A graphical diagnostic of topological order using ZX calculus
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911156426244096 |
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| author | Mas-Mendoza, Sergi East, Richard D. P. Filippone, Michele Grushin, Adolfo G. |
| author_facet | Mas-Mendoza, Sergi East, Richard D. P. Filippone, Michele Grushin, Adolfo G. |
| contents | Establishing a universal diagnostic of topological order remains an open theoretical challenge. In particular, diagnosing long-range entanglement through the entropic area law suffers from spurious contributions, failing to unambiguously identify topological order. Here we devise a protocol based on the ZX calculus, a graphical tensor network, to determine the topological order of a state circumventing entropy calculations. The protocol takes as input real-space bipartitions of a state and returns a ZX contour diagram, $\mathcal{D}_{\partial A}$, displaying long-range graph connectivity only for long-range entangled states. We validate the protocol by showing that the contour diagrams of the toric and color codes are equivalent except for the number of non-local nodes, which differentiates their topological order. The number of these nodes is robust to the choice of the boundary and ground-state superposition, and they are absent for trivial states, even those with spurious entropy contributions. Our results single out ZX calculus as a tool to detect topological long-range entanglement by leveraging the advantages of diagrammatic reasoning against entropic diagnostics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A graphical diagnostic of topological order using ZX calculus Mas-Mendoza, Sergi East, Richard D. P. Filippone, Michele Grushin, Adolfo G. Strongly Correlated Electrons Quantum Physics Establishing a universal diagnostic of topological order remains an open theoretical challenge. In particular, diagnosing long-range entanglement through the entropic area law suffers from spurious contributions, failing to unambiguously identify topological order. Here we devise a protocol based on the ZX calculus, a graphical tensor network, to determine the topological order of a state circumventing entropy calculations. The protocol takes as input real-space bipartitions of a state and returns a ZX contour diagram, $\mathcal{D}_{\partial A}$, displaying long-range graph connectivity only for long-range entangled states. We validate the protocol by showing that the contour diagrams of the toric and color codes are equivalent except for the number of non-local nodes, which differentiates their topological order. The number of these nodes is robust to the choice of the boundary and ground-state superposition, and they are absent for trivial states, even those with spurious entropy contributions. Our results single out ZX calculus as a tool to detect topological long-range entanglement by leveraging the advantages of diagrammatic reasoning against entropic diagnostics. |
| title | A graphical diagnostic of topological order using ZX calculus |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2509.12355 |