several syndrome-extraction circuits, achieving orders-of-magnitude sample-complexity savings over direct logical benchmarking. Our results establish syndrome-based learning as a practical approach to characterizing the logical channel in fault-tolerant quantum devices.

Comments
13 + 42 pages, 5 figures

Related papers

In-situ benchmarking of fault-tolerant quantum circuits. I. Clifford circuits

Xiao Xiao, Dominik Hangleiter, Dolev Bluvstein +2 more

Benchmarking physical devices and verifying logical algorithms are important tasks for scalable fault-tolerant quantum computing. Numerous protocols exist for benchmarking devices before running actual algorithms. In this work, we show that both physical and logical errors of fault-tolerant circuits can even be characterized in-situ using syndrome data. To achieve this, we map general fault-tolerant Clifford circuits to subsystem codes using the spacetime code formalism and develop a scheme for estimating Pauli noise in Clifford circuits using syndrome data. We give necessary and sufficient conditions for the learnability of physical and logical noise from given syndrome data, and show that we can accurately predict logical fidelities from the same data. Importantly, our approach requires only a polynomial sample size, even when the logical error rate is exponentially suppressed by the code distance, and thus gives an exponential advantage against methods that use only logical data such as direct fidelity estimation. We demonstrate the practical applicability of our methods in various scenarios using synthetic data as well as the experimental data from a recent demonstration of fault-tolerant circuits by Bluvstein et al. [Nature 626, 7997 (2024)]. Our methods provide an efficient, in-situ way of characterizing a fault-tolerant quantum computer to help gate calibration, improve decoding accuracy, and verify logical circuits.

quant-pharXiv:2601.21472•Jan 30, 2026•0 citations

In Situ Benchmarking of Fault-Tolerant Quantum Circuits: Clifford Circuits

Anonymous, Dominik Hangleiter, Dolev Bluvstein +2 more

Benchmarking physical devices and verifying logical algorithms are important tasks for scalable fault-tolerant quantum computing. Numerous protocols exist for benchmarking devices before running actual algorithms. In this work, we show that both physical and logical errors of fault-tolerant circuits can even be characterized using syndrome data. To achieve this, we map general fault-tolerant Clifford circuits to subsystem codes using the spacetime code formalism and develop a scheme for estimating Pauli noise in Clifford circuits using syndrome data. We give necessary and sufficient conditions for the learnability of physical and logical noise from given syndrome data, and show that we can accurately predict logical fidelities from the same data. Importantly, our approach requires only a polynomial sample size, even when the logical error rate is exponentially suppressed by the code distance, and thus gives an exponential advantage against methods that use only logical data such as direct fidelity estimation. We demonstrate the practical applicability of our methods in various scenarios using synthetic data as well as the experimental data from a recent demonstration of fault-tolerant circuits by Bluvstein [ , 7997 (2024)]. Our methods provide an efficient, way of characterizing a fault-tolerant quantum computer to help gate calibration, improve decoding accuracy, and verify logical circuits.

PRX Quantum•Aug 3, 2026•0 citations

Provably Efficient Self-Calibrating Quantum Fault Tolerance

Weiyuan Gong, Hong-Ye Hu

Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for such self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables a simple and efficient online optimization algorithm using only syndrome measurements collected during normal error correction. We prove convergence to an $\varepsilon$ detection rate within $O(1/\varepsilon^2)$ epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.

quant-pharXiv:2608.05686•Aug 7, 2026•0 citations

Characterization of syndrome-dependent logical noise in detector regions

Girling, Matthew, Ben Criger, Cristina Cîrstoiu

Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable noise-aware decoding and validate threshold-relevant assumptions. We introduce a protocol to directly estimate the logical Pauli channels (and pure errors) associated with detector regions formed of two or more syndrome extraction gadgets, conditioned on observing a particular parity in the syndrome outcomes. The method is SPAM-robust and most suitable for flag-based syndrome measurement schemes. For classical processing of the experimental data we implement a Bayesian modelling approach. We validate this new protocol on a small error-detecting code using Quantinuum H1-1, a trapped-ion device, and demonstrate that several noise diagnostic tests for fault tolerance improve significantly when using noise tailoring and mitigation strategies, such as swapped measurements for leakage protection, and Pauli frame randomization.

arXiv:2508.08188•Aug 11, 2025•0 citations

Measure Now, Mitigate Later: Virtual Error Cancellation for Logical Quantum Circuits

