Continuous-time quantum walks on star graphs
نویسنده
چکیده
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 walk tends to the uniform distribution.
منابع مشابه
Continuous-Time Quantum Walks on the Symmetric Group
In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that for several natural choices for generating sets, these quantum walks do not have uniform limiting distributions, and are effectively blind to large areas of...
متن کاملMixing in Continuous Quantum Walks on Graphs
Classical random walks on well-behaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that a continuous quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuous-time quantum walks on other well-behaved graphs do not exhibit this uniform mixing. We prove that the only graphs amongst balanced complete multipartite graphs th...
متن کاملQuantum central limit theorem for continuous-time quantum walks on odd graphs
The method of spectral distribution only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. The idea of calculation of the probability amplitudes for continuous-time quantum walk, in terms of the spectral distribution associated with the adjacency matrix of graphs was firs...
متن کاملNon-uniform Mixing in Continuous Quantum Walks
In this note, we study the mixing properties of continuous-time quantum random walks on graphs. We prove that the only graphs in the family of balanced complete multipartite graphs that have a uniform mixing property are K2, K3, K4, and K2,2. This is unlike the classical case where the uniform mixing property is satisfied by all such graphs. Our proof exploits the circulant structure of these g...
متن کاملStudy of continuous-time quantum walks on quotient graphs via quantum probability theory
In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of reductions, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the spectral distribution associated wit...
متن کامل