Abstract In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer (PQST): the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between PQST, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectral structure, applicable to a wide variety of fractal-like graphs. We illustrate this construction with explicit examples for several classes of diamond graphs.Abstract In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer (PQST): the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between PQST, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectral structure, applicable to a wide variety of fractal-like graphs. We illustrate this construction with explicit examples for several classes of diamond graphs.

arXiv:2003.11190Journal of Physics A Mathematical and TheoreticalOct 26, 202025 citations

Perfect quantum state transfer on Cayley graphs over semi-dihedral groups

Gaojun Luo, Xiwang Cao, Dandan Wang +1 more

Perfect quantum state transfer plays a crucial role in quantum information processing and quantum computation. There has been extensive study of perfect quantum state transfer on Cayley graphs over abelian groups. In this paper, we consider the existence of perfect quantum state transfer on Cayley graphs over semi-dihedral groups which are non-abelian groups. Using the representations of semi-dihedral groups, we provide some necessary and sufficient conditions for Cayley graphs over semi-dihedral groups admitting perfect quantum state transfer. By those conditions, we present examples of perfect quantum state transfer on Cayley graphs over semi-dihedral groups. In addition, we propose results about whether some new Cayley graphs over non-abelian groups admit perfect quantum state transfer.Perfect quantum state transfer plays a crucial role in quantum information processing and quantum computation. There has been extensive study of perfect quantum state transfer on Cayley graphs over abelian groups. In this paper, we consider the existence of perfect quantum state transfer on Cayley graphs over semi-dihedral groups which are non-abelian groups. Using the representations of semi-dihedral groups, we provide some necessary and sufficient conditions for Cayley graphs over semi-dihedral groups admitting perfect quantum state transfer. By those conditions, we present examples of perfect quantum state transfer on Cayley graphs over semi-dihedral groups. In addition, we propose results about whether some new Cayley graphs over non-abelian groups admit perfect quantum state transfer.

Linear and Multilinear AlgebraJul 15, 20218 citations

Quantum state transfer on Q-graphs

Xiaoqin Zhang, Shu‐Yu Cui, Gui‐Xian Tian

We study the existence of quantum state transfer in $\mathcal{Q}$ -graphs in this paper. The $\mathcal{Q}$ -graph of a graph $G$ , denoted by $\mathcal{Q}(G)$ , is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and joining two new vertices which lie on adjacent edges of $G$ by an edge. We show that, if all eigenvalues of a regular graph $G$ are integers, then its $\mathcal{Q}$ -graph $\mathcal{Q}(G)$ has no perfect state transfer. In contrast, we also prove that the $\mathcal{Q}$ -graph of a regular graph has pretty good state transfer under some mild conditions. Finally, applying the obtained results, we also exhibit many new families of $\mathcal{Q}$ -graphs having no perfect state transfer, but admitting pretty good state transfer.We study the existence of quantum state transfer in $\mathcal{Q}$-graphs in this paper. The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and joining two new vertices which lie on adjacent edges of $G$ by an edge. We show that, if all eigenvalues of a regular graph $G$ are integers, then its $\mathcal{Q}$-graph $\mathcal{Q}(G)$ has no perfect state transfer. In contrast, we also prove that the $\mathcal{Q}$-graph of a regular graph has pretty good state transfer under some mild conditions. Finally, applying the obtained results, we also exhibit many new families of $\mathcal{Q}$-graphs having no perfect state transfer, but admitting pretty good state transfer.

arXiv:2108.07590Aug 17, 20210 citations

Perfect state transfer on several types of graphs based on the quantum probability perspective

Qi Han, Rong Zhang, Shijiao Xing +2 more

The European Physical Journal PlusJun 17, 20253 citations

We study the existence of quantum state transfer in

\mathcal{Q}

-graphs in this paper. The

\mathcal{Q}

-graph of a graph

G

, denoted by

\mathcal{Q}(G)

, is the graph derived from

G

by plugging a new vertex to each edge of

G

and joining two new vertices which lie on adjacent edges of

G

by an edge. We show that, if all eigenvalues of a regular graph

G

are integers, then its

\mathcal{Q}

-graph

\mathcal{Q}(G)

has no perfect state transfer. In contrast, we also prove that the

\mathcal{Q}

-graph of a regular graph has pretty good state transfer under some mild conditions. Finally, applying the obtained results, we also exhibit many new families of

\mathcal{Q}

-graphs having no perfect state transfer, but admitting pretty good state transfer.