Related papers: Pretty good state transfer in discrete-time quantu…
Perfect state transfer is significant in quantum communication networks. There are very few graphs having this property. So, it is useful to find some new graphs having perfect state transfer. A good way to construct new graphs is by…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
We consider an exact state transmission, where a density matrix in one information processor A at time $t=0$ is exactly equal to that in another processor B at a later time. We demonstrate that there always exists a complete set of…
We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…
We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of approximate fractional revival in a graph in terms of the…
The quantum state transmission (QST) through the medium of high-dimensional many-particle system is studied with a symmetry analysis. We discover that, if the spectrum matches the symmetry of a fermion or boson system in a certain fashion,…
We study the existence of quantum state transfer in $\mathcal{Q}$-graphs in this paper. The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and…
An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer ($\PST$ for short) and multiple state…
This work recollects a non-universal set of quantum gates described by higher-dimensional Spin groups. They are also directly related with matchgates in theory of quantum computations and complexity. Various processes of quantum state…
Pure states correspond to one-dimensional subspaces of $\mathbb{C}^n$ represented by unit vectors. In this paper, we develop the theory of perfect state transfer (PST) between real pure states with emphasis on the adjacency and Laplacian…
We study the existence of state transfer with respect to the $q$-Laplacian matrix of a graph equipped with a non-trivial involution. We show that the occurrence of perfect state transfer between certain pair (or plus) states in such a graph…
In this paper we study quantum state transfer (also called quantum tunneling) on graphs when there is a potential function on the vertex set. We present two main results. First, we show that for paths of length greater than three, there is…
Quantum state transfer (QST) describes the coherent passage of quantum information from one node in a network to another. Experiments on QST span a diverse set of platforms and currently report transport across up to tens of nodes in times…
Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain; perfect state transfer,…
A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…