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arXiv:2603.18231 · IEEE International Symposium on Information Theory (ISIT)

Iterative Decoding of Stabilizer Codes under Radiation-Induced Correlated Noise

Anuj K. Nayak, Paul G. Baity, Peter J. Love, Nicholas Jeon, Byung-Jun Yoon, Adolfy Hoisie, Lav R. Varshney

quant-phcs.ITeess.SPSubmitted Mar 18, 2026• Announced Mar 20, 2026• 1 citation
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Abstract

Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle density is unknown and time-varying, resulting in a mismatch between the true noise statistics and the priors assumed by standard decoders, and consequently, degraded logical performance. We formalize joint noise sensing and decoding using syndrome measurements by modeling the QP density as a latent variable, which governs correlation in physical errors and syndrome measurements. Starting from a variational expectation--maximization approach, we derive an iterative algorithm that alternates between QP density estimation and syndrome-based decoding under the updated noise model. Simulations of surface-code and bivariate bicycle quantum memory under radiation-induced correlated noise demonstrate a measurable reduction in logical error probability relative to baseline decoding with a uniform prior. Beyond improved decoding performance, the inferred QP density provides diagnostic information relevant to device characterization, shielding, and chip design. These results indicate that integrating physical noise estimation into decoding can mitigate correlated noise effects and relax effective error-rate requirements for fault-tolerant quantum computation.

