Holographic codes seen through ZX-calculus
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917211046674432 |
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| author | Wan, Kwok Ho Price, H. C. W. Yao, Qing |
| author_facet | Wan, Kwok Ho Price, H. C. W. Yao, Qing |
| contents | We re-visit the pentagon holographic quantum error correcting code from a ZX-calculus perspective. By expressing the underlying tensors as ZX-diagrams, we study the stabiliser structure of the code via Pauli webs. In addition, we obtain a diagrammatic understanding of its logical operators, encoding isometries, Rényi entropy and toy models of black holes/wormholes. Then, motivated by the pentagon holographic code's ZX-diagram, we introduce a family of codes constructed from ZX-diagrams on its dual hyperbolic tessellations and study their logical error rates using belief propagation decoders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04467 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holographic codes seen through ZX-calculus Wan, Kwok Ho Price, H. C. W. Yao, Qing Quantum Physics We re-visit the pentagon holographic quantum error correcting code from a ZX-calculus perspective. By expressing the underlying tensors as ZX-diagrams, we study the stabiliser structure of the code via Pauli webs. In addition, we obtain a diagrammatic understanding of its logical operators, encoding isometries, Rényi entropy and toy models of black holes/wormholes. Then, motivated by the pentagon holographic code's ZX-diagram, we introduce a family of codes constructed from ZX-diagrams on its dual hyperbolic tessellations and study their logical error rates using belief propagation decoders. |
| title | Holographic codes seen through ZX-calculus |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.04467 |