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Analysis of quantum interactive proofs with restricted quantum communication and computation

Research Project

Project/Area Number 16K00015
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionNagoya University

Principal Investigator

Nishimura Harumichi  名古屋大学, 情報学研究科, 教授 (70433323)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Discontinued (Fiscal Year 2019)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords量子計算 / 対話型証明 / 計算量理論 / 量子計算の検証 / 量子計算量理論 / 量子対話型証明 / DQC1モデル / 量子コンピュータ / 量子通信
Outline of Final Research Achievements

The quantum interactive proofs is a natural extension of the quantum NP systems (one-round verification system) where multiple rounds of interaction are allowed between a unlimitedly powerful party (prover) and a polynomial-time computable party (verifier). While the quantum interactive proof is one of main topics in quantum computational complexity, it still has many unexplored points and the computational power has been unknown. To investigate this model in a more fine grained way, we have studied the computational power and the limitation of quantum interactive proofs by restricting quantum communication and computation in several approaches. Moreover, we have shown the power of restricted quantum computation models such as DQC1 models by using the analysis of quantum interactive proofs that are obtained in this research.

Academic Significance and Societal Importance of the Research Achievements

量子計算は近年社会的に大きな注目を集めている.特に従来の計算機で効率的に行えないような何らかのタスクを近未来的に実現可能な量子計算機で行えるかという問題は,量子超越性と呼ばれて世界的に研究が加速している.しかしながら,量子計算機の計算能力の理論的解明は量子超越性の理論を含めて道半ばである.本研究の研究成果は,量子計算機の真の能力を明らかにするための基盤を固めるという学術的意義を持っている.また,近未来的に実現可能な量子計算による検証を意識して,制限された量子対話型証明の研究を行うとともに量子超越性の理論に対する貢献を行ったことで,社会的にも意義のある成果と考えられる.

Report

(4 results)
  • 2019 Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (21 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (2 results) Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 3 results,  Acknowledgement Compliant: 1 results) Presentation (12 results) (of which Int'l Joint Research: 7 results,  Invited: 1 results) Remarks (2 results)

  • [Int'l Joint Research] National University of Singapole(シンガポール)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Maryland(米国)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error2018

    • Author(s)
      Keisuke Fujii, Hirotada Kobayashi, Tomoyuki Morimae, Harumichi Nishimura, Shuhei Tamate, Seiichiro Tani
    • Journal Title

      Physical Review Letters

      Volume: 120 Issue: 20 Pages: 200502-200502

    • DOI

      10.1103/physrevlett.120.200502

    • NAID

      120006533116

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy2018

    • Author(s)
      Morimae Tomoyuki、Takeuchi Yuki、Nishimura Harumichi
    • Journal Title

      Quantum

      Volume: 2 Pages: 106-106

    • DOI

      10.22331/q-2018-11-15-106

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Power of one nonclean qubit2017

    • Author(s)
      Tomoyuki Morimae, Keisuke Fujii, Harumichi Nishimura
    • Journal Title

      Phys. Rev. A

      Volume: 95 Issue: 4 Pages: 042336-042336

    • DOI

      10.1103/physreva.95.042336

    • NAID

      120006331829

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Merlinization of complexity classes above BQP2017

    • Author(s)
      Morimae Tomoyuki、Nishimura Harumichi
    • Journal Title

      Quantum Information and Computation

      Volume: 17 Pages: 959-972

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Modified group non-membership is in promise-AWPP relative to group oracles2017

    • Author(s)
      Tomoyuki Morimae, Harumichi Nishimura, Francois Le Gall
    • Journal Title

      Quantum Information and Computation

      Volume: 17 Pages: 0242-0250

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Presentation] Quantum Advantage for the LOCAL Model in Distributed Computing2019

    • Author(s)
      Francois Le Gall, Harumichi Nishimura, Ansis Rosmanis
    • Organizer
      36th International Symposium on Theoretical Aspects of Computer Science (STACS2019)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 量子計算量クラスについて2018

    • Author(s)
      西村治道
    • Organizer
      ImPACT未来開拓研究会2018
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups2018

    • Author(s)
      Francois Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi
    • Organizer
      43rd International Symposium on Mathematical Foundations of Computer Science (MFCS2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Rational proofs for quantum computing2018

    • Author(s)
      Tomoyuki Morimae, Harumichi Nishimura
    • Organizer
      18th Asian Quantum Information Science Conference (AQIS2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Interactive proofs with polynomial-time quantum prover for computing the order of solvable groups2018

    • Author(s)
      Francois Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi
    • Organizer
      18th Asian Quantum Information Science Conference (AQIS2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] make10の一般化について2018

    • Author(s)
      佐伯元春、西村治道
    • Organizer
      第13回組合せゲーム・パズル研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] Merlinization of complexity classes above BQP2017

    • Author(s)
      森前智行、西村治道
    • Organizer
      第37回量子情報技術研究会
    • Related Report
      2017 Research-status Report
  • [Presentation] Power of quantum computation with few clean qubits2016

    • Author(s)
      藤井啓祐,小林弘忠,森前智行,西村治道,玉手修平,谷誠一郎
    • Organizer
      第35回量子情報技術研究会
    • Place of Presentation
      高エネルギー加速器研究機構つくばキャンパス(つくば市)
    • Year and Date
      2016-11-24
    • Related Report
      2016 Research-status Report
  • [Presentation] Space-efficient error reduction for unitary quantum computations2016

    • Author(s)
      Bill Fefferman, Hirotada Kobayashi, Cedric Yen-Yu Lin, Tomoyuki Morimae, Harumichi Nishimura
    • Organizer
      16th Asian Quantum Information Science Conference (AQIS2016)
    • Place of Presentation
      Taipei (Taiwan)
    • Year and Date
      2016-08-28
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] メモリ限定量子計算量について2016

    • Author(s)
      西村治道
    • Organizer
      研究会「量子情報と有限長の新展開」
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2016-08-03
    • Related Report
      2016 Research-status Report
  • [Presentation] Power of quantum computation with few clean qubits2016

    • Author(s)
      Keisuke Fujii, Hirotada Kobayashi, Tomoyuki Morimae, Harumichi Nishimura, Shuhei Tamate, Seiichiro Tani
    • Organizer
      43rd International Colloquium on Automata, Languages, and Programming (ICALP2016)
    • Place of Presentation
      Rome (Italy)
    • Year and Date
      2016-07-12
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Space-efficient error reduction for unitary quantum computations2016

    • Author(s)
      Bill Fefferman, Hirotada Kobayashi, Cedric Yen-Yu Lin, Tomoyuki Morimae, Harumichi Nishimura
    • Organizer
      43rd International Colloquium on Automata, Languages, and Programming (ICALP2016)
    • Place of Presentation
      Rome (Italy)
    • Year and Date
      2016-07-12
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Remarks] 研究者のホームページ

    • URL

      http://www.math.cm.is.nagoya-u.ac.jp/~hnishimura

    • Related Report
      2018 Annual Research Report
  • [Remarks] 研究者個人のホームページ

    • URL

      http://www.math.cm.is.nagoya-u.ac.jp/~hnishimura/

    • Related Report
      2017 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2022-02-16  

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