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Theoretical Foundations of Resource-Bounded Quantum Computation

Research Project

Project/Area Number 22H00522
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Review Section Medium-sized Section 60:Information science, computer engineering, and related fields
Research InstitutionWaseda University (2024)
NTT Communication Science Laboratories (2022-2023)

Principal Investigator

谷 誠一郎  早稲田大学, 教育・総合科学学術院, 教授 (70396183)

Co-Investigator(Kenkyū-buntansha) 森前 智行  京都大学, 基礎物理学研究所, 准教授 (50708302)
森 立平  名古屋大学, 多元数理科学研究科, 准教授 (60732857)
西村 治道  名古屋大学, 情報学研究科, 教授 (70433323)
七島 幹人  東京工業大学, 情報理工学院, 助教 (90855222)
Project Period (FY) 2022-04-01 – 2027-03-31
Project Status Granted (Fiscal Year 2024)
Budget Amount *help
¥40,560,000 (Direct Cost: ¥31,200,000、Indirect Cost: ¥9,360,000)
Fiscal Year 2025: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2024: ¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000)
Fiscal Year 2023: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2022: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Keywords計算資源 / 量子計算 / 計算理論 / 量子計算複雑さ
Outline of Research at the Start

本研究では,「使用可能な量子計算資源量(例:量子メモリ,量子通信)に制約がある」という現実的な状況下において,量子計算の理論基盤を創出する. さらに,その成果を通じて,量子優位性(古典計算機に対する性能優位性)を発揮できる応用分野の開拓,及び,主要な問題に対して量子優位性を担保するために必要な量子計算資源量の明確化を目指す.

Outline of Annual Research Achievements

委託量子計算分野に関しては,量子状態の区別可能性と変換可能性の双対性を用いることにより、古典暗号では可能であることが未知の仮定のもとで,量子公開鍵暗号を構成した。また、基底状態に近い状態を入力として基底エネルギーを求める問題に対し、物理的に自然なハミルトニアンでもBQP完全やQMA完全になることを示し,さらに近似値や局所性の改善にも成功した。
分散量子計算分野では,ネットワーク上での量子非対話型証明(分散量子非対話型証明)に関し,先行研究では最終的な検証でのノード間量子通信を認めているが,証明部分の量子情報を増やすことにより,ノード間通信は古典で十分であることを証明した.また,集合等価性問題に対する分散量子非対話型証明プロトコルを提案し,量子優位性を明らかにした.
量子計算機単体分野では,古典計算では可能な「計算の巻き戻し」を量子計算に対して仮定すると,通常考えられているよりもはるかに大きい計算能力を発揮する状況証拠を得た.これは,測定が非可逆であるという量子力学の公理の合理性を,計算量理論的側面から支持するものである.また,応用的観点からは,無線通信における最適化問題を Groverのアルゴリズムで解く手法を提案し,必要な qubit数、ゲート数、反復回数を解析した。
量子情報処理の限界について理解を深めるため,暗号理論の最重要要素の1つである一方向性関数に対して,古典の設定における新しい3つの基本的特徴付け,(i)アルゴリズム的情報の平均時対称性による特徴付け,(ii)学習困難性に基づく特徴付け,及び,(iii)ある(自然な)約束問題の最悪時困難性による特徴づけを証明した.これは,安全な暗号の構成に本質的に必要となる計算困難性や情報の性質について従来の知見を強化する成果であり,将来的に暗号技術の安全性根拠の強化に繋がることが期待される.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

各研究項目において,計画していた検討が順調に進んでいるため.

Strategy for Future Research Activity

引き続き.量子計算の3つの主要分野(委託量子計算,分散量子計算,単体量子計算),及び,量子計算能力の限界に関する理解を深めるために必要な古典計算理論を柱として,組織的かつ横断的に研究を進めていく.このために,必要に応じてミーティングを実施するなどして,議論を深めていく.さらに,波及効果の大きい成果につなげるため,本課題の分担者以外の専門家とも必要に応じて交流・議論を行ない,隣接分野に対する理解を深める.

