Toward Self-Correcting Quantum Codes for Neutral Atom Arrays | CU Experts

; 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; ; ; ; Z; ; ℓ; ; ⋊; ; ; 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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