An analysis of quantum walks

Leonid Evgenevich Fedichkin, Fedor Pavlovich Meshchaninov

Tomohiro Yamasaki, Hirotada Kobayashi, Hiroshi Imai

Manuel Curado, Francisco Escolano, Edwin R. Hancock +2 more

Giuseppe Di Molfetta

This book provides an overview of quantum walks, limits, and transport equations. After an introduction to quantum computing, quantum simulation, and then symmetries, it then narrows down to describe quantum transport and quantum walks. It provides a review of the basics of quantum mechanics and the underlying mathematical framework. The fundamentals of quantum walks are described, followed by an overview of plastic quantum walks including limits, analysis, and interpretation of results. Key features • Introduces the subject • Presents an overview of quantum walks and plastic quantum walks • Demonstrates quantum walk-based simulation schemes • Includes the plasticity of a circuit, i.e. the property that allows quantum walks to be convergent in continuous time and continuous or discrete space • Discusses limits, analysis, and interpretation of results

Sanjay Chakraborty, Soharab Hossain Shaikh, Sudhindu Bikash Mandal +2 more

Traditional machine learning shares several benefits with quantum information processing field. The study of machine learning with quantum mechanics is called quantum machine learning. Data clustering is an important tool for machine learning where quantum computing plays a vital role in its inherent speed up capability. In this paper, a hybrid quantum algorithm for data clustering (quantum walk-based hybrid clustering (QWBHC)) is introduced where one-dimensional discrete time quantum walks (DTQW) play the central role to update the positions of data points according to their probability distributions. A quantum oracle is also designed and it is mainly implemented on a finite [Formula: see text]-regular bipartite graph where data points are initially distributed as a predefined set of clusters. An overview of a quantum walk (QW) based clustering algorithm on 1D lattice structure is also introduced and described in this paper. In order to search the nearest neighbors, a unitary and reversible DTQW gives a quadratic speed up over the traditional classical random walk. This paper also demonstrates the comparisons of our proposed hybrid quantum clustering algorithm with some state-of-the-art clustering algorithms in terms of clustering accuracy and time complexity analysis. The proposed quantum oracle needs [Formula: see text] queries to mark the nearest data points among clusters and modify the existing clusters. Finally, the proposed QWBHC algorithm achieves [Formula: see text] performance.

Diego de Falco, Dario Tamascelli