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In this article, we bypass this limitation by performing the classical Monte-Carlo method on the quantum algorithm itself, achieving a higher than classical precision using low-depth circuits. We require the quantum algorithm to be weakly biased in order to avoid error accumulation during this process. Our method is parallel and can be as weakly biased as the constituent algorithm in some cases.<\/jats:p>","DOI":"10.1145\/3748666","type":"journal-article","created":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T11:09:11Z","timestamp":1753528151000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Low-depth Amplitude Estimation without Really Trying"],"prefix":"10.1145","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1685-9026","authenticated-orcid":false,"given":"Dinh-Long","family":"Vu","sequence":"first","affiliation":[{"name":"National University of Singapore, Centre for Quantum Technologies","place":["Singapore, Singapore"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1643-7517","authenticated-orcid":false,"given":"Bin","family":"Cheng","sequence":"additional","affiliation":[{"name":"National University of Singapore, Centre for Quantum Technologies","place":["Singapore, Singapore"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6728-8163","authenticated-orcid":false,"given":"Patrick","family":"Rebentrost","sequence":"additional","affiliation":[{"name":"National University of Singapore, Centre for Quantum Technologies","place":["Singapore, Singapore"]}]}],"member":"320","published-online":{"date-parts":[[2025,9,16]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976014.5"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/305\/05215"},{"key":"e_1_3_3_4_2","unstructured":"Paul Burchard. 2019. 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