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arXiv · 2606.18240

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

Shobhit Bhatnagar·Michele Pacenti·Nithin Raveendran·David Declercq·Bane Vasić
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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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Shobhit Bhatnagar, Michele Pacenti, Nithin Raveendran, David Declercq, Bane Vasić. 2026-06-16. Impulse Decoding of Quantum LDPC Codes: Equivalence of Degeneracy and Code-Shortening. https://arxiv.org/abs/2606.18240

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