{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:33:02Z","timestamp":1765960382916,"version":"3.44.0"},"reference-count":42,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T00:00:00Z","timestamp":1754611200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["441423094"],"award-info":[{"award-number":["441423094"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["236615297"],"award-info":[{"award-number":["236615297"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["SFB 1119"],"award-info":[{"award-number":["SFB 1119"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Fujitsu Services GmbH","award":["Endowed professorship \"Quantum Inspired and Quantum Optimization\""],"award-info":[{"award-number":["Endowed professorship \"Quantum Inspired and Quantum Optimization\""]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not guarantee that only a correctly functioning quantum device can pass the test. We introduce a certification method for quantum gates tailored for a practical server-user scenario, where a classical user tests the results of exact quantum computations performed by a quantum server. This method is free from the systematic state preparation and measurement (SPAM) errors. For single-qubit gates, including those that form a universal set for single-qubit quantum computation, we demonstrate that our approach offers soundness guarantees based solely on the dimension assumption. Additionally, for a highly-relevant phase gate \u2013 which corresponds experimentally to a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03C0;<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>2<\/mml:mn><\/mml:math>-pulse \u2013 we prove that the method's sample complexity scales as <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi mathvariant=\"normal\">O<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mi>&amp;#x03B5;<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> relative to the average gate infidelity <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03B5;<\/mml:mi><\/mml:math>. By combining the SPAM-error-free and sound notion of certification with practical applicability, our approach paves the way for promising research into efficient and reliable certification methods for full-scale quantum computation.<\/jats:p>","DOI":"10.22331\/q-2025-08-08-1825","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T07:33:22Z","timestamp":1756280002000},"page":"1825","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Classical certification of quantum gates under the dimension assumption"],"prefix":"10.22331","volume":"9","author":[{"given":"Jan","family":"N\u00f6ller","sequence":"first","affiliation":[{"name":"Department of Computer Science, Technical University of Darmstadt, Darmstadt, 64289 Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolai","family":"Miklin","sequence":"additional","affiliation":[{"name":"Institute for Quantum Inspired and Quantum Optimization, Hamburg University of Technology, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Kliesch","sequence":"additional","affiliation":[{"name":"Institute for Quantum Inspired and Quantum Optimization, Hamburg University of Technology, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariami","family":"Gachechiladze","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Technical University of Darmstadt, Darmstadt, 64289 Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,8,8]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. 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