Report

(3 results)
  • 2023 Annual Research Report
  • 2022 Comments on the Screening Results   Annual Research Report
  • Research Products

    (34 results)

All 2024 2023 2022 Other

All Int'l Joint Research (6 results) Journal Article (18 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 17 results,  Open Access: 14 results) Presentation (9 results) (of which Int'l Joint Research: 5 results,  Invited: 1 results) Book (1 results)

  • [Int'l Joint Research] University of Warwick/University of Oxford(英国)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Massachusetts Institute of Technology(米国)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] KIAS(韓国)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] QuSoft/University of Amsterdam/CWI(オランダ)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Paderborn University(ドイツ)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] KIAS(韓国)

    • Related Report
      2022 Annual Research Report
  • [Journal Article] Probabilistic state synthesis based on optimal convex approximation2024

    • Author(s)
      Akibue Seiseki、Kato Go、Tani Seiichiro
    • Journal Title

      npj Quantum Information

      Volume: 10 Issue: 1

    • DOI

      10.1038/s41534-023-00793-7

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] From the Hardness of Detecting Superpositions to Cryptography: Quantum Public Key Encryption and Commitments2023

    • Author(s)
      Minki Hhan, Tomoyuki Morimae, Takashi Yamakawa
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 14004 Pages: 639-667

    • DOI

      10.1007/978-3-031-30545-0_22

    • ISBN
      9783031305443, 9783031305450
    • Related Report
      2023 Annual Research Report 2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Improved Hardness Results for the Guided Local Hamiltonian Problem2023

    • Author(s)
      Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, Francois Le Gall, Tomoyuki Morimae, Jordi Weggemans
    • Journal Title

      Leibniz International Proceedings in Informatics (LIPIcs)

      Volume: 261

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A Duality between One-Way Functions and Average-Case Symmetry of Information2023

    • Author(s)
      Hirahara Shuichi、Ilango Rahul、Lu Zhenjian、Nanashima Mikito、Oliveira Igor C.
    • Journal Title

      Proceedings of the 55th Annual ACM Symposium on Theory of Computing

      Volume: 55 Pages: 1039-1050

    • DOI

      10.1145/3564246.3585138

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Learning in Pessiland via Inductive Inference2023

    • Author(s)
      Hirahara Shuichi、Nanashima Mikito
    • Journal Title

      Proceedings of the 64th IEEE Annual Symposium on Foundations of Computer Science

      Volume: 64 Pages: 447-457

    • DOI

      10.1109/focs57990.2023.00033

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications2023

    • Author(s)
      Francois Le Gall, Masayuki Miyamoto, Harumichi Nishimura
    • Journal Title

      Leibniz International Proceedings in Informatics (LIPIcs)

      Volume: 272

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 情報と計算機2023

    • Author(s)
      西村治道
    • Journal Title

      数理科学

      Volume: 723 Pages: 36-42

    • Related Report
      2023 Annual Research Report
  • [Journal Article] Rewindable quantum computation and its equivalence to cloning and adaptive postselection2023

    • Author(s)
      Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, Seiichiro Tani
    • Journal Title

      Leibniz International Proceedings in Informatics, LIPIcs

      Volume: 266

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Proofs of quantumness from trapdoor permutations2023

    • Author(s)
      Tomoyuki Morimae, Takashi Yamakawa
    • Journal Title

      ITCS 2023, Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, LIPIcs

      Volume: 251

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Distributed Quantum Interactive Proofs2023

    • Author(s)
      Francois Le Gall, Masayuki Miyamoto, Harumichi Nishimura
    • Journal Title

      STACS 2023, Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, LIPIcs

      Volume: 254

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quantum Algorithm for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection2022

    • Author(s)
      Masaya Norimoto, Ryuhei Mori, and Naoki Ishikawa
    • Journal Title

      IEEE Transactions on Communications

      Volume: 71 Issue: 4 Pages: 1926-1939

    • DOI

      10.1109/tcomm.2023.3244924

    • Related Report
      2023 Annual Research Report 2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum commitments and signatures without one-way functions2022

    • Author(s)
      Tomoyuki Morimae, Takashi Yamakawa
    • Journal Title

      Crypto 2022, Lecture Notes in Computer Science

      Volume: 13507 Pages: 269-295

    • DOI

      10.1007/978-3-031-15802-5_10

    • ISBN
      9783031158018, 9783031158025
    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Certified Everlasting Zero-Knowledge Proof for QMA2022

    • Author(s)
      Taiga Hiroka, Tomoyuki Morimae, Ryo Nishimaki, Takashi Yamakawa
    • Journal Title

