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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.05132 |
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| _version_ | 1866915984484335616 |
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| author | Kasai, Kenta |
| author_facet | Kasai, Kenta |
| contents | For CSS syndrome decoding, the two check matrices impose binary parity-check constraints on the two Pauli error components. The posterior can therefore be written as a binary factor graph with two Tanner graphs coupled by the local joint prior at each qubit. We call the sum-product algorithm on this factorization joint belief propagation (joint BP). Joint BP retains the local channel correlation between the two Pauli components. This note compares joint BP with the four-state Pauli-label factor graph used for four-state BP. The two algorithms are shown to have the same posterior weights, messages, and beliefs after relabeling the four local Pauli states and marginalizing the irrelevant binary component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05132 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Factor-Graph Formulation of CSS Syndrome Decoding: Joint BP and Four-State BP Kasai, Kenta Quantum Physics Information Theory For CSS syndrome decoding, the two check matrices impose binary parity-check constraints on the two Pauli error components. The posterior can therefore be written as a binary factor graph with two Tanner graphs coupled by the local joint prior at each qubit. We call the sum-product algorithm on this factorization joint belief propagation (joint BP). Joint BP retains the local channel correlation between the two Pauli components. This note compares joint BP with the four-state Pauli-label factor graph used for four-state BP. The two algorithms are shown to have the same posterior weights, messages, and beliefs after relabeling the four local Pauli states and marginalizing the irrelevant binary component. |
| title | A Factor-Graph Formulation of CSS Syndrome Decoding: Joint BP and Four-State BP |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2605.05132 |