{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T08:28:40Z","timestamp":1770712120060,"version":"3.49.0"},"reference-count":3,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>In ``Playing Pool with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c0<\/mml:mi><\/mml:math>'' \\cite{Galperin}, Galperin invented an extraordinary method to learn the digits of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c0<\/mml:mi><\/mml:math> 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.<\/jats:p>","DOI":"10.22331\/q-2020-11-02-357","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T13:19:01Z","timestamp":1604323141000},"page":"357","source":"Crossref","is-referenced-by-count":7,"title":["Playing Pool with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\u03c8<\/mml:mo><\/mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">\u27e9<\/mml:mo><\/mml:math>: from Bouncing Billiards to Quantum Search"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4546-4939","authenticated-orcid":false,"given":"Adam R.","family":"Brown","sequence":"first","affiliation":[{"name":"Google, Mountain View, CA 94043, USA"},{"name":"Department of Physics, Stanford University, Stanford, CA 94305, USA"}]}],"member":"9598","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"G. Galperin, ``Playing pool with $\\pi$'', Regular and Chaotic Dynamics, v. 8, no. 4 (2003).","DOI":"10.1070\/RD2003v008n04ABEH000252"},{"key":"1","unstructured":"Grant Sanderson, ``The most unexpected answer to a counting puzzle'', https:\/\/youtu.be\/HEfHFsfGXjs."},{"key":"2","doi-asserted-by":"publisher","unstructured":"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.","DOI":"10.1145\/237814.237866"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2020-11-02-357\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T13:19:07Z","timestamp":1604323147000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2020-11-02-357\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,2]]},"references-count":3,"URL":"https:\/\/doi.org\/10.22331\/q-2020-11-02-357","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,2]]},"article-number":"357"}}