Related papers: Quantum walk based state transfer algorithms on th…
We systematically investigated perfect state transfer between antipodal nodes of discrete time quantum walks on variants of the cycles C_4, C_6 and C_8 for three choices of coin operator. Perfect state transfer was found, in general, to be…
This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence…
We present two quantum state sharing protocols where the channels are not maximally entangled states. By properly choosing the measurement basis it is possible to achieve unity fidelity transfer of the state if the parties collaborate. We…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
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…
This work focuses on understanding the quantum message complexity of two central problems in distributed computing, namely, leader election and agreement in synchronous message-passing communication networks. We show that quantum…
We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time…
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…
Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
A weighted graph $G$ with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in $G$. In this paper, we prove a fundamental result on equitable…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value. We first establish the…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is greatly larger than the marked number of vertices we are searching, $N \gg…
The lackadaisical quantum walk, a quantum analog of the lazy random walk, is obtained by adding a weighted self-loop transition to each state. Impacts of the self-loop weight $l$ on the final success probability in finding a solution make…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to…