| Project/Area Number |
15K13443
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Yokohama National University |
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Principal Investigator |
KONNO Norio 横浜国立大学, 大学院工学研究院, 教授 (80205575)
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| Project Period (FY) |
2015-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 量子ウォーク / 定常測度 / 四元数 / ゼータ関数 / 周期 / 無限粒子系 / 局在化 / 極限定理 / 時間平均極限測度 |
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| Outline of Final Research Achievements |
We studied stationary measures and time-averaged limit measures for various quantum walks. For examples, we obtained stationary measures of three-state quantum walk with one defect on the line. By using this result, we got a stationary measure of the three-state quantum walk without defect and clarified relation between stationary measure and time-averaged limit measure. And we obtained a similar result for one-dimensional two-phase quantum walk with one defect. Moreover we introduced the quaternionic quantum walk and got eigenvalues of the unitary matrix determines the quaternionic quantum walk on graphs by the corresponding graph zeta function. From this result, we clarified difference between quantum walk and quaternionic quantum walk.
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