2011 Fiscal Year Final Research Report
New Developments in Computer Algebra using Techniques from Quantum Computing
| Project/Area Number |
22800006
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
LE GALL Francois 東京大学, 大学院・情報理工学系研究科, 講師 (50584299)
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| Project Period (FY) |
2010 – 2011
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| Keywords | アルゴリズム / 計算機代数 / 量子計算 |
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| Research Abstract |
We developed new approaches based on techniques from quantum computing to efficiently handle computational problems with an algebraic structure. Among our main results, we constructed new algorithms for distinguishing, in the framework of property testing, classes of groups, and new quantum algorithms for computing efficiently the product of two Boolean matrices. As applications of these novel approaches, we succeeded in proving the hardness of decoding problems arising in quantum communication, and in constructing new protocols for several tasks such as privacy-preserving communication.
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