Oles Shtanko, Saswata Roy, Shashwat Kumar +1 more

Early fault-tolerant quantum algorithms are a key step in scalable quantum computing, but are ultimately constrained by residual, uncorrectable logical errors. Logical quantum error mitigation can eliminate this bias, however its standard requirements include prior noise characterization, more complex experiments, and substantial sampling overhead. Although no mitigation technique can simultaneously overcome all three constraints, we demonstrate that the first two---noise learning and need for modified circuits---can be completely bypassed for logical circuits by leveraging only syndrome records. Specifically, we introduce virtual error cancellation: a method that, unlike previous bias-free approaches, operates entirely in classical post-processing on universal quantum circuits. We develop and numerically test end-to-end protocols that reduce the sampling overhead beyond fundamental limitations of existing syndrome-aware mitigation techniques, including syndrome-based postselection. In particular, we propose a scheme that pairs the low-latency decoder used in the experiment with a high-complexity decoder run in post-processing. In numerical simulations of a distance-7 rotated surface code, we show that our full-stack dual-decoder algorithm exhibits an error that diminishes as the number of samples increases, capable of reaching more than three orders of magnitude of suppression compared to the decoded logical error rate in an experimentally achievable setting. These results establish syndrome records as a resource for correcting universal computational estimates after quantum execution.

quant-pharXiv:2610.12400•Oct 9, 2026•0 citations

Noise characterisation of fault-tolerant quantum computers

Evan T. Hockings

Noise is the fundamental challenge to quantum computation. Large-scale quantum computers will overcome this challenge with fault-tolerant architectures that leverage quantum error correction. This thesis introduces and investigates a scalable noise characterisation protocol suited to this key context. First, we introduce this protocol by building upon averaged circuit eigenvalue sampling (ACES), a framework for noise characterisation experiments that simultaneously estimates the Pauli error probabilities of all gates in a Clifford circuit and captures averaged spatial correlations between gates implemented simultaneously in the layers of the circuit. We demonstrate the scalability and performance of our protocol through circuit-level numerical simulations of the entire noise characterisation procedure. Then we demonstrate in circuit-level numerical simulation that this protocol is practically capable of calibrating a fast correlated matching decoder, enabling noise-aware decoding. We find that noise-aware decoding increases the error suppression factor of the code, leading to reductions in the logical error rate that increase exponentially with the code distance. Finally, we present several results obtained from experimentally implementing this protocol. We use the noise characterisation results to design an improved syndrome extraction circuit for a heavy hexagon memory that is adapted to the noise characteristics of the quantum device. The model error of our noise characterisation results suggests that the circuit-level Pauli noise model estimated by ACES can describe the essential features of quantum noise. We also operate a heavy hexagon memory and use noise estimates to predict performance and inform decoding. These results demonstrate that Pauli noise estimates can calibrate decoders to enable noise-aware decoding and inform the co-design of quantum error correcting codes, decoders, fault-tolerant circuits, and quantum devices.

