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Due to the unavailability of invariants for systems with more than one spatial dimension, the benefits of this framework have not yet been exploited in multi-dimensional systems. We construct a multi-dimensional Gaussian quantum invariant that permits the design of time-dependent potentials that let the ground state of an initial potential evolve towards the ground state of a final potential. The scope of this framework is demonstrated with the task of shuttling an ion around a corner which is a paradigmatic control problem in achieving scalability of trapped ion quantum information technology.<\/jats:p>","DOI":"10.22331\/q-2021-03-11-409","type":"journal-article","created":{"date-parts":[[2021,3,11]],"date-time":"2021-03-11T16:40:36Z","timestamp":1615480836000},"page":"409","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Quantum control with a multi-dimensional Gaussian quantum invariant"],"prefix":"10.22331","volume":"5","author":[{"given":"Selwyn","family":"Simsek","sequence":"first","affiliation":[{"name":"Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom"}]},{"given":"Florian","family":"Mintert","sequence":"additional","affiliation":[{"name":"Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom"}]}],"member":"9598","published-online":{"date-parts":[[2021,3,11]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"N. 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