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arXiv:2603.04156

Achieving Optimal-Distance Atom-Loss Correction via Pauli Envelope

Pengyu Liu, Shi Jie Samuel Tan, Eric Huang, Umut A. Acar, Hengyun Zhou, Chen Zhao

quant-phSubmitted Mar 4, 2026• Announced Mar 5, 2026• 0 citations
v1 · Mar 4, 2026v2 · Apr 4, 2026v3 · Oct 5, 2026
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Abstract

Atom loss is a major error source in neutral-atom quantum computers, accounting for over 40% of the total physical errors in recent experiments. Unlike Pauli errors, atom loss poses significant challenges for both syndrome extraction and decoding due to its nonlinearity and correlated nature. Current syndrome extraction circuits either require additional physical overhead or do not provide optimal loss tolerance. On the decoding side, existing methods are either computationally inefficient, achieve suboptimal logical error rates, or rely on machine learning without provable guarantees. To address these challenges, we propose the Pauli Envelope framework. This framework constructs a Pauli envelope that bounds the effect of atom loss while remaining low weight and efficiently computable. Guided by this framework, we first design a new atom-replenishing syndrome extraction circuit, the Mid-SWAP syndrome extraction, that reduces error propagation with no additional space-time cost. We then propose an optimal decoder for Mid-SWAP syndrome extraction: the Envelope-MLE decoder formulated as an MILP that achieves optimal effective code distance dloss ~ d for atom-loss errors. Inspired by the exclusivity constraint of the optimal decoder, we also propose an Envelope-Matching decoder to approximately enforce the exclusivity constraint within the MWPM framework. This decoder achieves d_loss ~ 2d/3, surpassing the previous best algorithmic decoder, which achieves dloss ~ d/2 even with an MILP formulation. Circuit-level simulations demonstrate that our approach attains up to 40% higher thresholds and 30% higher effective distances compared with existing algorithmic decoders and syndrome extraction circuits in the loss-dominated regime. On recent experimental data, our Envelope-MLE decoder improves the error suppression factor of a hybrid MLE--machine-learning decoder from 2.14 to 2.24.

