Related papers: Pretty Good State Transfer on Some NEPS
In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer: the transmission of quantum states without dissipation. The essential goal is to…
Chains of transmon qubits are considered promising systems to implement different quantum information tasks. In particular as channels that perform high-quality quantum state transfer. We study how changing the interaction strength between…
We study the protocol known as quantum state transfer for a strongly coupled antiferromagnetic spin chain or ring (acting as a spin bus), with weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that…
A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coefficients of certain bivariate dual-Hahn polynomials. For a…
The join $X\vee Y$ of two graphs $X$ and $Y$ is the graph obtained by joining each vertex of $X$ to each vertex of $Y$. We explore the behaviour of a continuous quantum walk on a weighted join graph having the adjacency matrix or Laplacian…
We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two…
By using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and…
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
We study state transfer in quantum walk on graphs relative to the adjacency matrix. Our motivation is to understand how the addition of pendant subgraphs affect state transfer. For two graphs $G$ and $H$, the Frucht-Harary corona product $G…
We prove that the corona product of two graphs has no Laplacian perfect state transfer whenever the first graph has at least two vertices. This complements a result of Coutinho and Liu who showed that no tree of size greater than two has…
In this paper, we study quantum walks on the extension of association schemes. Various state transfers can be achieved on these graphs, such as multiple state transfer among extreme points of a simplex, fractional revival on subsimplexes.…
We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two different values. We work…
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…
Let $G = (V, E)$ be a graph where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say that $A$ \emph{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$. A…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
We consider a spin network resembling an $\alpha$-helix structure and study quantum information transfer over this bio-inspired network. The model we use is the Davydov model in its elementary version without a phononic environment. We…
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
Let $G$ be a graph with nonnegative integer weights. A {\it unit acquisition move} transfers one unit of weight from a vertex to a neighbor that has at least as much weight. The {\it unit acquisition number} of a graph $G$, denoted…
There is perfect state transfer between two vertices of a graph, if a single excitation can travel with fidelity one between the corresponding sites of a spin system modeled by the graph. When the excitation is back at the initial site, for…
Pairwise compatibility graphs (PCGs) with non-negative integer edge weights recently have been used to describe rare evolutionary events and scenarios with horizontal gene transfer. Here we consider the case that vertices are separated by…