Related papers: A hybrid quantum walk model unifying discrete and …
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
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.
With the increasing crossover between quantum information and machine learning, quantum simulation of neural networks has drawn unprecedentedly strong attention, especially for the simulation of associative memory in Hopfield neural…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
The Metropolis-Hastings algorithm is a cornerstone of Markov Chain Monte Carlo methods, underpinning a wide range of applications in computational physics, Bayesian inference, and machine learning. Quantum variants of Metropolis-Hastings…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
Distributing arbitrary graph states across quantum networks is a central challenge for modular quantum computing and measurement-based quantum communication. We introduce the phase quantum walk (PQW), a discrete-time quantum walk in which…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
We demonstrate a platform for implementing quantum walks that overcomes many of the barriers associated with photonic implementations. We use coupled fiber-optic cavities to implement time-bin encoded walks in an integrated system. We show…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
Quantum walks are more than tools for building quantum algorithms. They have been used effectively to model and simulate quantum dynamics in many complex physical processes. Particularly, a variant of discrete-time quantum walk known as…
We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the…
The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs,…
We consider to what extent quantum walks can constitute models of thermalization, analogously to how classical random walks can be models for classical thermalization. In a quantum walk over a graph, a walker moves in a superposition of…