Holographic codes seen through ZX-calculus
Quantum Physics
2026-01-21 v2
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.
Keywords
Cite
@article{arxiv.2601.04467,
title = {Holographic codes seen through ZX-calculus},
author = {Kwok Ho Wan and H. C. W. Price and Qing Yao},
journal= {arXiv preprint arXiv:2601.04467},
year = {2026}
}
Comments
v2: Minor typos + much expanded introduction on ZX-diagrams