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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2022.12
URN: urn:nbn:de:0030-drops-165195
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16519/
Glaudell, Andrew N. ;
Ross, Neil J. ;
van de Wetering, John ;
Yeh, Lia
Qutrit Metaplectic Gates Are a Subset of Clifford+T
Abstract
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 ⊗ ? 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.
BibTeX - Entry
@InProceedings{glaudell_et_al:LIPIcs.TQC.2022.12,
author = {Glaudell, Andrew N. and Ross, Neil J. and van de Wetering, John and Yeh, Lia},
title = {{Qutrit Metaplectic Gates Are a Subset of Clifford+T}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {12:1--12:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16519},
URN = {urn:nbn:de:0030-drops-165195},
doi = {10.4230/LIPIcs.TQC.2022.12},
annote = {Keywords: Quantum computation, qutrits, gate synthesis, metaplectic gate, Clifford+T}
}
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Keywords: |
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Quantum computation, qutrits, gate synthesis, metaplectic gate, Clifford+T |
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Collection: |
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17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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04.07.2022 |
