Coupled-Layer Construction of Quantum Product Codes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914526976278528 |
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| author | Zhang, Shuyu Wei, Tzu-Chieh Tantivasadakarn, Nathanan |
| author_facet | Zhang, Shuyu Wei, Tzu-Chieh Tantivasadakarn, Nathanan |
| contents | Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of both code distance and encoding rate. However, despite its powerful algebraic formulation, the physical mechanism for assembling a general product code from its constituents remains unclear. In this letter, we show that the tensor and balanced product codes admit an intuitive coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. We also make a connection to concatenated codes by showing that the tensor product code can be obtained by gauging large-weight logicals in concatenated codes, making them qLDPC. Our framework accommodates both classical or quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08711 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coupled-Layer Construction of Quantum Product Codes Zhang, Shuyu Wei, Tzu-Chieh Tantivasadakarn, Nathanan Quantum Physics Strongly Correlated Electrons Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of both code distance and encoding rate. However, despite its powerful algebraic formulation, the physical mechanism for assembling a general product code from its constituents remains unclear. In this letter, we show that the tensor and balanced product codes admit an intuitive coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. We also make a connection to concatenated codes by showing that the tensor product code can be obtained by gauging large-weight logicals in concatenated codes, making them qLDPC. Our framework accommodates both classical or quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes. |
| title | Coupled-Layer Construction of Quantum Product Codes |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2603.08711 |