2020 Fiscal Year Annual Research Report
Theoretical Research on Quantum Supremacy
| Project/Area Number |
19F19079
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| Research Institution | Nagoya University |
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| Host Researcher |
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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| Foreign Research Fellow |
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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| Keywords | Quantum computing / Complexity theory / Algorithms |
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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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Research Products
(2 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
Pages: 10:1-10:17
DOI
Peer Reviewed / Open Access / Int'l Joint Research
