{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T01:52:52Z","timestamp":1775181172631,"version":"3.50.1"},"reference-count":88,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T00:00:00Z","timestamp":1767139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"RSF","doi-asserted-by":"publisher","award":["24-71-00084"],"award-info":[{"award-number":["24-71-00084"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Priority 2030 program at the NUST \u201cMISIS\u201d","award":["K1-2022-027"],"award-info":[{"award-number":["K1-2022-027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum computation with d-level quantum systems, also known as qudits, benefits from the possibility to use a richer computational space compared to qubits. However, for an arbitrary qudit-based hardware platform, the issue is that a generic qudit operation has to be decomposed into the sequence of native operations\u2014pulses that are adjusted to the transitions between two levels in a qudit. Typically, not all levels in a qudit are simply connected to each other due to specific selection rules. Moreover, the number of pulses plays a significant role, since each pulse takes a certain execution time and may introduce error. In this paper, we propose a resource-efficient algorithm to decompose single-qudit operations into the sequence of pulses that are allowed by qudit selection rules. Using the developed algorithm, the number of pulses is at most d(d\u22121)\/2 for an arbitrary single-qudit operation. For specific operations, the algorithm could produce even fewer pulses. We provide a comparison of qudit decompositions for several types of trapped ions, specifically Yb+171, Ba+137 and Ca+40 with different selection rules, and also decomposition for superconducting qudits. Although our approach deals with single-qudit operations, the proposed approach is important for realizing two-qudit operations since they can be implemented as a standard two-qubit gate that is surrounded by efficiently implemented single-qudit gates.<\/jats:p>","DOI":"10.3390\/e28010056","type":"journal-article","created":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T16:34:23Z","timestamp":1767198863000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Transition-Aware Decomposition of Single-Qudit Gates"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3114-4543","authenticated-orcid":false,"given":"Denis A.","family":"Drozhzhin","sequence":"first","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5760-441X","authenticated-orcid":false,"given":"Evgeniy O.","family":"Kiktenko","sequence":"additional","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4722-3418","authenticated-orcid":false,"given":"Aleksey K.","family":"Fedorov","sequence":"additional","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8321-7103","authenticated-orcid":false,"given":"Anastasiia S.","family":"Nikolaeva","sequence":"additional","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11032","DOI":"10.1073\/pnas.95.19.11032","article-title":"Quantum computing","volume":"95","author":"Brassard","year":"1998","journal-title":"Proc. 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