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Reports on Mathematical Physics

Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

Demosthenes Ellinas, Christos Konstandakis

Published Feb 1, 2016• 7 citations
Publisher
DOI
10.1016/s0034-4877(16)30008-8

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This paper investigates the application of quantum walk-based search algorithms to address the scalability challenges inherent in classical search algorithms when dealing with massive datasets. The core premise is that quantum superposition and interference, inherent properties of quantum systems, offer a potential pathway to significantly enhance the efficiency of search operations. We propose and analyze quantum walk algorithms designed to explore search spaces more effectively than their classical counterparts. The focus is on theoretical development and algorithmic design, without experimental validation. We explore key concepts such as walker position, probability amplitudes, and interference effects within the framework of quantum walks. The algorithms are designed to be adaptable to both quantum hardware and quantum simulators. This work aims to demonstrate the theoretical feasibility and potential advantages of utilizing quantum walk algorithms for large-scale data search, contributing to the growing field of quantum search algorithms.
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q . For a given q , we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.
Abstract In this section, we introduce the basics of quantum walk algorithm and its applications. Quantum walk is a natural extension of the concept of random walk in quantum way; therefore, the results obtained from the discussion are considered as the results by Quantum Computation. In principle, we can expect a certain type of the computation would be boosted. There are a variety of phenomena in Quantum walks, and much broader outcomes are often obtained than those from classical random walk. Such famous examples include quantum search algorithms and quantum simulations. In this article, we introduce a quantum simulation of QCD parton shower algorithm appearing in particle physics.