- Trading inverses for an irrep in the Solovay-Kitaev theorem
- Leibniz International Proceedings in Informatics
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- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
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].
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- Submitted manuscript
- 13th Conference on the Theory of Quantum Computation, Communication and Cryptography : TQC 2018, July 16-18, 2018, Sydney,
Edited by Stacey Jeffery.
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