Holographic codes seen through ZX-calculus

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. 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.

arXiv:2601.04467 [quant-ph]

(or arXiv:2601.04467v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.04467 Focus to learn more arXiv-issued DOI via DataCite

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