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We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.<\/jats:p>","DOI":"10.22331\/q-2025-05-12-1739","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T13:58:59Z","timestamp":1747058339000},"page":"1739","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Learning Quantum Processes with Quantum Statistical Queries"],"prefix":"10.22331","volume":"9","author":[{"given":"Chirag","family":"Wadhwa","sequence":"first","affiliation":[{"name":"School of Informatics, University of Edinburgh, Edinburgh, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mina","family":"Doosti","sequence":"additional","affiliation":[{"name":"School of Informatics, University of Edinburgh, Edinburgh, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Leslie G Valiant. ``A theory of the learnable''. 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