Related papers: Quantum State Transfer in Graphs with Tails
For any graph $X$ with the adjacency matrix $A$, the transition matrix of the continuous-time quantum walk at time $t$ is given by the matrix-valued function $\mathcal{H}_X(t)=\mathrm{e}^{itA}$. We say that there is perfect state transfer…
We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out. We also provide new examples…
The question of perfect state transfer existence in quantum spin networks based on weighted graphs has been recently presented by many authors. We give a simple condition for characterizing weighted circulant graphs allowing perfect state…
The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time…
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…
In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a combinatorial property called strong cospectrality. Here we determine the…
In the light of recent advances in fabricating single layer quantum chips and a possible road toward development of multi-layer quantum chips, we review, in a detailed way, the subject of quantum state transfer with particular emphasis on…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It…
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…
Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum…
For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between…
Using graphs with clusters, we provide a unified approach for constructing graphs with pair state transfer-relative to the adjacency, Laplacian, and signless Laplacian matrix-between the same pair of states at the same time, despite being…
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by…
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…
We show a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flippings, and extend this method to distribution of an arbitrary unknown multi-qubit…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
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…
Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which…
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…