中文

Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes

量子物理 2026-05-22 v1

摘要

Different quantum error correction schemes trade off overhead, error suppression, and hardware connectivity. Code concatenation can relax these tradeoffs by using an outer code whose non-local connectivity is supplied by logical operations of an inner code rather than directly by hardware. Prior works showed that this can reduce memory overhead for local low-rate inner codes such as the surface code. Here, we study concatenation over non-local, high-rate inner codes. Such inner codes experience correlated errors among the many logical qubits in a single codeblock. We handle this by treating each block as a single logical Galois qudit, enabling concatenation with algebraic outer codes with excellent parameters and, crucially, list decoders. In particular, we consider a memory system formed by concatenating quantum Reed-Solomon outer codes over the gross code. For fault-tolerant syndrome extraction, we develop a Galois qudit Shor scheme using "time-like" Reed-Solomon protection against measurement errors. Interestingly, a lightweight fault tolerance scheme, that would fail for qubits, works well for large-alphabet qudits, suggesting a very different theory of fault tolerance for such qudits. The whole protocol is optimised via improved bicycle instruction logical error rates, novel compilation strategies, and recent decoder post-selection rules. At uniform 10310^{-3} physical noise, the concatenated gross code reaches the teraquop regime, which it previously could not access, with a lower space overhead than the 288288-qubit two-gross code, while offering several advantages from the engineering standpoint. Beyond our main case study, we believe the core ideas of Galois qudits, quantum Reed-Solomon outer codes, and list decoding, will prove generically powerful and highly transferable ideas across high-rate quantum architectures.

关键词

引用

@article{arxiv.2605.21898,
  title  = {Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes},
  author = {Adam Wills and Michael E. Beverland and Lev S. Bishop and Jay M. Gambetta and Patrick Rall and Vikesh Siddhu and Andrew W. Cross},
  journal= {arXiv preprint arXiv:2605.21898},
  year   = {2026}
}