Achieving Optimal-Distance Atom-Loss Correction via Pauli Envelope

TL;DR

This paper introduces the Pauli Envelope framework for optimal atom-loss correction in neutral-atom quantum computers, leading to improved circuits and decoders with higher thresholds and better error suppression.

Contribution

The paper presents a novel Pauli Envelope framework, new syndrome extraction circuits, and decoders that outperform existing methods in atom-loss correction for quantum computing.

Findings

Achieves up to 40% higher thresholds in simulations.

Surpasses previous loss distance bounds with new decoders.

Shows correlated atom loss is easier to correct than independent loss.

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 \Lambda = 2.14 to \Lambda = 2.24 on recent experimental data.