Unified Approach for Nanotechnology CAD/Computation by Algorithmic Analysis of Periodic Crystal Structures

• Project/Area Number: 22650002
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: IMAI Hiroshi 東京大学, 大学院・情報理工学系研究科, 教授 (80183010)
• Project Period (FY): 2010 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥360,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: 量子計算理論 / ナノテクノロジー / 量子もつれ / 量子情報組合せ論 / 計算幾何 / 離散幾何 / 周期グラフ / 離散構造 / 結晶構造 / Voronoi図

Research Abstract

Problems of computationally handling periodic crystal structures arise in related to nanotechnology such as arranging atoms in a specified manner on crystal surface by using AFM and investigating quantum computation. We analyzed these problems in a unified way of clarifying nice mathematical structures of periodic structures and established a way of performing nanotechnology CAD for the reconfiguration of atoms and for universality of measurement-based quantum computing.

Research Products

• [Journal Article] Matroid Enumeration for Incidence Geometry (2012)
  • Author(s): Y. Matsumoto, S. Moriyama, H. Imai, and D. Bremner
  • Journal Title: Discrete and Computational Geometry Volume: 47 Issue: 1 Pages: 17-43
  • DOI: 10.1007/s00454-011-9388-y
  • Peer Reviewed
• [Journal Article] Fast Elliptic Curve Cryptography Using Minimal Weight Conversion of d Integers. AISC2012 (2012)
  • Author(s): V. Suppakitpaisarn, M. Edahiro and H. Imai
  • Journal Title: Conferences in Research and Practice in Information Technology Volume: Vol.125 Pages: 15-26
  • URL: http://crpit.com/confpapers/CRPITV125Suppakitpaisarn.pdf
• [Journal Article] Calculating Average Joint Hamming Weight for Minimal Weight Conversion of d Integer (2012)
  • Author(s): V. Suppakitpaisarn, M. Edahiro, and H. Imai
  • Journal Title: Lecture Notes in Computer Science Volume: Vol.7157 Pages: 229-240
  • DOI: 10.1007/978-3-642-28076-4_23
  • ISBN: 9783642280757, 9783642280764
• [Journal Article] Geometric Treatment of Periodic Graphs with Coordinate System Using Axis-Fibre and an Application to a Motion Planning (2012)
  • Author(s): N. Fu, A. Hashikura and H. Imai
  • Journal Title: Proceedings of 2012 International Symposium on Voronoi Diagrams in Science and Engineering Volume: (to appear)
• [Journal Article] Fast Elliptic Curve Cryptography Using Minimal Weight Conversion of d Integers (2012)
  • Author(s): V.Suppakitpaisarn, M.Edahiro, H.Imai
  • Journal Title: AISC2012, Conferences in Research and Practice in Information Technology Volume: Vol.125 Pages: 15-26
  • Peer Reviewed
• [Journal Article] Proximity and Motion Planning on 1_1-embeddable Tilings (2011)
  • Author(s): Norie Fu, Akihiro Hashikura, Hiroshi Imai
  • Journal Title: In proceedings of the 8th Voronoi diagrams in science and engineering (ISVD) Volume: － Pages: 150-159
  • DOI: 10.1109/isvd.2011.28
  • Peer Reviewed
• [Journal Article] Distance and Axis Decomposition of/1-embeddable Tilings (2011)
  • Author(s): A. Hashikura, N. Fu and H. Imai
  • Journal Title: Proceedings of the 14^<th> Korea-Japan Joint Workshop on Algorithms and Computation Volume: Vol.1 Pages: 130-136
• [Journal Article] Revisiting hyperbolic Voronoi diagrams in two and higher dimensions from theoretical, applied and generalized viewpoints (2011)
  • Author(s): T. Tanuma, H. Imai, and S. Moriyama
  • Journal Title: Transactons on Computational Science Volume: Vol.14 Pages: 1-30
  • DOI: 10.1007/978-3-642-25249-5_1
  • ISBN: 9783642252488, 9783642252495
  • Peer Reviewed
• [Journal Article] Distance and Axis Decomposition of l_1-embeddable Tilings (2011)
  • Author(s): A.Hashikura, N.Fu, E.Imai
  • Journal Title: Proceedings of The 14th Korea-Japan Joint Workshop on Algorithms and Computation Volume: Vol.1 Pages: 130-136
  • Peer Reviewed
• [Journal Article] Voronoi Diagrams on Periodic Graphs, Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering (2010)
  • Author(s): N. Fu, H. Imai and S. Moriyama
  • Journal Title: IEEE Xplorer Pages: 189-198
  • DOI: 10.1109/isvd.2010.26
• [Journal Article] Revisiting Hyperbolic Voronoi Diagrams from Theoretical, Applied and Generalized Viewpoints, Proceedings of International Symposium on Voronoi Diagrams in Science and Engineering (2010)
  • Author(s): T. Tanuma, H. Imai and S. Moriyama
  • Journal Title: IEEE Xplorer Pages: 23-32
  • DOI: 10.1109/isvd.2010.13
• [Journal Article] Voronoi Diagrams on Periodic Graphs (2010)
  • Author(s): N.Fu, H.Imai, S.Moriyama
  • Journal Title: Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering Volume: IEEE Xplorer Pages: 189-198
  • Peer Reviewed
• [Journal Article] Revisiting Hyperbolic Voronoi Diagrams from Theoretical, Applied and Generalized Viewpoints (2010)
  • Author(s): T.Tanuma, H.Imai, S.Moriyama
  • Journal Title: Proceedings of 2010 International Symposium on Voronoi Diagrams in Science and Engineering Volume: IEEE Xplorer Pages: 23-32
  • Peer Reviewed
• [Presentation] Quantum Coloring Games via Symmetric SAT Games (2011)
  • Author(s): J. Fukawa, F. Le Gall, and H. Imai
  • Organizer: 11th Asian Quantum Information Science Conference
  • Place of Presentation: Busan, Korea
  • Year and Date: 2011-08-25
• [Presentation] 幾何から量子そしてその先 (2011)
  • Author(s): 今井浩
  • Organizer: 「計算幾何学の発展と未来」研究集会
  • Place of Presentation: 京都大学
  • Year and Date: 2011-03-11
• [Presentation] 幾何から量子そしてその先 (2011)
  • Author(s): 今井浩
  • Organizer: 「計算幾何学の発展と未来」研究集会
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2011-03-11
• [Presentation] 量子シミュレーションの計算量理論へ (2011)
  • Author(s): 今井浩
  • Organizer: 電子情報通信学会第25回量子情報技術研究会
  • Place of Presentation: QIT25,大阪大学
• [Presentation] 量子グラフ状態による情報処理 (2010)
  • Author(s): 今井浩、夫紀恵、森山園子
  • Organizer: 「ナノ量子情報エレクトロニクスの進展」シンポジウム
  • Place of Presentation: 東京大学
  • Year and Date: 2010-12-22
• [Presentation] Feynmanの2つの提唱からグラフと計算量への展開 (2010)
  • Author(s): 今井浩
  • Organizer: 電子情報通信学会第23回量子情報技術研究会
  • Place of Presentation: 東京大学
  • Year and Date: 2010-11-15
• [Presentation] periodic graphのstatic graphに関する一考察 (2010)
  • Author(s): 橋倉彰宏、夫紀恵、今井浩
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 長岡技術科学大学
  • Year and Date: 2010-09-29