Towards self-correcting quantum codes for neutral atom arrays

• URL: http://arxiv.org/abs/2507.21396v1
• Date: Tue, 29 Jul 2025 00:08:26 GMT
• Title: Towards self-correcting quantum codes for neutral atom arrays
• Abstract summary: "ZSZ codes" are low-overhead quantum error-correcting codes based on the group $mathbbZ_ell rtimes mathbbZ_m$.<n>We benchmark the performance of this code family under local "self-correcting" decoders.<n>These results suggest that ZSZ codes are promising candidates for scalable self-correcting quantum memories.
• Score: 2.1874189959020427
• License: http://creativecommons.org/licenses/by/4.0/
• 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 "ZSZ codes", a simple non-abelian generalization of the bivariate bicycle codes based on the group $\mathbb{Z}_\ell \rtimes \mathbb{Z}_m$. 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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