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  • Open Access

Toward Self-Correcting Quantum Codes for Neutral Atom Arrays

Jinkang Guo1,2, Yifan Hong1,2,3, Adam Kaufman1,4, and Andrew Lucas1,2,*

  • *Contact author: andrew.j.lucas@colorado.edu
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PRX Quantum 7, 010301 – Published 2 January, 2026

DOI: https://doi.org/10.1103/mfmt-fwkg

Abstract

Discovering low-overhead quantum error-correcting codes is of significant interest for fault-tolerant quantum computation. For hardware capable of long-range connectivity, the bivariate bicycle codes offer significant overhead reduction compared to surface codes with similar performance. In this work, we present “Z semidirect Z (ZSZ) codes,” a simple nonabelian generalization of the bivariate bicycle codes based on the group Zℓ⋊Zm. We numerically demonstrate that certain instances of this code family achieve competitive performance with the bivariate bicycle codes under circuit-level depolarizing noise using a belief-propagation and ordered-statistics decoder, with an observed threshold around 0.5%. We also benchmark the performance of this code family under local “self-correcting” decoders, where we observe significant improvements over the bivariate bicycle codes, including evidence of a sustainable threshold around 0.095%, which is higher than the 0.06% that we estimate for the four-dimensional toric code under the same noise model. These results suggest that ZSZ codes are promising candidates for scalable self-correcting quantum memories. Finally, we describe how ZSZ codes can be realized with neutral atoms trapped in movable tweezer arrays, where a complete round of syndrome extraction can be achieved using simple global motions of the atomic arrays.

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Popular Summary

Quantum states are vulnerable to environmental noise and decoherence. Quantum error-correcting codes can detect and fix such errors in a scalable way, allowing for fault-tolerant quantum information processing. A useful family of such codes is the quantum low-density parity-check (LDPC) code, where fault tolerance is possible because errors are detected using the outcomes of few-qubit measurements. Such decoders are highly desirable, as the time needed to perform error correction does not scale with the number of qubits in the code. Many LDPC codes are further capable of autonomous (passive) error correction, where errors on a single qubit are (typically) detected by measuring only a few nearby qubits. Unfortunately, autonomously decodable LDPC codes thus far require complex qubit interactions which are not nicely realized out of local interactions in three spatial dimensions.

We present the “ZSZ codes,” a simple family of quantum LDPC codes. Large-scale simulations imply that ZSZ codes are capable of passive error correction and moreover can do so with a higher tolerance for errors than other known LDPC codes. Most importantly, the ZSZ codes are tailored for neutral-atom quantum processing, where each qubit is stored in an atomic state, and each atom can be physically transported in space via adjustable optical lattices. The interactions among qubits needed to perform error correction correspond to relatively simple rearrangements of these optical lattices, such as global translations or stretching of the array. ZSZ codes are thus a potential candidate for the demonstration of autonomous quantum error correction in experiments.

Article Text

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Outline

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PRX Quantum 7, 010301– Published 2 January, 2026
  • Received 11 August 2025
  • Revised 31 October 2025
  • Accepted 26 November 2025
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