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An example is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy<jats:sup>3<\/jats:sup>. Certified randomness has many applications but is impossible to achieve solely by classical computation. Here we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the Internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations<jats:sup>4,5<\/jats:sup>: a client generates quantum \u2018challenge\u2019 circuits using a small randomness seed, sends them to an untrusted quantum server to execute and verifies the results of the server. We analyse the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of 1.1\u2009\u00d7\u200910<jats:sup>18<\/jats:sup> floating-point operations per second across multiple supercomputers, we certify 71,313 bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of present-day quantum computers.<\/jats:p>","DOI":"10.1038\/s41586-025-08737-1","type":"journal-article","created":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T18:07:39Z","timestamp":1743012459000},"page":"343-348","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Certified randomness using a trapped-ion quantum processor"],"prefix":"10.1038","volume":"640","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6184-8214","authenticated-orcid":false,"given":"Minzhao","family":"Liu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8657-2848","authenticated-orcid":false,"given":"Ruslan","family":"Shaydulin","sequence":"additional","affiliation":[]},{"given":"Pradeep","family":"Niroula","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9459-8140","authenticated-orcid":false,"given":"Matthew","family":"DeCross","sequence":"additional","affiliation":[]},{"given":"Shih-Han","family":"Hung","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8174-6004","authenticated-orcid":false,"given":"Wen Yu","family":"Kon","sequence":"additional","affiliation":[]},{"given":"Enrique","family":"Cervero-Mart\u00edn","sequence":"additional","affiliation":[]},{"given":"Kaushik","family":"Chakraborty","sequence":"additional","affiliation":[]},{"given":"Omar","family":"Amer","sequence":"additional","affiliation":[]},{"given":"Scott","family":"Aaronson","sequence":"additional","affiliation":[]},{"given":"Atithi","family":"Acharya","sequence":"additional","affiliation":[]},{"given":"Yuri","family":"Alexeev","sequence":"additional","affiliation":[]},{"given":"K. 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The authors declare no other competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}