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Controllability tests can be used in the design of quantum devices to reduce the number of external controls. Their practical use is hampered, however, by the exponential scaling of their numerical effort with the number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit. We show that controllability is linked to the number of independent parameters, which can be obtained by dimensional expressivity analysis. We exemplify the application of the algorithm to qubit arrays with nearest-neighbour couplings and local controls. Our work provides a systematic approach to the resource-efficient design of quantum chips.<\/jats:p>","DOI":"10.22331\/q-2023-12-21-1214","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T12:35:11Z","timestamp":1703162111000},"page":"1214","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity"],"prefix":"10.22331","volume":"7","author":[{"given":"Fernando","family":"Gago-Encinas","sequence":"first","affiliation":[{"name":"Fachbereich Physik and Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, Arnimallee 14, 14195 Berlin, Germany"}]},{"given":"Tobias","family":"Hartung","sequence":"additional","affiliation":[{"name":"Northeastern University London, Devon House, St Katharine Docks, London, E1W 1LP, United Kingdom"},{"name":"Khoury College of Computer Sciences, Northeastern University, 440 Huntington Avenue, 202 West Village H Boston, MA 02115, USA"}]},{"given":"Daniel M.","family":"Reich","sequence":"additional","affiliation":[{"name":"Fachbereich Physik and Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, Arnimallee 14, 14195 Berlin, Germany"}]},{"given":"Karl","family":"Jansen","sequence":"additional","affiliation":[{"name":"NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany"}]},{"given":"Christiane P.","family":"Koch","sequence":"additional","affiliation":[{"name":"Fachbereich Physik and Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, Arnimallee 14, 14195 Berlin, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2023,12,21]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Michael A Nielsen and Isaac L Chuang. ``Quantum computation and quantum information''. 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