Related papers: Perfect State Transfer on Oriented Graphs
Discrete-time quantum walks are well-known for exhibiting localization, a quantum phenomenon where the walker remains at its initial location with high probability. In companion with a joint Letter, we introduce oscillatory localization,…
We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created.…
By considering distance-regular graphs as spin networks, first we introduce some particular spin Hamiltonians which are extended version of those of Refs.\cite{8,9''}. Then, by using spectral analysis techniques and algebraic combinatoric…
In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one dimensional cases, such as 1d spin chains. We…
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. We define the adjacency, incidence and Laplacian matrices of an oriented hypergraph and study each of them. We extend several matrix…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
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…
The transfer of quantum states has played an important role in quantum information processing. In fact, transfer of quantum states from point $A$ to $B$ with unit fidelity is very important for us and we focus on this case. In recent years,…
This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states,…
Suppose $C$ is a subset of non-zero vectors from the vector space $\mathbb{Z}_2^d$. The cubelike graph $X(C)$ has $\mathbb{Z}_2^d$ as its vertex set, and two elements of $\mathbb{Z}_2^d$ are adjacent if their difference is in $C$. If $M$ is…
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…
Graphs defined over a finite ring are well-studied in the literature. Due to their nature, these types of graphs connect several branches of mathematics, including algebra, number theory, matrix theory, and representation theory. In recent…
The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…
We investigate the quantum state transfer in a chain of particles satisfying q-deformed oscillators algebra. This general algebraic setting includes the spin chain and the bosonic chain as limiting cases. We study conditions for perfect…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional revival (FR) as well as to the role played by orthogonal…
We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…
The issue of quantum states' transfer -- in particular, for so-called Perfect State Transfer (PST) -- in the networks represented by the spin chains seems to be one of the major concerns in quantum computing. Especially, in the context of…
We show that deciding whether a graph admits perfect state transfer can be done in polynomial time with respect to the size of the graph on a classical computer.
Quantum spin networks can be used to transport information between separated registers in a quantum information processor. To find a practical implementation, the strict requirements of ideal models for perfect state transfer need to be…