Graphical Calculus for Fermionic Tensors
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908479796543488 |
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| author | Ren, Yuanjie Bu, Kaifeng Bauer, Andreas |
| author_facet | Ren, Yuanjie Bu, Kaifeng Bauer, Andreas |
| contents | We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors primarily correspond to fermionic modes, but also include qubits and fixed odd-parity states. Our graphical calculus extends the ZX calculus for systems involving qubits. We apply the calculus in order to represent various objects, operations, and computations in physics, including fermionic Gaussian states, the partial trace of Majorana modes, purification protocols, fermionization and bosonization maps, and the construction of fermionic codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graphical Calculus for Fermionic Tensors Ren, Yuanjie Bu, Kaifeng Bauer, Andreas Quantum Physics Strongly Correlated Electrons We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors primarily correspond to fermionic modes, but also include qubits and fixed odd-parity states. Our graphical calculus extends the ZX calculus for systems involving qubits. We apply the calculus in order to represent various objects, operations, and computations in physics, including fermionic Gaussian states, the partial trace of Majorana modes, purification protocols, fermionization and bosonization maps, and the construction of fermionic codes. |
| title | Graphical Calculus for Fermionic Tensors |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.03976 |