Analysis of quantum interactive proofs with restricted quantum communication and computation

• Project/Area Number: 16K00015
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Nagoya 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: ¥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．

Research Products

• [Int'l Joint Research] National University of Singapole(シンガポール)
• [Int'l Joint Research] University of Maryland(米国)
• [Journal Article] Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error (2018)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy (2018)
  • Author(s): Morimae Tomoyuki、Takeuchi Yuki、Nishimura Harumichi
  • Journal Title: Quantum Volume: 2 Pages: 106-106
  • DOI: 10.22331/q-2018-11-15-106
  • Peer Reviewed / Open Access
• [Journal Article] Power of one nonclean qubit (2017)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Merlinization of complexity classes above BQP (2017)
  • Author(s): Morimae Tomoyuki、Nishimura Harumichi
  • Journal Title: Quantum Information and Computation Volume: 17 Pages: 959-972
  • Peer Reviewed
• [Journal Article] Modified group non-membership is in promise-AWPP relative to group oracles (2017)
  • Author(s): Tomoyuki Morimae, Harumichi Nishimura, Francois Le Gall
  • Journal Title: Quantum Information and Computation Volume: 17 Pages: 0242-0250
  • Peer Reviewed
• [Presentation] Quantum Advantage for the LOCAL Model in Distributed Computing (2019)
  • Author(s): Francois Le Gall, Harumichi Nishimura, Ansis Rosmanis
  • Organizer: 36th International Symposium on Theoretical Aspects of Computer Science (STACS2019)
  • 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
  • Invited
• [Presentation] Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups (2018)
  • Author(s): Francois Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi
  • Organizer: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS2018)
  • Int'l Joint Research
• [Presentation] Rational proofs for quantum computing (2018)
  • Author(s): Tomoyuki Morimae, Harumichi Nishimura
  • Organizer: 18th Asian Quantum Information Science Conference (AQIS2018)
  • Int'l Joint Research
• [Presentation] Interactive proofs with polynomial-time quantum prover for computing the order of solvable groups (2018)
  • Author(s): Francois Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi
  • Organizer: 18th Asian Quantum Information Science Conference (AQIS2018)
  • 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
• [Presentation] Merlinization of complexity classes above BQP (2017)
  • Author(s): 森前智行、西村治道
  • Organizer: 第37回量子情報技術研究会
• [Presentation] Power of quantum computation with few clean qubits (2016)
  • 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
• [Presentation] Space-efficient error reduction for unitary quantum computations (2016)
  • 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
  • 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
• [Presentation] Power of quantum computation with few clean qubits (2016)
  • 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
  • Int'l Joint Research
• [Presentation] Space-efficient error reduction for unitary quantum computations (2016)
  • 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
  • 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
• [Remarks] 研究者個人のホームページ
  • URL: http://www.math.cm.is.nagoya-u.ac.jp/~hnishimura/