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This research establishes a new canonical form for stabilizer parity check matrices and accelerates Clifford group computations from $O(n^6)$ to $O(n^3)$, directly advancing the efficiency of quantum error correction protocols. By deriving tighter finite blocklength bounds for Pauli noise, the study clarifies theoretical limits on reliable quantum communication without relying on suboptimal guessing arguments.
Canonical Form and Finite Blocklength Bounds for Stabilizer Codes
arXiv:2408.15202v3 Announce Type: replace Abstract: First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which improves upon the previously known time $O(n^6)$. Finally, the related problem of finite blocklength bounds for stabilizer codes and Pauli noise is studied. A finite blocklength refinement of the hashing bound is derived, and it is shown that no argument that uses guessing the error as a substitute for guessing the coset can lead to a significantly better achievability bound.
Abstract:First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which improves upon the previously known time $O(n^6)$. Finally, the related problem of finite blocklength bounds for stabilizer codes and Pauli noise is studied. A finite blocklength refinement of the hashing bound is derived, and it is shown that no argument that uses guessing the error as a substitute for guessing the coset can lead to a significantly better achievability bound.
This article has been accepted in IEEE Transactions on Information Theory. The third version on arXiv includes revisions made during peer review. To obtain the final published version, visit this https URL or use the information provided in the Journal Reference and DOI fields
arXiv:2408.15202 [quant-ph]
(or arXiv:2408.15202v3 [quant-ph] for this version)
IEEE Transactions on Information Theory, vol. 72, no. 6, pp. 3979-4000, June 2026
https://doi.org/10.1109/TIT.2026.3688060 DOI(s) linking to related resources
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