The unexpected isomorphism between a billiard system and a quantum algorithm

Abstract

The mathematician Gregory Galperin developed in his article “Playing Pool with π”, an incredible method for calculating the digits of the number π with an arbitrary precision, making use of an elementary system of Physics in Classical Mechanics: elastic collisions in one dimension. Inspired by Galperin's work, Adam Brown demonstrated that there is an isomorphism between the physical system used by Galperin and the famous quantum search algorithm: Grover's algorithm. The present project aims to understand the reason for this isomorphism. We develop the results in an original way explicitly demonstrating how the isomorphism between these two systems arises from their configuration spaces.