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Atom loss is a major error source in neutral-atom quantum computers, accounting for over 40% of the total physical errors in recent experiments. Unlike Pauli errors, atom loss poses significant challenges for both syndrome extraction and decoding due to its nonlinearity and correlated nature. Current syndrome extraction circuits either require additional physical overhead or do not provide optimal loss tolerance. On the decoding side, existing methods are either computationally inefficient, achieve suboptimal logical error rates, or rely on machine learning without provable guarantees. To address these challenges, we propose the Pauli Envelope framework. This framework constructs a Pauli envelope that bounds the effect of atom loss while remaining low weight and efficiently computable. Guided by this framework, we first design a new atom-replenishing syndrome extraction circuit, the Mid-SWAP syndrome extraction, that reduces error propagation with no additional space-time cost. We then propose an optimal decoder for Mid-SWAP syndrome extraction: the Envelope-MLE decoder formulated as an MILP that achieves optimal effective code distance dloss ~ d for atom-loss errors. Inspired by the exclusivity constraint of the optimal decoder, we also propose an Envelope-Matching decoder to approximately enforce the exclusivity constraint within the MWPM framework. This decoder achieves d_loss ~ 2d/3, surpassing the previous best algorithmic decoder, which achieves dloss ~ d/2 even with an MILP formulation. Circuit-level simulations demonstrate that our approach attains up to 40% higher thresholds and 30% higher effective distances compared with existing algorithmic decoders and syndrome extraction circuits in the loss-dominated regime. On recent experimental data, our Envelope-MLE decoder improves the error suppression factor of a hybrid MLE--machine-learning decoder from 2.14 to 2.24.
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral-atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault-tolerant quantum computation in systems with loss error detection.
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited connectivity. In this work, we explore a non-Pauli stabilizer code that can be used to complete a universal gate set on topological toric and surface codes in strictly two dimensions. Fault-tolerant syndrome extraction for the non-Pauli code requires mid-circuit XXX corrections, a key difference to conventional Pauli codes. We construct and benchmark a just-in-time (JIT) matching decoder to reliably decide these corrections. Under a phenomenological error model with equally likely physical and measurement errors, we find a high threshold of ≈2.5 %\approx 2.5\,\%≈2.5%, close to the ≈2.9 %\approx 2.9\,\%≈2.9% of a decoder with access to the full syndrome history. We also perform a finite-size scaling analysis to estimate how the logical error rate scales below threshold and verify an exponential suppression in both physical error rate and in the system size. A second global decoding step for ZZZ errors is required and the non-Clifford gates in the circuit reduce the threshold from ≈2.9 %\approx 2.9\,\%≈2.9% to ≈1.8 %\approx 1.8\,\%≈1.8% with a naive decoder. We show how ZZZ decoding can be improved using knowledge of the XXX corrections, pushing the threshold to ≈2.2 %\approx 2.2\,\%≈2.2%. Our results suggest non-Clifford logic in 2D codes could perform comparably to 2D quantum memory. Our formalism for efficient benchmarking and decoding directly generalizes to a broader family of CSS codes whose XXX stabilizers are twisted by diagonal Clifford operators, and spacetime versions thereof, defined by CSS-like circuits enriched by CCZCCZCCZ, CSCSCS, and TTT gates.
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral-atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault-tolerant quantum computation in systems with loss error detection.
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low and high) ML-based decoding scheme, where the first level corrects errors on physical qubits and the second one corrects any existing logical errors, for different noise models. Our results show that our proposed decoding method achieves ∼10×\sim10 \times∼10× and ∼2×\sim2 \times∼2× higher values of pseudo-threshold and threshold respectively, than for MWPM. We show that usage of more sophisticated ML models with higher training/testing time, do not provide significant improvement in the decoder performance. Finally, data generation for training the ML decoder requires significant overhead hence lower volume of training data is desirable. We have shown that our decoder maintains a good performance with the train-test-ratio as low as 40:6040:6040:60.
Qubit loss is a major source of error in quantum computation, as it invalidates the algebraic structure of the standard stabilizer formalism for quantum error-correcting codes. On the one hand, it complicates decoding; on the other hand, it introduces stochastic flicker patterns in stabilizers as a hallmark of qubit loss. Here, we develop an artificial-intelligence-enabled decoder based on a spatiotemporal Graph Neural Network (STGNN) architecture to extract spatial and temporal correlations from syndrome histories. Our decoder performs a dual-head task, simultaneously correcting standard Pauli errors and identifying the locations of qubit loss. Our decoder achieves significantly higher logical accuracy than both the traditional minimum-weight perfect matching (MWPM) algorithm and even delayed-erasure MWPM decoders that use qubit loss information from the final round as input. Our decoder can also identify more than 90% of loss locations after accumulating stabilizer measurements over the subsequent ten rounds, thereby facilitating qubit reinitialization, for instance, via the continuous loading technique on the atom array platform. For both tasks, our STGNN performs nearly identically to a modified version of AlphaQubit, but it employs a parallel input structure, giving it an advantage in inference time over modified AlphaQubit's recurrent input structure. This work provides a robust and scalable framework for correcting qubit loss errors, paving the way for more efficient fault-tolerant quantum computation.
Qubit leakage and loss, particularly Rydberg-induced decay during two-qubit gates, pose significant challenges to fault-tolerant quantum computing with neutral atom arrays, as they propagate to correlated errors and degrade code distance. Here, we present a hardware-efficient scheme for addressing Rydberg decay using the SWAP-Leakage Reduction Circuit (SWAP-LRC) protocol, which leverages ancilla-data qubit swaps for in-line leakage mitigation. This strategy eliminates the need for atom-species-specific mid-circuit detection or additional ancillary qubits. Based on experimental detection capabilities, we present two specialized decoders. For detectable leakage/loss (e.g., in 171^{171}171Yb), our Located Decoder achieves a high threshold of 2.33\% per CNOT gate and an improved error distance, significantly outperforming conventional Pauli error models. More interestingly, for scenarios where only one error type is detectable (e.g., atom loss for 87^{87}87Rb), our Critical Decoder specifically targets and mitigates the most detrimental critical faults caused by correlated leakage, achieving an error distance comparable to standard Pauli errors. Our findings offer insights for handling complex non-Pauli errors for neutral atom quantum computation.