2021 Fiscal Year Final Research Report
Extended Formulations of Quantum Optimization and Their Applications to Classical/Quantum Computation
| Project/Area Number |
15H01677
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Imai Hiroshi 東京大学, 大学院情報理工学系研究科, 教授 (80183010)
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| Co-Investigator(Kenkyū-buntansha) |
山下 茂 立命館大学, 情報理工学部, 教授 (30362833)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Keywords | 量子計算 / 量子最適化 / 量子回路設計 / 量子グラフ状態 / エクスパンダグラフ / 分散量子計算 / 凸多面体 / 量子近似最適化 |
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| Outline of Final Research Achievements |
This research performed theoretical and experimental verification on quantum advantege on polyhedral aspect of quantum nonlocality and analyze quantum optimization with applications to quantum circuit design. Based on the relationship between the generalized Bell inequality and the cut polyhedron, the scalable inequality for the quantum graph state was tested on real approximate quantum computer to verify the quantum violation. We analyzed a classical-quantum approximation optimization method that approximates the maximal cut problem, which gave a direct polynomial order of the polyhedron of a lower-truncated transverse matroid. Using an expander graph and graph minor theory, the quantum superiority in the quantum graph state was theoretically shown.
Using an optimization method, we were able to show a truly quantum-optimized quantum circuit that goes beyond the scope of classical logic to minimize the number of T-gates, which is indispensable for error-resistant quantum circuits.
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| Free Research Field |
量子計算
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| Academic Significance and Societal Importance of the Research Achievements |
初期の量子コンピュータが、ノイズの関係で浅い回路の範囲で有効であると見通し、基本問題の一般化Bell不等式の研究を理論的に進めたことで、研究期間中に利用可能となった100量子ビット以上の量子コンピュータでの計算で量子性が検証できた。このことは、これからの量子計算能力実証のベースになるものである。さらに、量子グラフ状態でのグラフ理論を活用して、量子計算機の能力が古典コンピュータを超えるものであることも示せており、将来展望を開く成果となっている。量子回路設計でも多様な最適化回路を提示することができ、量子回路にそれらが実装されることで、社会問題の解決を支える基礎の構築ができている。
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