Quantum

Local Clifford equivalence to CSS codes: Polynomial-time classification and conversion

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 22/10/2026, 04:13:24 UTC.

Briefings

A new algorithm determines if a stabilizer code is locally Clifford-equivalent to a CSS code in polynomial time, enabling efficient conversion and decoder reuse. The study resolves open classification questions for published constructions, specifically for graph states where equivalence maps to bipartite graph properties in local-complementation orbits. The algorithm uses O(mn^2+n^4) operations for m redundant generator rows on n qubits.

Key points

• The algorithm provides a deterministic polynomial-time method to classify stabilizer codes as locally Clifford-equivalent to CSS codes.
• For graph states, local Clifford equivalence corresponds to the existence of a bipartite graph in the local-complementation orbit.

Context

Calderbank-Shor-Steane (CSS) codes use separate X and Z stabilizer checks for fault-tolerant operations. Previous work obscured this structure, and this research provides a classification algorithm to make CSS decoding and fault-tolerant constructions accessible across all local Clifford equivalence classes.

Limitations

The evidence is a preprint (arXiv:2610.28737v1) with no peer review. Results are based on theoretical analysis and may not apply to all physical implementations. The algorithm's performance depends on the specific code parameters m and n.

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