2026-07-22T14:20:38Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16519 2024-03-06T10:57:43Z ddc:004 open_access

Qutrit Metaplectic Gates Are a Subset of Clifford+T Glaudell, Andrew N. Ross, Neil J. van de Wetering, John Yeh, Lia Quantum computation qutrits gate synthesis metaplectic gate Clifford+T A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes Clifford+T approximately universal, is injectable by a magic state, and supports magic state distillation. However, it was claimed that a better gate set for qutrits might be Clifford+R, where R = diag(1,1,-1) is the metaplectic gate, as certain protocols and gates could more easily be implemented using the R gate than the T gate. In this paper we show that the qutrit Clifford+R unitaries form a strict subset of the Clifford+T unitaries when we have at least two qutrits. We do this by finding a direct decomposition of R ⊗ 𝕀 as a Clifford+T circuit and proving that the T gate cannot be exactly synthesized in Clifford+R. This shows that in fact the T gate is more expressive than the R gate. Moreover, we additionally show that it is impossible to find a single-qutrit Clifford+T decomposition of the R gate, making our result tight. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrew N. Glaudell and Neil J. Ross and John van de Wetering and Lia Yeh 2022 Is Part Of LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2022.12 urn:nbn:de:0030-drops-165195 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.12 eng https://creativecommons.org/licenses/by/4.0/legalcode