Comments
14 pages, 14 figures, 2 tables, 2 algorithms

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Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle density is unknown and time-varying, resulting in a mismatch between the true noise statistics and the priors assumed by standard decoders, and consequently, degraded logical performance. We formalize joint noise sensing and decoding using syndrome measurements by modeling the QP density as a latent variable, which governs correlation in physical errors and syndrome measurements. Starting from a variational expectation--maximization approach, we derive an iterative algorithm that alternates between QP density estimation and syndrome-based decoding under the updated noise model. Simulations of surface-code and bivariate bicycle quantum memory under radiation-induced correlated noise demonstrate a measurable reduction in logical error probability relative to baseline decoding with a uniform prior. Beyond improved decoding performance, the inferred QP density provides diagnostic information relevant to device characterization, shielding, and chip design. These results indicate that integrating physical noise estimation into decoding can mitigate correlated noise effects and relax effective error-rate requirements for fault-tolerant quantum computation.
ABSTRACT The quest for universal superconducting quantum computing is hindered by noise and errors. It has been proven that Quantum Error Correction (QEC) codes will lay at the foundation of fault‐tolerant quantum computing. However, cosmic‐ray‐induced correlated errors, the most detrimental events that can impact superconducting quantum computers, are yet to be efficiently tackled. In order to reach fault tolerance, we must also develop radiation aware methods to complement QEC. In this paper, the first algorithm to effectively exploit syndrome information for the efficient detection of radiation events in superconducting quantum devices at runtime is proposed. A thorough analysis of simulated Rotated Surface codes injecting over 11 million physics‐modeled radiation‐induced faults is performed. The properties of the X and Z check bases, the impact of code distance, and the decoder's time to solution constraints are considered. The technique detects of injected faults, regardless of the impact's position. Moreover, both the radiation impact center and the area affected are accurately identified, with an overhead lower than the decoding time. Additionally, the fault identification information is used to propose a radiation fault correction technique that improves of up to the output correctness compared to existing decoders.
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.
Syndrome histories are normally used to detect and correct errors in fault-tolerant quantum computation, but they can also reveal information about the logical operations executed during computation. We study logical-operation identification using syndrome histories alone or together with other classical measurement outcomes. We develop an exact inference method and a scalable approximation that account for unknown circuit faults and ideal measurement randomness. We evaluate automorphisms, logical Pauli measurements, T injections, and logical circuits combining these instructions on [[18,4,2]][[18,4,2]][[18,4,2]] and [[72,12,6]][[72,12,6]][[72,12,6]] bivariate bicycle (BB) codes under multiple noise models and error rates. A single logical instruction can be identified with over 94\% accuracy under circuit-level noise with error rates between 10−510^ {-5} 10−5 and 10−310^{-3}10−3. We also achieve over 99\% accuracy for automorphism-based logical circuits and 78.32\% for logical circuits combining all three instructions. We further analyze identification ambiguities arising from insufficient or indistinguishable measurement information, fault timing, and approximation inference. Together, these results extend the role of syndromes beyond error decoding to identifying executed logical operations and circuits during fault-tolerant quantum computation. They also suggest that access to syndrome histories and related classical measurement outcomes may unintentionally reveal information about the executed computation.
Fault-tolerant quantum computation critically depends on the ability to detect and correct physical qubit errors faster than they accumulate. The surface code (SC) has emerged as the most experimentally promising quantum error correction (QEC) framework due to its high threshold and local stabilizer structure, yet its practical performance is bottlenecked by decoder efficiency. Traditional decoding approaches such as minimum-weight perfect matching (MWPM) achieve near-optimal accuracy under independent noise but struggle with correlated errors, circuit-level noise, and real-time latency constraints. This paper investigates how neural network (NN)-based decoders reduce logical error rates in SC quantum systems by learning complex syndrome-to-correction mappings from data. We propose a hybrid convolutional-recurrent neural architecture that processes stabilizer measurement syndromes across both spatial and temporal dimensions, enabling the decoder to capture correlated error patterns inherent in realistic hardware. Systematic simulations under depolarizing, biased, and circuit-level noise models demonstrate that the proposed neural decoder achieves a logical error rate reduction of up to 41.3% compared to MWPM at a physical error rate of p = 0.008, while maintaining sub-millisecond decoding latency compatible with superconducting qubit cycle times. These results establish that data-driven neural decoders represent a scalable and hardware-compatible pathway toward achieving the logical error rates required for practical fault-tolerant quantum computing.
Correlated errors may devastate quantum error corrections that are necessary for the realization of fault-tolerant quantum computation. Recent experiments with superconducting qubits indicate that they can arise from quasiparticle (QP) bursts induced by cosmic-ray muons and γ-rays. Here, we use charge-parity jump and bit flip for monitoring QP bursts and two muon detectors in the dilution refrigerator for detecting muon events. We directly observe QP bursts leading to correlated errors that are induced solely by muons and separate the contributions of muons and γ-rays. We further investigate the dynamical process of QP burst and the impact of QP trapping on correlated errors and particle detection. The proposed method, which monitors multiqubit simultaneous charge-parity jumps, has high sensitivity to QP bursts and may find applications for the detection of cosmic-ray particles, low-mass dark matter, and far-infrared photons. The correlated errors in superconducting qubits have been linked to high-energy particle impacts from cosmic rays, but a direct observation has been lacking. Here, the authors measure the quasiparticle bursts and correlated errors and separate the contributions of cosmic-ray muons and γ-rays in a 63-qubit processor.
Accurate noise estimation is essential for fault-tolerant quantum computing, since decoding per formance depends critically on the fidelity of circuit-level noise parameters. We introduce a differ entiable Maximum Likelihood Estimation (dMLE) framework that learns these parameters directly from experimental syndrome data using likelihood gradients, with no decoder in the training loop. Mapping syndrome likelihoods to statistical-mechanical models enables exact and efficient evalua tion via planar solvers for repetition codes and tensor networks (TNs) for surface codes, extending the exact treatment to code distance d = 5 with a small number of rounds, and, via spatial subsam pling combined with time-translation symmetry, to larger codes and larger round counts. Across four experimental superconducting datasets, dMLE reduces logical error rates by up to 30.6% for repetition codes. On the Sycamore d = 3 surface code, a TN decoder using the dMLE prior attains a logical error rate comparable to that reported for state-of-the-art AlphaQubit, using standard syndromes alone without auxiliary leakage data. On the larger d = 5 surface code the dMLE prior lowers the logical error rate of the TN and Tesseract decoders by 7.18% and 5.23% relative to a prior optimized by reinforcement learning; at d = 7 it lowers that of Tesseract by 4.56% and 4.83% in the X and Z bases.