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

2026-04-17

AI Summary

This work addresses the critical bottleneck of high physical qubit overhead in large-scale quantum computing by introducing ultra-high-rate quantum low-density parity-check (LDPC) codes tailored for reconfigurable neutral-atom arrays. By establishing structural conditions on affine permutation matrices that respect parallel control constraints, the authors co-design codes such as [[2304,1156,≤14]] that simultaneously enable efficient syndrome extraction, atomic rearrangement, and high encoding rates. Coupled with a hierarchical decoder, the scheme achieves a logical error rate as low as 1.3×10⁻¹³ per logical qubit per cycle under a circuit-level noise model with physical error rate p = 0.1%. This represents the first demonstration at practical scales of a quantum error-correcting code exceeding a 1/2 encoding rate while drastically reducing resource overhead and approaching teraquaop-level performance.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Large language models for search

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.

Problem

• quantum error correction
• high-rate encoding
• qubit overhead
• logical error rate
• ultra-high-rate codes

Innovation

• ultra-high-rate quantum codes
• reconfigurable atom arrays
• quantum error correction
• affine permutation matrices
• hierarchical decoding