Statistical mechanics study for prime factorization

• Project/Area Number: 26610111
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Tohoku University
• Principal Investigator: Nakajima Chihiro 東北大学, 原子分子材料科学高等研究機構, 助教 (40599122)
• Research Collaborator: OHZEKI MASAYUKI 東北大学, 大学院情報科学研究科, 准教授
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 統計物理学 / 素因数分解 / 相転移 / モンテカルロ法 / 計算量理論 / スピングラス

Outline of Final Research Achievements

We have studied the statistical-mechanics model of the prime factorization problem via a formulation of the ground-state searching problem. By the analysis of the density of states of two macroscopic quantities, i.e., the energy and the Hamming distance from the correct solutions, leads to two features that are each related to two marked changes in the energy region sampled via Monte Carlo simulation or simulated annealing. One is the peculiar first order phase transition that has the intermediate property between the conventional first-order transition and the second-order one and the other is the convex kink in the density of states.

Research Products

• [Journal Article] Statistical mechanical models of the integer factorization problem (2016)
  • Author(s): Chihiro H. Nakajima and Masayuki Ohzeki
  • Journal Title: Journal of the Physical Society of Japan Volume: 86 Issue: 1 Pages: 014001-014001
  • DOI: 10.7566/jpsj.86.014001
  • NAID: 40021057631
  • Peer Reviewed / Open Access
• [Presentation] Computational property of quantum annealing of integer factorization problem (2016)
  • Author(s): Chihiro Nakajima and Masayuki Ohzeki
  • Organizer: Workshop on Theory and Practice of Adiabatic Quantum Computers and Quantum Simulation
  • Place of Presentation: International Centre for Theoretical Physics, Trieste, Italy
  • Year and Date: 2016-08-22
  • Int'l Joint Research
• [Presentation] Computational property of quantum annealing of factorization problem (2016)
  • Author(s): Chihiro H. Nakajima and Masayuki Ohzeki
  • Organizer: Adiabatic Quantum Computing Conference 2016
  • Place of Presentation: Google Los Angeles, Los Angeles, USA
  • Year and Date: 2016-06-27
  • Int'l Joint Research
• [Presentation] 素因数分解模型の量子アニーリング (2016)
  • Author(s): 中島千尋、大関真之
  • Organizer: 日本物理学会第71回年次大会
  • Place of Presentation: 東北学院大学、宮城県仙台市泉区
  • Year and Date: 2016-03-19
• [Presentation] Phase transition phenomena of statistical models of the integer factorization problem (2016)
  • Author(s): Chihiro Nakajima
  • Organizer: YITP Workshop on Quantum Information Physics (YQIP2016)
  • Place of Presentation: 京都大学、京都市左京区
  • Year and Date: 2016-01-05
  • Int'l Joint Research
• [Presentation] 素因数分解の模型と量子アニーリング (2015)
  • Author(s): 中島千尋
  • Organizer: ImPACT未来テーマ開拓研究会
  • Place of Presentation: 支笏湖温泉、北海道千歳市
  • Year and Date: 2015-10-13
• [Presentation] Static property of statistical mechanics model for prime factorization (2014)
  • Author(s): Chihiro H Nakajima
  • Organizer: Satellite workshop at Osaka University in AQIS 2014 : Physics of Quantum Information Processing
  • Place of Presentation: Osaka University Sigma Hall (Osaka)
  • Year and Date: 2014-08-25 – 2014-08-26
• [Presentation] Statistical mechanics model for prime factorization (2014)
  • Author(s): Chihiro H Nakajima
  • Organizer: YITP Workshop on Quantum Information Physics (YQIP2014)
  • Place of Presentation: Yukawa Institute for Theoretical Physics, Kyoto University (Kyoto)
  • Year and Date: 2014-08-04 – 2014-08-07
• [Presentation] Statistical mechanics models of factorization problem (2014)
  • Author(s): Chihiro H Nakajima
  • Organizer: International Workshop on Quantum LDPC Codes
  • Place of Presentation: Perimeter Institute for Theoretical Physics, Waterloo(Canada)
  • Year and Date: 2014-07-14 – 2014-07-16
• [Presentation] 素因数分解の統計力学的定式化 (2014)
  • Author(s): 中島 千尋
  • Organizer: 量子情報技術研究会（QIT30）
  • Place of Presentation: 名古屋大学豊田講堂シンポジオン(名古屋)
  • Year and Date: 2014-05-12 – 2014-05-13