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

Adam R. Brown

doi:10.22331/q-2020-11-02-357

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

Published:	2020-11-02, volume 4, page 357
Eprint:	arXiv:1912.02207v2
Doi:	https://doi.org/10.22331/q-2020-11-02-357
Citation:	Quantum 4, 357 (2020).

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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.

Popular summary

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.

► BibTeX data

@article{Brown2020playingpool,
  doi = {10.22331/q-2020-11-02-357},
  url = {https://doi.org/10.22331/q-2020-11-02-357},
  title = {Playing {P}ool with {$|ψ\rangle$}: from {B}ouncing {B}illiards to {Q}uantum {S}earch},
  author = {Brown, Adam R.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {357},
  month = nov,
  year = {2020}
}

► 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.
https://www.youtube.com/watch?v=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.
https://doi.org/10.1145/237814.237866
arXiv:quant-ph/9605043

Cited by

[1] Maria Mannone and Davide Rocchesso, Quantum Computing in the Arts and Humanities 193 (2022) ISBN:978-3-030-95537-3.

[2] Yin Cai and Fu-Lin Zhang, "Hear π from quantum Galperin billiards", Canadian Journal of Physics 101 9, 491 (2023).

[3] Jiang Liu, "A Classical $\pi$ Machine and Grover's Algorithm", arXiv:2105.10257, (2020).

[4] X. M. Aretxabaleta, M. Gonchenko, N. L. Harshman, S. G. Jackson, M. Olshanii, and G. E. Astrakharchik, "The dynamics of digits: Calculating pi with Galperin's billiards", arXiv:1712.06698, (2017).

The above citations are from Crossref's cited-by service (last updated successfully 2023-12-07 03:23:36) and SAO/NASA ADS (last updated successfully 2023-12-07 03:23:39). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.