Related papers: Perfect state transfer on distance-regular graphs …
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,…
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…
Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on the corresponding Laplacian matrix, and those graphs for which…
Perfect state transfer between qubits on a uniformly coupled network, with interactions specified by a graph, has advantages over an engineered chain, such as much faster transfer times (independent of the distance between the input and…
We study perfect state transfer and multiple state transfer in oriented normal Cayley graphs. We construct examples in a variety of groups, ranging from abelian to nonsolvable, and establish some general restrictions and nonexistence…
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 study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups, called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state…
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…
The \textit{transition matrix} of a graph $\Gamma$ with adjacency matrix $A$ is defined by $H(\tau ) := \exp(-\mathbf{i}\tau A)$, where $\tau \in \mathbb{R}$ and $\mathbf{i} = \sqrt{-1}$. The graph $\Gamma$ exhibits \textit{perfect state…
We characterize perfect state transfer on real-weighted graphs of the Johnson scheme $\mathcal{J}(n,k)$. Given $\mathcal{J}(n,k)=\{A_1, A_2, \cdots, A_k\}$ and $A(X) = w_0A_0 + \cdots + w_m A_m$, we show, using classical number theory…
We give a complete characterization of pretty good state transfer on paths between any pair of vertices with respect to the quantum walk model determined by the XY-Hamiltonian. If $n$ is the length of the path, and the vertices are indexed…
The quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. It is not easy to achieve in practice. The original idea of PST depends on the fundamentals of the continuous-time quantum walk. A path…
Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ relative to $A$ is defined by $H(t):=\exp{\left(-itA\right)},\;t\in\Rl$. The graph $G$ is said to admit pretty good state transfer between a pair of vertices $u$ and…
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…
In this paper, we study pretty good state transfer (PGST) in Grover walks on graphs. We consider transfer of quantum states that are localized at the vertices of a graph and we use Chebyshev polynomials to analyze PGST between such states.…
The paper investigates perfect state transfer (PST) in Grover walks on Cayley graphs over the dihedral group $D_n$. The Grover walk is a discrete-time quantum walk widely studied in quantum information processing. A Cayley graph…
We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer…
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.
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…
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…