Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays

TL;DR

This paper introduces a new family of ultra-high-rate quantum error-correcting codes compatible with reconfigurable atom arrays, achieving extremely low logical error rates suitable for practical quantum computing.

Contribution

It identifies structural conditions on affine permutation matrices enabling encoding rates above 1/2, supporting efficient implementation and decoding on neutral atom arrays.

Findings

Achieved logical error rates of ~10^{-13} with a 2304-qubit code.

Demonstrated codes with encoding rates exceeding 1/2.

Approaching the teraquop regime for practical quantum error correction.

Abstract

Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead through high-rate encodings, yet finite-size instances with practical logical error rates often achieve encoding rates only around or below $1/10$. Here, building on a recent ultra-high-rate construction by Kasai, we identify new structural conditions on the underlying affine permutation matrices that make encoding rates exceeding $1/2$ compatible with efficient implementation on reconfigurable neutral atom arrays. These conditions define a co-designed family of ultra-high-rate quantum codes that supports efficient syndrome extraction and atom rearrangement under realistic parallel control constraints. Using a hierarchical decoder with high accuracy and good throughput, we study the performance under a circuit-level noise model with $p=0.1\%$, achieving per-logical-per-round error rates of $1.3_{-0.9}^{+3.0} \times 10^{-13}$ with a $[[2304,1156,\leq 14]]$ code and $2.9_{-1.5}^{+3.1} \times 10^{-11}$ with a $[[1152,580,\leq 12]]$ code. These results approach the teraquop regime, highlighting the promise of this code family for practical ultra-high-rate quantum error correction.