Related papers: Continuous-time Quantum Walks on Cayley Graphs of …
A weighted graph $G$ with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in $G$. In this paper, we prove a fundamental result on equitable…
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…
In this paper we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e. the limit state if…
This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph $G$ has perfect state transfer if and only if its quotient $G/\pi$, under any equitable partition $\pi$, has perfect state transfer, we…
Consider the random Cayley graph of a finite group $G$ with respect to $k$ generators chosen uniformly at random, with $1 \ll k \lesssim \log |G|$. The results of this article supplement those in the three main papers on random Cayley…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
A non-complete graph is \emph{$2$-distance-transitive} if, for $i=1,2$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance $i$ in the graph, there exists an element of the graph automorphism group that maps…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
A blow-up of $n$ copies of a graph $G$ is the graph $\overset{n}\uplus~G$ obtained by replacing every vertex of $G$ by an independent set of size $n$, where the copies of vertices in $G$ are adjacent in the blow-up if and only if the…
We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every…
In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., p_c < p_u. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical…
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex…
An interesting fact is that most of the known connected $2$-arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are $(\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$. This motivates the study…
Quantum walks generated by the adjacency matrix or the Laplacian are known to exhibit low transfer fidelity on general graphs. In this paper, we study continuous-time quantum walks governed by the generalized Laplacian operator L_k = A+kD,…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…