Weakly Hadamard diagonalizable graphs and Quantum State Transfer
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913425200775168 |
|---|---|
| author | McLaren, Darian Monterde, Hermie Plosker, Sarah |
| author_facet | McLaren, Darian Monterde, Hermie Plosker, Sarah |
| contents | Hadamard diagonalizable graphs are undirected graphs for which the corresponding Laplacian is diagonalizable by a Hadamard matrix. Such graphs have been studied in the context of quantum state transfer. Recently, the concept of a weak Hadamard matrix was introduced: a $\{-1,0, 1\}$-matrix $P$ such that $PP^T$ is tridiagonal, as well as the concept of weakly Hadamard diagonalizable graphs. We therefore naturally explore quantum state transfer in these generalized Hadamards. Given the infancy of the topic, we provide numerous properties and constructions of weak Hadamard matrices and weakly Hadamard diagonalizable graphs in order to better understand them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01859 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weakly Hadamard diagonalizable graphs and Quantum State Transfer McLaren, Darian Monterde, Hermie Plosker, Sarah Combinatorics Quantum Physics 15A18, 05C50, 81P45 Hadamard diagonalizable graphs are undirected graphs for which the corresponding Laplacian is diagonalizable by a Hadamard matrix. Such graphs have been studied in the context of quantum state transfer. Recently, the concept of a weak Hadamard matrix was introduced: a $\{-1,0, 1\}$-matrix $P$ such that $PP^T$ is tridiagonal, as well as the concept of weakly Hadamard diagonalizable graphs. We therefore naturally explore quantum state transfer in these generalized Hadamards. Given the infancy of the topic, we provide numerous properties and constructions of weak Hadamard matrices and weakly Hadamard diagonalizable graphs in order to better understand them. |
| title | Weakly Hadamard diagonalizable graphs and Quantum State Transfer |
| topic | Combinatorics Quantum Physics 15A18, 05C50, 81P45 |
| url | https://arxiv.org/abs/2307.01859 |