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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• Revised Apr 4, 2026 (v2)
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. Its nonlinear and correlated nature poses significant challenges: current syndrome extraction circuits require additional overhead or sacrifice loss tolerance, and existing decoders are computationally inefficient, suboptimal, or lack provable guarantees. To address these challenges, we propose the Pauli Envelope framework, which bounds the effect of atom loss with low-weight, efficiently computable Pauli approximations, generalizing existing loss-to-Pauli methods and enabling rigorous analysis. Guided by this framework, we design improved atom-replenishing syndrome extraction circuits, the Mid-SWAP syndrome extraction, which achieves optimal loss distance and minimal space-time overhead for rotated surface codes. We also propose two decoders: an Envelope-MLE decoder achieving the optimal loss distance d_loss ~ d, and an Envelope-Matching decoder achieving d_loss ~ 2d/3 via Minimum-Weight Perfect Matching (MWPM), surpassing the previous best (d_loss ~ d/2) and readily integrating with fast correlated decoding techniques for transversal logical circuits. Circuit-level simulations demonstrate up to 40% higher thresholds and 30% higher effective distances compared with existing methods in the loss-dominated regime. Moreover, we explore correlated atom loss and show that it is easier to correct than independent loss, with thresholds rising from 5.15% to 7.82%. Remarkably, our Envelope-MLE decoder improves the error suppression factor of a hybrid MLE--machine-learning decoder from Λ= 2.14 to Λ= 2.24 on recent experimental data.

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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. Its nonlinear and correlated nature poses significant challenges: current syndrome extraction circuits require additional overhead or sacrifice loss tolerance, and existing decoders are computationally inefficient, suboptimal, or lack provable guarantees. To address these challenges, we propose the Pauli Envelope framework, which bounds the effect of atom loss with low-weight, efficiently computable Pauli approximations, generalizing existing loss-to-Pauli methods and enabling rigorous analysis. Guided by this framework, we design improved atom-replenishing syndrome extraction circuits, the Mid-SWAP syndrome extraction, which achieves optimal loss distance and minimal space-time overhead for rotated surface codes. We also propose two decoders: an Envelope-MLE decoder achieving the optimal loss distance d_loss ~ d, and an Envelope-Matching decoder achieving d_loss ~ 2d/3 via Minimum-Weight Perfect Matching (MWPM), surpassing the previous best (d_loss ~ d/2) and readily integrating with fast correlated decoding techniques for transversal logical circuits. Circuit-level simulations demonstrate up to 40% higher thresholds and 30% higher effective distances compared with existing methods in the loss-dominated regime. Moreover, we explore correlated atom loss and show that it is easier to correct than independent loss, with thresholds rising from 5.15% to 7.82%. Remarkably, our Envelope-MLE decoder improves the error suppression factor of a hybrid MLE--machine-learning decoder from Λ= 2.14 to Λ= 2.24 on recent experimental data.
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.