Related papers: Quantum State Transfer on a Class of Circulant Gra…
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…
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 all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties,…
We consider a system of qubits coupled via nearest-neighbour interaction governed by the Heisenberg Hamiltonian. We further suppose that all coupling constants are equal to $1$. We are interested in determining which graphs allow for a…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
Given a known or unknown phase encoded in a higher-dimensional qudit gate, it is possible to send copies of a gate that encodes the phase to multiple receivers based on a generalized quantum teleportation. We extend this quantum gate…
Recent technological advances have allowed the fabrication of large arrays of coupled qubits serving as prototypes of quantum processors. However, the optimal control of such systems is notoriously hard, which limits the potential of…
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…
We investigate state transfer on a hypercube by means of a quantum walk where the sender and the receiver vertices are marked by a weighted loops. First, we analyze search for a single marked vertex, which can be used for state transfer…
This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…
In this paper, we consider the problem on the existence of perfect state transfer(PST for short) on semi-Cayley graphs over abelian groups (which are not necessarily regular), i.e on the graphs having semiregular and abelian subgroups of…
In 2018, Chen and Godsil proposed the concept of Laplacian perfect pair state transfer which is a brilliant generalization of Laplacian perfect state transfer. In this paper, we study the existence of Laplacian perfect pair state transfer…
A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following: - The…
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…
In this work we introduce the concept of a quantum walk on a hypergraph. We show that the staggered quantum walk model is a special case of a quantum walk on a hypergraph.
The aim of this review paper is to discuss some applications of orthogonal polynomials in quantum information processing. The hope is to keep the paper self contained so that someone wanting a brief introduction to the theory of orthogonal…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…