•Jan 1, 2025•0 citations
Characterizing errors in quantum circuits is essential for device calibration, yet detecting rare error events requires a large number of samples. This challenge is particularly severe in calibrating fault-tolerant, error-corrected circuits, where logical error probabilities are suppressed to higher order relative to physical noise and are therefore difficult to calibrate through direct logical measurements. Recently, Wagner et al. [PRL 130, 200601 (2023)] showed that, for phenomenological Pauli noise models, the logical channel can instead be inferred from syndrome measurement data generated during error correction. Here, we extend this framework to realistic circuit-level noise models. From a unified code-theoretic perspective and spacetime code formalism, we derive necessary and sufficient conditions for learning the logical channel from syndrome data alone and explicitly characterize the learnable degrees of freedom of circuit-level Pauli faults. Using Fourier analysis and compressed sensing, we develop efficient estimators with provable guarantees on sample complexity and computational cost. We further present an end-to-end protocol and demonstrate its performance on several syndrome-extraction circuits, achieving orders-of-magnitude sample-complexity savings over direct logical benchmarking. Our results establish syndrome-based learning as a practical approach to characterizing the logical channel in fault-tolerant quantum devices.
Benchmarking physical devices and verifying logical algorithms are important tasks for scalable fault-tolerant quantum computing. Numerous protocols exist for benchmarking devices before running actual algorithms. In this work, we show that both physical and logical errors of fault-tolerant circuits can even be characterized in-situ using syndrome data. To achieve this, we map general fault-tolerant Clifford circuits to subsystem codes using the spacetime code formalism and develop a scheme for estimating Pauli noise in Clifford circuits using syndrome data. We give necessary and sufficient conditions for the learnability of physical and logical noise from given syndrome data, and show that we can accurately predict logical fidelities from the same data. Importantly, our approach requires only a polynomial sample size, even when the logical error rate is exponentially suppressed by the code distance, and thus gives an exponential advantage against methods that use only logical data such as direct fidelity estimation. We demonstrate the practical applicability of our methods in various scenarios using synthetic data as well as the experimental data from a recent demonstration of fault-tolerant circuits by Bluvstein et al. [Nature 626, 7997 (2024)]. Our methods provide an efficient, in-situ way of characterizing a fault-tolerant quantum computer to help gate calibration, improve decoding accuracy, and verify logical circuits.
Benchmarking physical devices and verifying logical algorithms are important tasks for scalable fault-tolerant quantum computing. Numerous protocols exist for benchmarking devices before running actual algorithms. In this work, we show that both physical and logical errors of fault-tolerant circuits can even be characterized using syndrome data. To achieve this, we map general fault-tolerant Clifford circuits to subsystem codes using the spacetime code formalism and develop a scheme for estimating Pauli noise in Clifford circuits using syndrome data. We give necessary and sufficient conditions for the learnability of physical and logical noise from given syndrome data, and show that we can accurately predict logical fidelities from the same data. Importantly, our approach requires only a polynomial sample size, even when the logical error rate is exponentially suppressed by the code distance, and thus gives an exponential advantage against methods that use only logical data such as direct fidelity estimation. We demonstrate the practical applicability of our methods in various scenarios using synthetic data as well as the experimental data from a recent demonstration of fault-tolerant circuits by Bluvstein [ , 7997 (2024)]. Our methods provide an efficient, way of characterizing a fault-tolerant quantum computer to help gate calibration, improve decoding accuracy, and verify logical circuits.
Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for such self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables a simple and efficient online optimization algorithm using only syndrome measurements collected during normal error correction. We prove convergence to an ε\varepsilonε detection rate within O(1/ε2)O(1/\varepsilon^2)O(1/ε2) epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.
Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable noise-aware decoding and validate threshold-relevant assumptions. We introduce a protocol to directly estimate the logical Pauli channels (and pure errors) associated with detector regions formed of two or more syndrome extraction gadgets, conditioned on observing a particular parity in the syndrome outcomes. The method is SPAM-robust and most suitable for flag-based syndrome measurement schemes. For classical processing of the experimental data we implement a Bayesian modelling approach. We validate this new protocol on a small error-detecting code using Quantinuum H1-1, a trapped-ion device, and demonstrate that several noise diagnostic tests for fault tolerance improve significantly when using noise tailoring and mitigation strategies, such as swapped measurements for leakage protection, and Pauli frame randomization.
Early fault-tolerant quantum algorithms are a key step in scalable quantum computing, but are ultimately constrained by residual, uncorrectable logical errors. Logical quantum error mitigation can eliminate this bias, however its standard requirements include prior noise characterization, more complex experiments, and substantial sampling overhead. Although no mitigation technique can simultaneously overcome all three constraints, we demonstrate that the first two---noise learning and need for modified circuits---can be completely bypassed for logical circuits by leveraging only syndrome records. Specifically, we introduce virtual error cancellation: a method that, unlike previous bias-free approaches, operates entirely in classical post-processing on universal quantum circuits. We develop and numerically test end-to-end protocols that reduce the sampling overhead beyond fundamental limitations of existing syndrome-aware mitigation techniques, including syndrome-based postselection. In particular, we propose a scheme that pairs the low-latency decoder used in the experiment with a high-complexity decoder run in post-processing. In numerical simulations of a distance-7 rotated surface code, we show that our full-stack dual-decoder algorithm exhibits an error that diminishes as the number of samples increases, capable of reaching more than three orders of magnitude of suppression compared to the decoded logical error rate in an experimentally achievable setting. These results establish syndrome records as a resource for correcting universal computational estimates after quantum execution.
Noise is the fundamental challenge to quantum computation. Large-scale quantum computers will overcome this challenge with fault-tolerant architectures that leverage quantum error correction. This thesis introduces and investigates a scalable noise characterisation protocol suited to this key context. First, we introduce this protocol by building upon averaged circuit eigenvalue sampling (ACES), a framework for noise characterisation experiments that simultaneously estimates the Pauli error probabilities of all gates in a Clifford circuit and captures averaged spatial correlations between gates implemented simultaneously in the layers of the circuit. We demonstrate the scalability and performance of our protocol through circuit-level numerical simulations of the entire noise characterisation procedure. Then we demonstrate in circuit-level numerical simulation that this protocol is practically capable of calibrating a fast correlated matching decoder, enabling noise-aware decoding. We find that noise-aware decoding increases the error suppression factor of the code, leading to reductions in the logical error rate that increase exponentially with the code distance. Finally, we present several results obtained from experimentally implementing this protocol. We use the noise characterisation results to design an improved syndrome extraction circuit for a heavy hexagon memory that is adapted to the noise characteristics of the quantum device. The model error of our noise characterisation results suggests that the circuit-level Pauli noise model estimated by ACES can describe the essential features of quantum noise. We also operate a heavy hexagon memory and use noise estimates to predict performance and inform decoding. These results demonstrate that Pauli noise estimates can calibrate decoders to enable noise-aware decoding and inform the co-design of quantum error correcting codes, decoders, fault-tolerant circuits, and quantum devices.