2013 Fiscal Year Annual Research Report
| Project/Area Number |
13J06353
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| Research Institution | University of Fukui |
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Principal Investigator |
VILLAGRA Marcos 福井大学, 工学研究科, 特別研究員(PD)
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| Keywords | Quantum Computing / Cryptography / Quantum Communication / Algebra |
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| Research Abstract |
During the first year of the project, I did research in a model of communication called "interactive proof system", or IP. An IP is a communication game between two players, Alice and Bob, where Alice wants to convince Bob that certain assrtion is true ; if the assertion is false and Alice tries to cheat Bob, then Bob can tell that Alice is cheating. An lP has many applications ranging from cryptography, nondeteministic computation, and formal language theory. Two different types of IPs were researched : 1) Zero-Khowledge IP, and 2) Non-interactive IP. In both cases, the IP protocol involved quantum computers.
First, in a Zero-Knowledge IP, the IP protol does not leak any information to a potential malicious player who tries to break the s㏄urity of the prot㏄ol. I developed mathematical techniques that help to mathematically prove that certain computational Problems cannot have a Quantum Zero-Knowledge IP realized by a quantum computer with limited memory. Second, in Non-interactive IPs, I studied the mathematical properties when the IP protocol is executed by quantum and classical computers with no memory. Among these propert ; es I discovered connections to certain algebraic structures called semigroups.
My research involved the study of mathematical properties of IPs realized by quantum computers with limited memory (so-called quantum automata). Since quantum automata seems more realizable than a full quantum computer, understanding and predicting its properties could potentially help to develop a mathematical theory for future quantum-mechanical machines.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
During the first year I discovered new results related to the topics mentioned in 9 above. However, considerable time was spent writing and documenting the findings in a scientific article. The papers were initially submitted to peer-reviewed conferences and were rejected. Nevertheless, the initial reviews helped me to improve the results.
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| Strategy for Future Research Activity |
The current research plan will continue as originally stated. The problems mentioned in point 11 above are currently being addressed and I expect to publish the results by fiscal year 26.
After the subjects of Zero-Knowledge and Non-interactive IPs are done, I will continue my research on IPs and nondeterministic computation using more powerful models of quantum and classical computers, including pushdown automata and 2-way quantum automata.
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Research Products
(3 results)
