Statistical mechanics study for prime factorization

2016 Fiscal Year Final Research Report

• 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
• 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.

Free Research Field

統計力学