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arXiv:1912.02207 · Quantum

Playing Pool with |ψ⟩ : from Bouncing Billiards to Quantum Search

Adam R. Brown

Published Nov 2, 2020• 10 citations
arXivHTMLPDF

Abstract

In ``Playing Pool with π '' \cite{Galperin}, Galperin invented an extraordinary method to learn the digits of π by counting the collisions of billiard balls. Here I demonstrate an exact isomorphism between Galperin's bouncing billiards and Grover's algorithm for quantum search. This provides an illuminating way to visualize Grover's algorithm.

DOI
10.22331/q-2020-11-02-357

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In ``Playing Pool with π '' \cite{Galperin}, Galperin invented an extraordinary method to learn the digits of π by counting the collisions of billiard balls. Here I demonstrate an exact isomorphism between Galperin's bouncing billiards and Grover's algorithm for quantum search. This provides an illuminating way to visualize Grover's algorithm.
This study investigates the applications and adaptations of the Grover's search algorithm, an algorithm that uses quantum technologies to provide quadratic speedup while searching unsorted data. Through extensive literature review, the applications of Grover's algorithm such as database search, machine learning, cryptography, and optimization is explored in order to further understand areas open to alteration in the algorithm. Visuals are provided with the aim of enhancing the comprehension of Grover's algorithm. This study underscores how various components of Grover's search-like the oracle, diffusion operator, and iteration count-can be modified to solve complex problems more efficiently than classical search algorithms. A table generalizing aspects of modification and each of their benefits is given as an output. The growing importance of quantum technologies and the United Nations' selection of 2025 as the International Year of Quantum Science and Technology makes this research timely.
Certain classes of integrable quantum billiards provide a versatile arena for time-domain atom optics experiments. In order to learn how to fully exploit the fractional revival behavior that governs these kinds of systems, we here develop a convenient theoretical framework for their description. As an illustrative example, we present a billiard-internal realization of Grover's quantum search algorithm. The considered devices are scalable and could be used for the construction of quantum computers using trapped neutral atoms.