Laplacian quantum walks on blow-up graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916692846706688 |
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| author | Monterde, Hermie Pal, Hiranmoy Kirkland, Steve |
| author_facet | Monterde, Hermie Pal, Hiranmoy Kirkland, Steve |
| contents | This paper is a sequel to the work of Bhattacharjya et al.\ (J. Phys. A-Math. 57.33: 335303, https://doi.org/10.1088/1751-8121/ad6653) on quantum state transfer on blow-up graphs, where instead of the adjacency matrix, we take the Laplacian matrix as the time-independent Hamiltonian associated with a blow-up graph. We characterize strong cospectrality, periodicity, perfect state transfer (LPST) and pretty good state transfer (LPGST) on blow-up graphs. We present several constructions of blow-up graphs with LPST and produce new infinite families of regular graphs where each vertex is involved in LPST. We also determine LPST and LPGST in blow-ups of classes of trees. Finally, if $n\equiv 0$ (mod 4), then the blow-up of $n$ copies of a graph $G$ has no LPST, but we show that under certain conditions, the addition of an appropriate matching this blow-up graph results in LPST. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Laplacian quantum walks on blow-up graphs Monterde, Hermie Pal, Hiranmoy Kirkland, Steve Combinatorics Quantum Physics 05C50, 05C76, 15A16, 81P45 This paper is a sequel to the work of Bhattacharjya et al.\ (J. Phys. A-Math. 57.33: 335303, https://doi.org/10.1088/1751-8121/ad6653) on quantum state transfer on blow-up graphs, where instead of the adjacency matrix, we take the Laplacian matrix as the time-independent Hamiltonian associated with a blow-up graph. We characterize strong cospectrality, periodicity, perfect state transfer (LPST) and pretty good state transfer (LPGST) on blow-up graphs. We present several constructions of blow-up graphs with LPST and produce new infinite families of regular graphs where each vertex is involved in LPST. We also determine LPST and LPGST in blow-ups of classes of trees. Finally, if $n\equiv 0$ (mod 4), then the blow-up of $n$ copies of a graph $G$ has no LPST, but we show that under certain conditions, the addition of an appropriate matching this blow-up graph results in LPST. |
| title | Laplacian quantum walks on blow-up graphs |
| topic | Combinatorics Quantum Physics 05C50, 05C76, 15A16, 81P45 |
| url | https://arxiv.org/abs/2504.11585 |