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To make the most of quantum hardware it is crucial to process information in the most efficient way. One promising avenue is to use higher-dimensional systems, qudits, as the fundamental units of quantum information, in order to replace a fraction of the qubit-entangling gates with qudit-local gates. Here, we show how the complexity of multi-qubit circuits can be lowered significantly by employing qudit encodings, which we quantify by considering exemplary circuits with exactly known (multi-qubit) gate complexity. We discuss general principles for circuit compression, derive upper and lower bounds on the achievable advantage, and highlight the key role played by entanglement and the available gate set. Explicit experimental schemes for photonic as well as for trapped-ion implementations are provided and demonstrate a significant expected gain in circuit performance for both platforms.<\/jats:p>","DOI":"10.22331\/q-2023-10-16-1141","type":"journal-article","created":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T14:00:10Z","timestamp":1697464810000},"page":"1141","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":13,"title":["On the role of entanglement in qudit-based circuit compression"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5043-1122","authenticated-orcid":false,"given":"Xiaoqin","family":"Gao","sequence":"first","affiliation":[{"name":"Department of Physics, University of Ottawa, Advanced Research Complex, 25 Templeton Street, K1N 6N5, Ottawa, ON, Canada"},{"name":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8319-1321","authenticated-orcid":false,"given":"Paul","family":"Appel","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1950-8640","authenticated-orcid":false,"given":"Nicolai","family":"Friis","sequence":"additional","affiliation":[{"name":"Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria"},{"name":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5055-6240","authenticated-orcid":false,"given":"Martin","family":"Ringbauer","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Innsbruck, Institut f\u00fcr Experimentalphysik, Technikerstrasse 25, 6020 Innsbruck, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1985-4623","authenticated-orcid":false,"given":"Marcus","family":"Huber","sequence":"additional","affiliation":[{"name":"Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria"},{"name":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2023,10,16]]},"reference":[{"key":"0","unstructured":"Arkady K. 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