Continuous-time Quantum Walks on Cayley Graphs of Extraspecial Groups
نویسندگان
چکیده
We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups called extraspecial groups. By applying general results for in association schemes we determine the precise conditions perfect state transfer and fractional revival. Using partial spreads, construct 2-groups that admit these phenomena. also show there is no graph an group admits instantaneous uniform mixing.
منابع مشابه
Quantum Walks on Cayley Graphs
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterise quantum walks on free groups and p...
متن کاملContinuous-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...
متن کاملExploring scalar quantum walks on Cayley graphs
A quantum walk, i.e., the quantum evolution of a particle on a graph, is termed scalar if the internal space of the moving particle (often called the coin) has dimension one. Here, we study the existence of scalar quantum walks on Cayley graphs, which are built from the generators of a group. After deriving a necessary condition on these generators for the existence of a scalar quantum walk, we...
متن کاملOn the eigenvalues of Cayley graphs on generalized dihedral groups
Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$. Then the energy of $Gamma$, a concept defined in 1978 by Gutman, is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$. Also the Estrada index of $Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$. In this paper, we compute the eigen...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic combinatorics
سال: 2022
ISSN: ['2589-5486']
DOI: https://doi.org/10.5802/alco.237