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arXiv · 2601.04467

Holographic codes seen through ZX-calculus

Kwok Ho Wan·H. C. W. Price·Qing Yao·Zhenghao Zhong·Ainhoa Zapirain
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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, R\'enyi 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. Finally, we show how to construct spacetime ZX-diagrams that realise a fault-tolerant quantum channel in which every internal edge is a protected fault location.

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Kwok Ho Wan, H. C. W. Price, Qing Yao, Zhenghao Zhong, Ainhoa Zapirain. 2026-01-08. Holographic codes seen through ZX-calculus. https://arxiv.org/abs/2601.04467

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