Related papers: Tree-Line graphs and their quantum walks
Wu, Zhang and Li [4] conjectured that the set of vertices of any simple graph $G$ can be equitably partitioned into $\lceil(\Delta(G)+1)/2\rceil$ subsets so that each of them induces a forest of $G$. In this note, we prove this conjecture…
In this paper, we define k-equivalence, a relation on graphs that relies on their associated cellular algebras. We show that a k-Boson quantum walk cannot distinguish pairs of graphs that are k- equivalent. The existence of pairs of…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family…
We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…
Let $G$ be a group. \textit{The permutability graph of cyclic subgroups of $G$}, denoted by $\Gamma_c(G)$, is a graph with all the proper cyclic subgroups of $G$ as its vertices and two distinct vertices in $\Gamma_c(G)$ are adjacent if and…
Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic…
We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a…
A $(q,r)$\emph{-tree-coloring} of a graph $G$ is a $q$-coloring of vertices of $G$ such that the subgraph induced by each color class is a forest of maximum degree at most $r.$ An \emph{equitable $(q, r)$-tree-coloring} of a graph $G$ is a…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
The commuting graph ${\Gamma(G)}$ of a group $G$ is the simple undirected graph with group elements as a vertex set and two elements $x$ and $y$ are adjacent if and only if $xy=yx$ in $G$. By eliminating the identity element of $G$ and all…