Theoretical Research on Quantum Supremacy
| Project/Area Number |
19F19079
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 外国 |
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| Review Section |
Basic Section 60010:Theory of informatics-related
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| Research Institution | Nagoya University |
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Principal Investigator |
ルガル フランソワ 名古屋大学, 多元数理科学研究科, 准教授 (50584299)
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| Co-Investigator(Kenkyū-buntansha) |
ROSMANIS ANSIS 名古屋大学, 多元数理科学研究科, 外国人特別研究員
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| Project Period (FY) |
2019-07-24 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2020: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2019: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Quantum computing / Complexity theory / Algorithms |
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| Outline of Research at the Start |
様々な側面から効率の良い量子アルゴリズムの構築に取り組み、量子コンピュータの新しい応用分野の開拓を目指す。理論的にも応用的にも重要な計算問題において、量子計算の古典計算に対する優位性（量子スプレマシー）を確立することを最終目標とする。
第1世代の大規模量子コンピュータは分散型システムとして実現される見込みがあるため、本研究課題では特に量子分散計算に着目する予定である。量子分散アルゴリズムの計算時間の新しい解析手法を開発することによって、分散計算の枠組みにおいての量子スプレマシーの確立を目指す。
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| Outline of Annual Research Achievements |
This academic year we worked on various problems related to quantum algorithms and post-quantum cryptography.
We investigated the problem of graph coloring by distributed quantum algorithms. In particular, for the problem of 3-coloring a circle, prior to our work, no nontrivial limitations on the power of quantum algorithms were known. We managed to show that there is a certain correlation among the colors of non-adjacent vertices that holds for every 3-coloring. As a result, we proved that one round of one way quantum communication is not sufficient to solve the problem.
In cryptography, random permutations, random functions, and various computational problems on them play important roles. However, unlike for random functions, for random permutations we currently do not know many techniques to prove quantum hardness results. We studied the problem of inverting a permutation, and showed how the recently-introduced compressed oracle framework can be used to prove optimal query lower bounds for the problem.
We also studied the computational power of shallow-depth quantum circuits for parity that permit controlled single-qubit gates of unbounded number of control bits. While these unbounded gates might make the model much more powerful, we obtained some preliminary results suggesting that that is not the case. In particular, we classified topologies of all depth-2 circuits in few classes, and for most of them we already showed that they cannot compute the parity of more than 4 input bits, which is already achievable by one and two qubit gates.
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| Research Progress Status |
令和2年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和2年度が最終年度であるため、記入しない。
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Report
(2 results)
Research Products
(4 results)
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[Journal Article] Quantum Coupon Collector2020
Author(s)
Srinivasan Arunachalam, Aleksandrs Belovs, Andrew M. Childs, Robin Kothari, Ansis Rosmanis and Ronald de Wolf
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Journal Title
Leibniz International Proceedings in Informatics (Proceedings of the 15th Conference on the Theory of Quantum Computation, Communication and Cryptography)
Volume: 158
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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