2019 Fiscal Year Final Research Report
Analysis of quantum interactive proofs with restricted quantum communication and computation
| Project/Area Number |
16K00015
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 量子計算 / 対話型証明 / 計算量理論 |
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| Outline of Final Research Achievements |
The quantum interactive proofs is a natural extension of the quantum NP systems (one-round verification system) where multiple rounds of interaction are allowed between a unlimitedly powerful party (prover) and a polynomial-time computable party (verifier). While the quantum interactive proof is one of main topics in quantum computational complexity, it still has many unexplored points and the computational power has been unknown. To investigate this model in a more fine grained way, we have studied the computational power and the limitation of quantum interactive proofs by restricting quantum communication and computation in several approaches. Moreover, we have shown the power of restricted quantum computation models such as DQC1 models by using the analysis of quantum interactive proofs that are obtained in this research.
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| Free Research Field |
量子計算
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| Academic Significance and Societal Importance of the Research Achievements |
量子計算は近年社会的に大きな注目を集めている．特に従来の計算機で効率的に行えないような何らかのタスクを近未来的に実現可能な量子計算機で行えるかという問題は，量子超越性と呼ばれて世界的に研究が加速している．しかしながら，量子計算機の計算能力の理論的解明は量子超越性の理論を含めて道半ばである．本研究の研究成果は，量子計算機の真の能力を明らかにするための基盤を固めるという学術的意義を持っている．また，近未来的に実現可能な量子計算による検証を意識して，制限された量子対話型証明の研究を行うとともに量子超越性の理論に対する貢献を行ったことで，社会的にも意義のある成果と考えられる．
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