Stabilizer-Code Channel Transforms Beyond Repetition Codes for Improved Hashing Bounds

• URL: http://arxiv.org/abs/2601.15505v2
• Date: Sat, 24 Jan 2026 04:25:14 GMT
• Title: Stabilizer-Code Channel Transforms Beyond Repetition Codes for Improved Hashing Bounds
• Authors: Tyler Kann, Matthieu R. Bloch, Shrinivas Kudekar, Ruediger Urbanke,
• Abstract summary: A known way to improve achievable rates for certain asymmetric Pauli channels is to apply a small inner stabilizer code to a few channel uses.<n>We generalize this induced-channel viewpoint to arbitrary stabilizer codes used purely as channel transforms.<n>We perform a structured search over small transforms and report instances that improve the baseline hashing bound for a family of Pauli channels.
• Score: 8.283026597815734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum hashing bound guarantees that rates up to $1-H(p_I, p_X, p_Y, p_Z)$ are achievable for memoryless Pauli channels, but it is not generally tight. A known way to improve achievable rates for certain asymmetric Pauli channels is to apply a small inner stabilizer code to a few channel uses, decode, and treat the resulting logical noise as an induced Pauli channel; reapplying the hashing argument to this induced channel can beat the baseline hashing bound. We generalize this induced-channel viewpoint to arbitrary stabilizer codes used purely as channel transforms. Given any $ [\![ n, k ]\!] $ stabilizer generator set, we construct a full symplectic tableau, compute the induced joint distribution of logical Pauli errors and syndromes under the physical Pauli channel, and obtain an achievable rate via a hashing bound with decoder side information. We perform a structured search over small transforms and report instances that improve the baseline hashing bound for a family of Pauli channels with skewed and independent errors studied in prior work.

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