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

Authors François Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi

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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum computing
  • interactive proofs
  • group-theoretic problems

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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.

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François Le Gall, Tomoyuki Morimae, Harumichi Nishimura, and Yuki Takeuchi. Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.MFCS.2018.26

Author Details

François Le Gall
  • Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
Tomoyuki Morimae
  • Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
Harumichi Nishimura
  • Graduate School of Informatics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8601, Japan
Yuki Takeuchi
  • NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
  • Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan

Funding

  • Le Gall, François: Partially supported by the JSPS KAKENHI grants No. 15H01677, No. 16H01705 and No. 16H05853.
  • Morimae, Tomoyuki: Supported by JST PRESTO No. JPMJPR176A, and the Grant-in-Aid for Young Scientists (B) No. JP17K12637 of JSPS.
  • Nishimura, Harumichi: Partially supported by the JSPS KAKENHI grants No. 26247016, No. 16H01705 and No. 16K00015.
  • Takeuchi, Yuki: Supported by the Program for Leading Graduate Schools: Interactive Materials Science Cadet Program.

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