Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: University of Arizona
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Collaborative Research: CIF: Medium: QODED: Quantum codes Optimized for the Dynamics between Encoded Computation and Decoding using Classical Coding Techniques, CIF: Small: Quantum LDPC Codes and Low-Complexity Iterative Decoders, Collaborative Research: Secure and Efficient Post-quantum Cryptography: from Coding Theory to Hardware Architecture, CIF: Small: Learning To Correct Errors
OpenAlex ID: W7165010446
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