Towards self-correcting quantum codes for neutral atom arrays

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 Z_n⋊ 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.