Study on satial structures induced by quantum walks
| Project/Area Number |
16K17637
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Yokohama National University (2018)
Tohoku University (2016-2017) |
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Principal Investigator |
SEGAWA Etsuo 横浜国立大学, 大学院教育強化推進センター, 准教授 (30634547)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 量子ウォーク / 単体的複体 / 局在化 / クリークカバー / 位相測定 / 吸収壁 / 組み合わせ的フロー / 結晶格子 / 単体複体 / 極限分布 / 円分多項式 / 応用数学 |
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| Outline of Final Research Achievements |
We considered quantum walks which are quantum analogue of random walks. Quantum walks exhibit some interesting behaviors; for examples, periodicity, localization, linear spreading and so on. In this study, we fixed such a typical behavior and tried to determine a class of graph in which the quantum walk exhibits this behavior. This is a kind of inverse problem. Then we showed that if the infinite graph has a cycle, then there is an initial state to give the localization. This means that the time evolution operator of quantum walk has an eigenfunctions whose support is the cycle. Moreover to extract such a sensitivity to the cycle of the quantum walk, we constructed quantum walks on simplicial complex. We obtained some behaviors of quantum walks which reflect some spatial structures.
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| Academic Significance and Societal Importance of the Research Achievements |
量子ウォーク(QW)はファインマンの提唱する量子シミュレータの一つとして考えることができ、実際に幾つかの量子ダイナミクスを離散的与えることができる。従って、量子現象を近似的に再現するQWの挙動を明示的に示すことは重要である。本研究ではグラフを眺めただけでQWの挙動が預言できることをコンセプトに、局在化や周期性など特有の性質を与えるための空間構造を数学的に特定することができた。量子情報の分野から出てきた量子ウォークは、数学的な考察でより明示的に解りやすく説明ができるようになったところも現れ、数学の諸分野との連携が強化された。さらにQWから動機される新しい数学的な問題を提起することも期待される。
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Report
(4 results)
Research Products
(77 results)
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[Presentation] 量子酔歩によるグラフの周遊2017
Author(s)
瀬川悦生
Organizer
第13回組合せ論若手研究集会
Place of Presentation
慶応大学, 矢上キャンパス, 神奈川県横浜市
Year and Date
2017-03-05
Related Report
Invited
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[Presentation] Sensitivity of a quantum walk to boundary2016
Author(s)
Hideaki Obuse and Etsuo Segawa
Organizer
Workshop of Quantum Simulation and Quantum Walks 2016
Place of Presentation
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, チェコ
Year and Date
2016-11-17
Related Report
Int'l Joint Research / Invited
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[Presentation] Construction of the eigenspace of Grover walk2016
Author(s)
Etsuo Segawa
Organizer
12th Sendai Workshop on Non-commutative Stochastic Analysis and Applications
Place of Presentation
Graduate School of Information Scinces, Tohoku univerity, 宮城県仙台市
Year and Date
2016-10-19
Related Report
Int'l Joint Research / Invited
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