Study on classical and quantum models on graphs
| Project/Area Number |
24540116
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Yokohama National University |
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Principal Investigator |
KONNO Norio 横浜国立大学, 工学(系)研究科(研究院), 教授 (80205575)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 量子ウォーク / 複雑ネットワーク / アダマールウォーク / 定常測度 / 極限定理 / 局在化 / 時間平均極限測度 / グローヴァーウォーク / ゼータ関数 / オープン量子ランダムウォーク |
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| Outline of Final Research Achievements |
We obtained stationary measures, time-averaged limit measures, and weak limit measures for quantum walks on various graphs. For examples, we got a formula of characteristic polynomials of the unitary matrix determines the quantum walk on graphs by the weighted zeta function. We obtained stationary measures of two-state quantum walk on the line, in particular, a non-uniform stationary measure for the Hadamard walk. Moreover we got stationary measures, time-averaged limit measures, and weak limit measures for a class of quantum walks with one defect and clarified the localization. We analyzed localization of quantum walks on glued trees and spidernets.
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Report
(4 results)
Research Products
(20 results)