      Crypto 2022, Lecture Notes in Computer Science

      Volume: 13507 Pages: 239-268

    • DOI

      10.1007/978-3-031-15802-5_9

    • ISBN
      9783031158018, 9783031158025
    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Exponential-time quantum algorithms for graph coloring problems2022

    • Author(s)
      Kazuya Shimizu and Ryuhei Mori
    • Journal Title

      Algorithmica

      Volume: 84 Issue: 12 Pages: 3603-3621

    • DOI

      10.1007/s00453-022-00976-2

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Brief Announcement: Distributed Quantum Interactive Proofs2022

    • Author(s)
      Francois Le Gall, Masayuki Miyamoto, Harumichi Nishimura
    • Journal Title

      DISC 2022, Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, LIPIcs

      Volume: 246

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Space-Bounded Unitary Quantum Computation with Postselection2022

    • Author(s)
      Seiichiro Tani
    • Journal Title

      MFCS 2022, Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, LIPIcs

      Volume: 241

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Divide-and-conquer verification method for noisy intermediate-scale quantum computation2022

    • Author(s)
      Yuki Takeuchi, Yasuhiro Takahashi, Tomoyuki Morimae, Seiichiro Tani
    • Journal Title

      Quantum

      Volume: 6 Pages: 758-758

    • DOI

      10.22331/q-2022-07-07-758

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Computational self-testing for entangled magic states2022

    • Author(s)
      Mizutani Akihiro、Takeuchi Yuki、Hiromasa Ryo、Aikawa Yusuke、Tani Seiichiro
    • Journal Title

      Physical Review A

      Volume: 106 Issue: 1

    • DOI

      10.1103/physreva.106.l010601

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] 量子通信路のエンコードとその応用2023

    • Author(s)
      尾形勇輔
    • Organizer
      第48回量子情報技術研究会
    • Related Report
      2023 Annual Research Report
  • [Presentation] More Distributed Quantum Merlin-Arthur Protocols: Improvement and Extension2023

    • Author(s)
      Harumichi Nishimura
    • Organizer
      Shenzhen-Nagoya Workshop on Quantum Science 2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Divide-and-conquer verification method for noisy intermediate-scale quantum computation2023

    • Author(s)
      Yuki Takeuchi, Yasuhiro Takahashi, Tomoyuki Morimae, Seiichiro Tani
    • Organizer
      23rd Asian Quantum Information Science Conference (AQIS 2023)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Probabilistic unitary and state synthesis with optimal accuracy2023

    • Author(s)
      Seiseki Akibue, Go Kato, Seiichiro Tani
    • Organizer
      23rd Asian Quantum Information Science Conference (AQIS 2023)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 群非所属問題の証拠生成に対する検証プロトコル2023

    • Author(s)
      川合達也, 西村治道
    • Organizer
      情報処理学会 第8回量子ソフトウェア研究会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Power of Distributed Quantum Merlin-Arthur Proofs2022

    • Author(s)
      Harumichi Nishimura
    • Organizer
      SUSTech-Nagoya workshop on Quantum Science 2022
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Computational self-testing for entangled magic states2022

    • Author(s)
      Akihiro Mizutani, Yuki Takeuchi, Ryo Hiromasa, Yusuke Aikawa, and Seiichiro Tani
    • Organizer
      Beyond IID in Information Theory 10 (BIID’10)
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 近似精度において最適な確率的量子コンパイラ2022

    • Author(s)
      秋笛 清石, 加藤 豪, 谷 誠一郎
    • Organizer
      電子情報通信学会 量子情報技術研究会 (QIT47)
    • Related Report
      2022 Annual Research Report
  • [Presentation] Computational self-testing for entangled magic states2022

    • Author(s)
      Akihiro Mizutani, Yuki Takeuchi, Ryo Hiromasa, Yusuke Aikawa, and Seiichiro Tani
    • Organizer
      電子情報通信学会 量子情報技術研究会 (QIT46)
    • Related Report
      2022 Annual Research Report
  • [Book] 基礎から学ぶ量子計算2022

    • Author(s)
      西村 治道
    • Total Pages
      264
    • Publisher
      オーム社
    • ISBN
      9784274229695
    • Related Report
      2022 Annual Research Report

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Published: 2022-04-19   Modified: 2025-04-17  

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