We explore the scattering of waves in designed asymmetric one-dimensional waveguide
networks. We show that the reflection between two ports of an asymmetric network can be …

Degeneracies in the energy spectra of physical systems are commonly considered to be
either of accidental character or induced by symmetries of the Hamiltonian. We develop an …

We introduce the concept of group state transfer on graphs, summarize its relationship to
other concepts in the theory of quantum walks, set up a basic theory, and discuss examples …

In this article, we give characterization for existence of quantum fractional revival in unitary
Cayley graph utilizing adjacency matrix Hamiltonian. Unitary Cayley graph $ X=(Z_n, S) $ is …

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Perfect state transfer and fractional revival can be used to move information between pairs of
vertices in a quantum network. While perfect state transfer has received a lot of attention …

In this paper, we investigate the existence of fractional revival on semi-Cayley graphs over
finite abelian groups. We give some necessary and sufficient conditions for semi-Cayley …

We initiate the study of pretty good quantum fractional revival in graphs, a generalization of
pretty good quantum state transfer in graphs. We give a complete characterization of pretty …

A quantum spin network can be modelled by an undirected graph whose vertices and edges
represent qubits and their interactions in the network, respectively. One major problem …

Quantum walks on graphs are fundamental to quantum computing and have led to many
interesting open problems in algebraic graph theory. This review article highlights three key …