Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems

Ali Abu-Nada; Lian-Ao Wu

Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems

量子物理 2026-08-12 v1

作者: Ali Abu-Nada , Lian-Ao Wu

摘要

Leakage beyond the computational subspace is a major source of error in multilevel quantum hardware. We show that any $[[n,k,d]]$ stabilizer code can be embedded isometrically into a single $D$ -dimensional system while preserving its complete error-correcting structure. We further derive a necessary and sufficient condition for exact leakage correction, proving that leakage is correctable precisely when it does not distinguish between logical states. These results establish a unified framework for quantum error correction in multilevel quantum systems.

引用

@article{arxiv.2608.12450,
  title  = {Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems},
  author = {Ali Abu-Nada and Lian-Ao Wu},
  journal= {arXiv preprint arXiv:2608.12450},
  year   = {2026}
}