{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T01:53:54Z","timestamp":1775613234570,"version":"3.50.1"},"reference-count":98,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T00:00:00Z","timestamp":1757030400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"Randomized benchmarking (RB) protocols are widely used to measure an average error rate for a set of quantum logic gates. However, the standard version of RB is limited because it only benchmarks a processor's native gates indirectly, by using them in composite n<\/mml:mi><\/mml:math>-qubit Clifford gates. Standard RB's reliance on n<\/mml:mi><\/mml:math>-qubit Clifford gates restricts it to the few-qubit regime, because the fidelity of a typical composite n<\/mml:mi><\/mml:math>-qubit Clifford gate decreases rapidly with increasing n<\/mml:mi><\/mml:math>. Furthermore, although standard RB is often used to infer the error rate of native gates, by rescaling standard RB's error per Clifford to an error per native gate, this is an unreliable extrapolation. Direct RB is a method that addresses these limitations of standard RB, by directly benchmarking a customizable gate set, such as a processor's native gates. Here we provide a detailed introduction to direct RB, we discuss how to design direct RB experiments, and we present two complementary theories for direct RB. The first of these theories uses the concept of error propagation or scrambling in random circuits to show that direct RB is reliable for gates that experience stochastic Pauli errors. We prove that the direct RB decay is a single exponential, and that the decay rate is equal to the average infidelity of the benchmarked gates, under broad circumstances. This theory shows that group twirling is not required for reliable RB. Our second theory proves that direct RB is reliable for gates that experience general gate-dependent Markovian errors, using similar techniques to contemporary theories for standard RB. Our two theories for direct RB have complementary regimes of applicability, and they provide complementary perspectives on why direct RB works. Together these theories provide comprehensive guarantees on the reliability of direct RB.<\/jats:p>","DOI":"10.22331\/q-2025-09-05-1848","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T10:00:12Z","timestamp":1757066412000},"page":"1848","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["A Theory of Direct Randomized Benchmarking"],"prefix":"10.22331","volume":"9","author":[{"given":"Anthony M.","family":"Polloreno","sequence":"first","affiliation":[{"name":"JILA, NIST and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA"},{"name":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"}]},{"given":"Arnaud","family":"Carignan-Dugas","sequence":"additional","affiliation":[{"name":"Institute for Quantum Computing and the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"},{"name":"Keysight Technologies Canada, Kanata, ON K2K 2W5, Canada"}]},{"given":"Jordan","family":"Hines","sequence":"additional","affiliation":[{"name":"Department of Physics, University of California, Berkeley, CA 94720"},{"name":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"}]},{"given":"Robin","family":"Blume-Kohout","sequence":"additional","affiliation":[{"name":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"}]},{"given":"Kevin","family":"Young","sequence":"additional","affiliation":[{"name":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"}]},{"given":"Timothy","family":"Proctor","sequence":"additional","affiliation":[{"name":"Quantum Performance Laboratory, Sandia National Laboratories, Livermore, CA 94550 and Albuquerque, NM 87185"}]}],"member":"9598","published-online":{"date-parts":[[2025,9,5]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Seth T Merkel, Jay M Gambetta, John A Smolin, Stefano Poletto, Antonio D C\u00f3rcoles, Blake R Johnson, Colm A Ryan, and Matthias Steffen. ``Self-consistent quantum process tomography''. 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