Impulse Decoding of Quantum LDPC Codes: Equivalence of Degeneracy and Code-Shortening

• URL: http://arxiv.org/abs/2606.18240v1
• Date: Tue, 16 Jun 2026 17:58:26 GMT
• Title: Impulse Decoding of Quantum LDPC Codes: Equivalence of Degeneracy and Code-Shortening
• Abstract summary: We show that degeneracy is closely related to the classical operation of shortening of a linear block code.<n>We present a parallel decoding scheme for quantum low-density parity-check codes, which we term impulse decoding.<n>We then present another algorithm based on decoding of residual errors, which when combined with impulse decoding achieves further performance improvement under circuit-level noise.
• Score: 1.9355898755215148
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum error correction is essential for building scalable quantum computers. Within the stabilizer formalism, the Calderbank-Shor-Steane framework constructs quantum codes from pairs of classical linear codes. A distinctive feature in this setting is degeneracy, where multiple equivalent error estimates exist-a phenomenon that has no classical counterpart, and the lack of a meaningful classical coding-theoretic interpretation of which has remained a gap in the literature. In this paper, we demonstrate that degeneracy is closely related to the classical operation of shortening of a linear block code. Interestingly, the shortening here takes place at the decoder rather than at the encoder. Leveraging this insight, we present a parallel decoding scheme for quantum low-density parity-check codes, which we term impulse decoding, that significantly outperforms belief propagation with ordered statistics decoding, as well as several other existing techniques, under both code-capacity and circuit-level noise, with significantly lesser complexity. We then present another algorithm based on decoding of residual errors, which when combined with impulse decoding achieves further performance improvement under circuit-level noise.

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