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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.07645 |
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| _version_ | 1866916710894796800 |
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| author | Burchardt, Adam Hahn, Frederik |
| author_facet | Burchardt, Adam Hahn, Frederik |
| contents | This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity $\mathcal{O}(n^3)$ in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical representation in terms of leaves, axils, and twins. It captures both, the connection structure of a graph and the $2$-body marginal properties of the associated graph state. We relate the foliage partition to the size of LC-orbits and use it to bound the number of LC-automorphisms of graphs. We also show the invariance of the foliage partition when generalized to weighted graphs and qudit graph states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07645 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States Burchardt, Adam Hahn, Frederik Quantum Physics This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity $\mathcal{O}(n^3)$ in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical representation in terms of leaves, axils, and twins. It captures both, the connection structure of a graph and the $2$-body marginal properties of the associated graph state. We relate the foliage partition to the size of LC-orbits and use it to bound the number of LC-automorphisms of graphs. We also show the invariance of the foliage partition when generalized to weighted graphs and qudit graph states. |
| title | The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2305.07645 |