dorsal/arxiv
View SchemaBias-Aware BP Decoding of Quantum Codes via Directional Degeneracy
| Authors | Mohammad Rowshan |
|---|---|
| Categories | |
| ArXiv ID | 2601.07240vv1 |
| URL | https://arxiv.org/abs/2601.07240 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
We study directionally informed belief propagation (BP) decoding for quantum CSS codes, where anisotropic Tanner-graph structure and biased noise concentrate degeneracy along preferred directions. We formalize this by placing orientation weights on Tanner-graph edges, aggregating them into per-qubit directional weights, and defining a \emph{directional degeneracy enumerator} that summarizes how degeneracy concentrates along those directions. A single bias parameter~$\beta$ maps these weights into site-dependent log-likelihood ratios (LLRs), yielding anisotropic priors that plug directly into standard BP$\rightarrow$OSD decoders without changing the code construction. We derive bounds relating directional and Hamming distances, upper bound the number of degenerate error classes per syndrome as a function of distance, rate, and directional bias, and give a MacWilliams-type expression for the directional enumerator. Finite-length simulations under code-capacity noise show significant logical error-rate reductions -- often an order of magnitude at moderate physical error rates -- confirming that modest anisotropy is a simple and effective route to hardware-aware decoding gains.
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"abstract": "We study directionally informed belief propagation (BP) decoding for quantum CSS codes, where anisotropic Tanner-graph structure and biased noise concentrate degeneracy along preferred directions. We formalize this by placing orientation weights on Tanner-graph edges, aggregating them into per-qubit directional weights, and defining a \\emph{directional degeneracy enumerator} that summarizes how degeneracy concentrates along those directions. A single bias parameter~$\\beta$ maps these weights into site-dependent log-likelihood ratios (LLRs), yielding anisotropic priors that plug directly into standard BP$\\rightarrow$OSD decoders without changing the code construction. We derive bounds relating directional and Hamming distances, upper bound the number of degenerate error classes per syndrome as a function of distance, rate, and directional bias, and give a MacWilliams-type expression for the directional enumerator. Finite-length simulations under code-capacity noise show significant logical error-rate reductions -- often an order of magnitude at moderate physical error rates -- confirming that modest anisotropy is a simple and effective route to hardware-aware decoding gains.",
"arxiv_id": "2601.07240",
"authors": [
"Mohammad Rowshan"
],
"categories": [
"cs.IT",
"math.IT",
"quant-ph"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Bias-Aware BP Decoding of Quantum Codes via Directional Degeneracy",
"url": "https://arxiv.org/abs/2601.07240",
"version": "v1"
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