optimal control of dynamical quantum systems

2018 Fiscal Year Final Research Report

• Project/Area Number: 26400385
• 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: Tokyo Institute of Technology
• Principal Investigator: Takahashi Kazutaka 東京工業大学, 理学院, 助教 (70415214)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: 断熱状態制御の方法 / 量子アニーリング

Outline of Final Research Achievements

“Shortcuts to adiabaticity“ is known as a method accelerating adiabatic dynamics.　I found, after studying many applications, that the method is very general and can be applied to any dynamical systems including quantum, classical, and statistical systems. The Hamiltonian of the system is separated into two parts, and each can be interpreted as the energy of the system and the generator of the time evolution.
As one of the main achievement, we found that the Lax formalism for classical nonlinear integrable systems is shown to be equivalent to shortcuts to adiabaticity. This equivalence gives nontrivial solutions of quantum and classical dynamics. The most important point is that we found not only specific solutions but also several series of solutions exhaustively.

Free Research Field

量子・統計物理学

Academic Significance and Societal Importance of the Research Achievements

動力学の問題を解くことは一般に難しいが、本研究によって統一的な見方が得られた。当初は制御の問題を想定して研究を行っていたが、必ずしもそれに限らない描像を得たことは意義が大きい。動力学を理解する端緒となることが期待される。
また、これも想定外であったが、本研究の成果は量子力学に限らず古典力学や統計力学の系にも適用ができる。今後は本研究で得られた描像に立ってさまざまな系の動的な性質や制御問題を調べるという研究が行われることを期待している。