A study on relationships between stochastic and quantum models and random graph structures

• Project/Area Number: 23740093
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kanagawa University
• Principal Investigator: IDE Yusuke 神奈川大学, 工学部, 助教 (70553999)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 量子ウォーク / 固有空間解析 / graph Laplacian / 直交多項式 / 有限グラフ / パス / 複雑ネットワーク / センサネットワーク

Research Abstract

In this study, we concentrate on analysis of transition probabilities of discrete-time and continuous-time quantum walks on various graphs including random graphs. For the discrete-time case, we obtain some limit theorems for long-time average of the transition probabilities by detailed study of eigenspace of the Jacobi matrices. For the continuous-time case, we show relationships between local graph structures and the transition probabilities by detailed study of eigenspace of the Laplacian matrices.

Research Products

• [Journal Article] Localization of discrete time quantum walks on the glued trees (2014)
  • Author(s): Yusuke Ide, Norio Konno, Etsuo Segawa, Xin-Ping Xu
  • Journal Title: Entropy Volume: Vol.16, No.3 Issue: 3 Pages: 1501-1514
  • DOI: 10.3390/e16031501
  • Peer Reviewed / Open Access
• [Journal Article] Some basic properties of a rotor-router model with i.i.d. initial rotor-routers on the line (2014)
  • Author(s): Yusuke Ide, Norio Konno, Masato Takei
  • Journal Title: Proceedings of SSS'13 The 45th International Symposium on Stochastic Systems Theory and Its Applications Volume: (印刷中)
  • NAID: 130007377503
  • Peer Reviewed
• [Journal Article] Analytical solutions for quantum walks on 1D chain with different shift operators (2014)
  • Author(s): Xin-Ping Xu, Xiao-Kun, Zhang, Yusuke Ide, Norio Konno
  • Journal Title: Annals of Physics Volume: Vol.344 Pages: 194-212
  • DOI: 10.1016/j.aop.2014.02.018
  • Peer Reviewed
• [Journal Article] Combinatorial and approximative analyses in a spatially random division process (2013)
  • Author(s): Yukio Hayashi, Takayuki Komaki, Yusuke Ide, Takuya Machida, and Norio Konno
  • Journal Title: Physica A Volume: 392(9) Issue: 9 Pages: 2212-2225
  • DOI: 10.1016/j.physa.2013.01.025
  • NAID: 120005367956
  • Peer Reviewed
• [Journal Article] Time averaged distribution of a discrete-time quantum walk on the path (2012)
  • Author(s): Yusuke Ide, Norio Konno, Etsuo Segawa
  • Journal Title: Quantum Information Processing Volume: Vol.11, No.5 Issue: 5 Pages: 1207-1218
  • DOI: 10.1007/s11128-012-0424-5
  • Peer Reviewed
• [Journal Article] Symmetry and localization of quantum walk induced by extra link in cycles (2012)
  • Author(s): Xin-Ping Xu, Yusuke Ide, Norio Konno
  • Journal Title: Physical Review A Volume: Vol.85, No.4 Issue: 4 Pages: 42327-42327
  • DOI: 10.1103/physreva.85.042327
  • Peer Reviewed
• [Presentation] Q 学習による完全グラフ上の経路学習におけるTTL と学習経路長の関係 (2014)
  • Author(s): 井手勇介, 右田正夫, 菊池光, 今井崇雅
  • Organizer: 電子情報通信学会2014年総合大会, B-7-76
  • Place of Presentation: 新潟大学五十嵐キャンパス
  • Year and Date: 2014-03-21
• [Presentation] Fully interconnected subgraph decomposition and continuous time quantum walks (2014)
  • Author(s): Yusuke Ide
  • Organizer: "AMS Special Session on Quantum Walks, Quantum Computation, and Related Topics I" at 2014 Joint Mathematics Meetings
  • Place of Presentation: Baltimore convention center, Baltimore, US
  • Year and Date: 2014-01-17
• [Presentation] Fully interconnected subgraph decomposition and continuous time quantum walks (2014)
  • Author(s): Yusuke Ide
  • Organizer: AMS Special Session on Quantum Walks, Quantum Computation, and Related Topics I
  • Place of Presentation: Baltimore Convention Center, Baltimore, US
  • Invited
• [Presentation] Q 学習による完全グラフ上の経路学習における TTL と学習経路長の関係 (2014)
  • Author(s): 井手勇介，右田正夫，菊池光，今井崇雅
  • Organizer: 電子情報通信学会2014年総合大会
  • Place of Presentation: 新潟大学五十嵐キャンパス
• [Presentation] Some basic properties of a rotor-router model with i.i.d. initial rotor-routers on the line (2013)
  • Author(s): Yusuke Ide, Norio Konno, Masato Takei
  • Organizer: The 45th International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学50周年記念館
  • Year and Date: 2013-11-02
• [Presentation] Continuous time quantum walks on some graphs (2013)
  • Author(s): Yusuke Ide
  • Organizer: 量子ウォークの数理の新展開 : 物質制御への応用
  • Place of Presentation: 九州大学マス・フォア・インダストリ研究所
  • Year and Date: 2013-06-19
• [Presentation] Time averaged distribution of discrete time quantum walks on the path (2013)
  • Author(s): Yusuke Ide
  • Organizer: "AMS Special Session on Quantum Walks" at 2013 Joint Mathematics Meetings
  • Place of Presentation: San Diego convention center, San Diego, US
  • Year and Date: 2013-01-10
• [Presentation] Continuous time quantum walks on some graphs (2013)
  • Author(s): Yusuke Ide
  • Organizer: 量子ウォーク数理の新展開: 物質制御への応用
  • Place of Presentation: 九州大学 マス・フォア・インダストリ研究所
  • Invited
• [Presentation] Some basic properties of a rotor-router model with i.i.d. initial rotor-routers on the line (2013)
  • Author(s): Yusuke Ide, Norio Konno, Masato Takei
  • Organizer: The 45th ISCIE International Symposium on Stochastic Systems Theory and Its Applications
  • Place of Presentation: 琉球大学 50周年記念館
• [Presentation] Time averaged distribution of discrete time quantum walks on the path (2013)
  • Author(s): Yusuke Ide
  • Organizer: “AMS Special Session on Quantum Walks” at 2013 Joint Mathematics Meetings
  • Place of Presentation: San Diego convention center
  • Invited
• [Presentation] Time averaged probability of DTQWs on the path with general coin (2012)
  • Author(s): Yusuke Ide
  • Organizer: Workshop of quantum dynamics and quantum walks
  • Place of Presentation: 岡崎コンファレンスセンター
  • Year and Date: 2012-11-24
• [Presentation] Time averaged distribution of a discrete-time quantum walk on the path (2011)
  • Author(s): Yusuke Ide
  • Organizer: International Workshop on Theoretical Aspects of the Discrete Time Quantum Walk
  • Place of Presentation: Instituto de Fisica Corpuscular, Valencia, Spain
  • Year and Date: 2011-11-07
• [Remarks]
  • URL: http://kenkyu.kanagawa-u.ac.jp/kgdb/KgApp?kyoinId=ymbygoosggg
• [Remarks] 神奈川大学 研究者情報
  • URL: http://kenkyu.kanagawa-u.ac.jp/kgdb/KgApp?kyoinId=ymbygoosggg
• [Remarks] 神奈川大学 研究者情報
  • URL: http://kenkyu.kanagawa-u.ac.jp/kgdb/KgApp?kyoinId=ymbygoosggg
• [Remarks]
  • URL: http://kenkyu.kanagawa-u.ac.jp/kgdb/KgApp?kyoinId=ymbygoosggg