2011 Fiscal Year Final Research Report
Studies on topological quantum computation
| Project/Area Number |
21654053
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu University (2011)
Naruto University of Education (2009-2010) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MURKAMI Hitoshi 東京工業大学, 理工学研究科, 准教授 (70192771)
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| Project Period (FY) |
2009 – 2011
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| Keywords | トポロジー / 結び目理論 / 量子情報 |
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| Research Abstract |
Entanglement entropy is one of the characteristic quantities in the topological quantum computation. The entanglement entropy, especially topological entanglement entropy, is intimately related to the quantum invariants of knots and 3-manifolds. We studied the colored Jones polynomials for knots and links. We exactly analyzed the colored Jones polynomial for torus knots, and we obtained explicit relationship with classical topological invariants such as torsions. We also studied the Fourier expansion of modular forms, and obtained a relationship between their asymptotic behavior and the entropy of complex manifolds.
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