Numerical simulations of strongly entangled states: Sampling by matrix product states

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K14377
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Tokyo Medical and Dental University (2021-2022); Kindai University (2020)
• Principal Investigator: Goto Shimpei 東京医科歯科大学, 教養部, プロジェクト助教 (90754739)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 有限温度量子多体系 / 数値シミュレーション / 行列積状態 / ランダム量子状態 / 量子ダイナミクス

Outline of Final Research Achievements

We developed an efficient numerical approach to simulate quantum many-body systems at finite temperatures by combining matrix product states and the random sampling approach. The developed approach has advantages which are present in previous approaches. Besides, we also found the class of random quantum states which would be easily prepared in quantum computers. The quantum states possess enough randomness to efficiently simulate quantum many-body systems at finite temperatures. These results have developed the techniques of simulating quantum many-body systems at finite temperatures on classical computers, and would give useful insight to design an algorithm for simulating quantum many-body systems at finite temperatures on quantum computers.

Free Research Field

量子多体系

Academic Significance and Societal Importance of the Research Achievements

量子多体系の有限温度の数値シミュレーションは化学反応や物質の性質を理解するために非常に有用である。その基礎技術を向上させていくことにはもちろん社会的な意義があるし、また有限温度系の理解を深めるという意味でも学術的な意義がある。また古典計算機のための数値シミュレーションの改良から量子計算機でも有用なことが期待されるシミュレーション手法へとシームレスに発展させることができた。量子計算機の実装が社会的な注目を集めている現況では、量子計算機上で動く可能性があるシミュレーション手法の提案も学術的意義および社会的意義がある。