Holographic codes seen through ZX-calculus

• URL: http://arxiv.org/abs/2601.04467v1
• Date: Thu, 08 Jan 2026 01:00:45 GMT
• Title: Holographic codes seen through ZX-calculus
• Authors: Kwok Ho Wan, H. C. W. Price, Qing Yao,
• Abstract summary: We re-visit the pentagon holographic quantum error correcting code from a ZX-calculus perspective.<n>By expressing the underlying tensors as ZX-diagrams, we study the stabiliser structure of the code via Pauli webs.
• Score: 1.5038537438390556
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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