# Playing Pool with $|ψ\rangle$: from Bouncing Billiards to Quantum Search

Google, Mountain View, CA 94043, USA
Department of Physics, Stanford University, Stanford, CA 94305, USA

### Abstract

In Playing Pool with $\pi$'' [1], Galperin invented an extraordinary method to learn the digits of $\pi$ 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.

In the 1990s, an extraordinary method was invented for generating the digits of π by counting the collisions of billiard balls. This paper shows that the billiard ball algorithm is step-for-step mathematically identical to a seemingly completely unrelated process: the proposed quantum search algorithm to be performed on quantum computers.

### ► References

[1] G. Galperin, Playing pool with $\pi$'', Regular and Chaotic Dynamics, v. 8, no. 4 (2003).
https:/​/​doi.org/​10.1070/​RD2003v008n04ABEH000252

[2] Grant Sanderson, The most unexpected answer to a counting puzzle'', https:/​/​youtu.be/​HEfHFsfGXjs.
[3] L. K. Grover, A Fast quantum mechanical algorithm for database search,'' Proceedings, 28th Annual ACM Symposium on the Theory of Computing (STOC), 1996, pages 212-219; arXiv:quant-ph/​9605043.