Related papers: Quantum walks can find a marked element on any gra…
We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin…
Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix $U$ and the vertex-face incidence structure. Using the…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
Quantum walks are expected to provide useful algorithmic tools for quantum computation. This paper introduces absorbing probability and time of quantum walks and gives both numerical simulation results and theoretical analyses on Hadamard…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a…
A randomly walking quantum particle evolving by Schr\"odinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time $\Theta(N^{3/4})$. In this paper, we give a weighted version of this graph that…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We demonstrate an implementation of the hitting time of a discrete time quantum random walk on cubelike graphs using IBM's Qiskit platform. Our implementation is based on efficient circuits for the Grover and Shift operators. We verify the…
Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
We study quantum walks through chains consisting of two and three star graphs. The first star has a distinguished vertex labelled START and the last has one labelled END. There are multiple paths between these two vertices, and the object…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
The time evolutions of discrete-time quantum walks on graphs are determined by the local adjacency relations of the graphs. In this paper, first, we construct a discrete-time quantum walk model that reflects the embedding on the surface so…
We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes coming out of a central hub. If there are…