| 研究概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
3: やや遅れている
理由
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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| 今後の研究の推進方策 |
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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