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Prog. Phys."],"published-print":{"date-parts":[[2025,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A leading approach to algorithm design aims to minimize the number of operations in an algorithm\u2019s compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer\u2019s potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm\u2019s number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.<\/jats:p>","DOI":"10.1088\/1361-6633\/adac8b","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T22:52:50Z","timestamp":1737499970000},"page":"037601","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Resilience\u2013runtime tradeoff relations for quantum algorithms"],"prefix":"10.1088","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2075-4996","authenticated-orcid":true,"given":"Luis","family":"Pedro Garc\u00eda-Pintos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2065-1695","authenticated-orcid":true,"given":"Tom","family":"O\u2019Leary","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tanmoy","family":"Biswas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3235-3444","authenticated-orcid":true,"given":"Jacob","family":"Bringewatt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lukasz","family":"Cincio","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lucas T","family":"Brady","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi-Kai","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2025,2,3]]},"reference":[{"key":"ropadac8bbib1","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1201\/9781003358817-7","article-title":"Quantum computing 40 years later","author":"Preskill","year":"2023"},{"key":"ropadac8bbib2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/npjqi.2015.23","article-title":"Quantum algorithms: an overview","volume":"2","author":"Montanaro","year":"2016","journal-title":"npj Quantum Inf."},{"key":"ropadac8bbib3","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1038\/nature08812","article-title":"Quantum Computers","volume":"464","author":"Ladd","year":"2010","journal-title":"Nature"},{"key":"ropadac8bbib4","author":"Lidar","year":"2013"},{"key":"ropadac8bbib5","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1080\/00107514.2019.1667078","article-title":"Quantum error correction: an introductory guide","volume":"60","author":"Roffe","year":"2019","journal-title":"Contemp. 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