License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2018.6
URN: urn:nbn:de:0030-drops-92539
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9253/
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Bouland, Adam ; Ozols, Maris

Trading Inverses for an Irrep in the Solovay-Kitaev Theorem

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LIPIcs-TQC-2018-6.pdf (0.5 MB)

Abstract

The Solovay-Kitaev theorem states that universal quantum gate sets can be exchanged with low overhead. More specifically, any gate on a fixed number of qudits can be simulated with error epsilon using merely polylog(1/epsilon) gates from any finite universal quantum gate set G. One drawback to the theorem is that it requires the gate set G to be closed under inversion. Here we show that this restriction can be traded for the assumption that G contains an irreducible representation of any finite group G. This extends recent work of Sardharwalla et al. [Sardharwalla et al., 2016], and applies also to gates from the special linear group. Our work can be seen as partial progress towards the long-standing open problem of proving an inverse-free Solovay-Kitaev theorem [Dawson and Nielsen, 2006; Kuperberg, 2015].

BibTeX - Entry

@InProceedings{bouland_et_al:LIPIcs:2018:9253,
  author =	{Adam Bouland and Maris Ozols},
  title =	{{Trading Inverses for an Irrep in the Solovay-Kitaev Theorem}},
  booktitle =	{13th Conference on the Theory of Quantum Computation,  Communication and Cryptography (TQC 2018)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-080-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{111},
  editor =	{Stacey Jeffery},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9253},
  URN =		{urn:nbn:de:0030-drops-92539},
  doi =		{10.4230/LIPIcs.TQC.2018.6},
  annote =	{Keywords: Solovay-Kitaev theorem, quantum gate sets, gate set compilation}
}

Keywords: Solovay-Kitaev theorem, quantum gate sets, gate set compilation
Collection: 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)
Issue Date: 2018
Date of publication: 16.07.2018

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