Issue |
RAIRO-Oper. Res.
Volume 59, Number 3, May-June 2025
|
|
---|---|---|
Page(s) | 1325 - 1340 | |
DOI | https://doi.org/10.1051/ro/2025046 | |
Published online | 14 May 2025 |
Quantum state transfer on 𝒬-graphs
1
Department of Mathematics, Zhejiang Normal University, Jinhua, P.R. China
2
Xingzhi College, Zhejiang Normal University, Jinhua, P.R. China
* Corresponding author: gxtian@zjnu.cn
Received:
10
May
2024
Accepted:
10
April
2025
Given a graph G, the graph 𝒬(G) is obtained by inserting a new vertex into every edge of G, then connecting those inserted vertices on the neighbouring edges in G. We usually refer to 𝒬(G) as the 𝒬-graph of G. This article mainly focuses on the effects of 𝒬-graph operation on quantum state transfer. It is shown that if G is an integral r-regular graph for r ≥ 2, then 𝒬(G) always avoids perfect state transfer. In contrast, we also show that, this 𝒬-graph exists pretty good state transfer under some special circumstances. Subsequently, by applying the results obtained above, we also display many new classes of 𝒬-graphs that avoid perfect state transfer but exist pretty good state transfer.
Mathematics Subject Classification: 05C50 / 15A18 / 81P68
Key words: Quantum walk / spectrum / 𝒬-graph / perfect state transfer / pretty good state transfer
© The authors. Published by EDP Sciences, ROADEF, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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