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DOI: 10.4230/LIPIcs.MFCS.2018.26
URN: urn:nbn:de:0030-drops-96087
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9608/
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Le Gall, François ; Morimae, Tomoyuki ; Nishimura, Harumichi ; Takeuchi, Yuki

Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups

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Abstract

In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e., non-quantum) computation. Understanding the computational power of this model, which corresponds to polynomial-time quantum computation that can be efficiently verified classically, is a well-known open problem in quantum computing. Our result shows that computing the order of a solvable group, which is one of the most general problems for which quantum computing exhibits an exponential speed-up with respect to classical computing, can be realized in this model.

BibTeX - Entry

@InProceedings{legall_et_al:LIPIcs:2018:9608,
  author =	{Fran{\c{c}}ois Le Gall and Tomoyuki Morimae and Harumichi Nishimura and Yuki Takeuchi},
  title =	{{Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9608},
  URN =		{urn:nbn:de:0030-drops-96087},
  doi =		{10.4230/LIPIcs.MFCS.2018.26},
  annote =	{Keywords: Quantum computing, interactive proofs, group-theoretic problems}
}

Keywords: Quantum computing, interactive proofs, group-theoretic problems
Seminar: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 20.08.2018


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