Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

Continuous-Time Quantum Walk on the Line

Quantum walks have recently been introduced and investigated, with the hope that they may be useful in constructing new efficient quantum algorithms. For reviews of quantum walks, see Refs. [4, 16, 24]. There are two distinct types of the quantum walk: one is a discrete-time case [2, 5, 12, 14, 17, 18, 19, 22, 23], the other is a continuous-time case [1, 3, 7, 8, 10, 15, 20]. The quantum walk c...

Continuous-time quantum walks on star graphs

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N -fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K2 graphs (Complete graph with two vertices) and the probability of observing wal...

Continuous-Time Quantum Walks and Trapping

Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy transfer one has to leave the classical, masterequation-type formalism and advance towards an increasingly quantum-mechanical picture, while still retaining...

On the relationship between continuous- and discrete-time quantum walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discretetime random walks, the two types of quantum w...

A Quantum Jensen-Shannon Graph Kernel Using the Continuous-Time Quantum Walk