Identification and full control of high-dimensional quantum many body system under limited access

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400400
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Osaka City University
• Principal Investigator: Maruyama Koji 大阪市立大学, 大学院理学研究科, 客員准教授 (00425646)
• Co-Investigator(Kenkyū-buntansha): 加藤 豪 日本電信電話株式会社NTTコミュニケーション科学基礎研究所, メディア情報研究部, 主任研究員 (20396188) ; 尾張 正樹 静岡大学, 情報学部, 准教授 (80723444)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 量子制御 / 数理物理 / 量子コンピュータ / 量子システム同定

Outline of Final Research Achievements

We have found that even if the direct access is restricted to a small subsystem (S) and the pre-knowledge on the entire system is severely limited, there is a possible method to identify the hamiltonian H_{SE} that governs the global system dynamics. In addition, we have clarified there could be 'equivalence classes', each of which contains infinitely many distinct sets of the system hamiltonian and the state that should give identical observable effect on S.
We then have further studied the fundamental structures of the dynamical Lie algebra and the Hilbert space under the condition of restricted direct access. It turned out that there is a clear distinction between the cases of d_S=2 and d_S=>3, where d_S is the dimension of the accessible subsystem S. While the algebra is always su(*) in subspaces when d_S=>3, it is not necessarily the case when d_S=2. The structure we revealed clearly explains the nature of the equivalence class in terms of controllability and observability.

Free Research Field

量子制御理論、量子情報理論、情報熱力学