Paper Abstract and Keywords |
Presentation |
2019-11-19 11:50
Fine-grained quantum supremacy based on Orthogonal Vectors, 3-SUM and All-Pairs Shortest Paths Ryu Hayakawa, Tomoyuki Morimae (Kyoto Univ.), Suguru Tamaki (Hyogo Univ.) |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Fine-grained quantum supremacy is a study of excluding possibilities of superpolynomial time classical simulations of quantum computing. We show that under conjectures on Orthogonal Vectors (OV), 3-SUM, All–Pairs Shortest Paths (APSP) and their variants, strong and weak classical simulations of quantum computing are impossible in certain exponential times of the number of qubits. Those conjectures are widely used in classical fine–grained complexity theory in which polynomial time hardnesses are conjectured. All previous results of fine-grained quantum supremacy are based on ETH, SETH, or their variants that are conjectures for SAT in which exponential time hardnesses are conjectured. We show that there exist quantum circuits which cannot be classically simulated in certain exponential times of the number of qubits first by considering the Quantum Random Access Memory (QRAM) based quantum computing model and next by considering the non-QRAM model quantum computation. In the case of the QRAM model, the size of the circuits is linear in the number of qubits and in the case of the non-QRAM model, the size of the circuits is exponential in the number of qubits but the results are even non-trivial. We have omitted the proofs of theorems due to the space limitations. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
fine-grained complexity / quantum computing / quantum supremacy / / / / / |
Reference Info. |
IEICE Tech. Rep. |
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Conference Information |
Committee |
QIT |
Conference Date |
2019-11-18 - 2019-11-19 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Gakushuin University |
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(See Japanese page) |
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Quantum Information |
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Registration To |
QIT |
Conference Code |
2019-11-QIT |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
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(See Japanese page) |
Title (in English) |
Fine-grained quantum supremacy based on Orthogonal Vectors, 3-SUM and All-Pairs Shortest Paths |
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fine-grained complexity |
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quantum computing |
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quantum supremacy |
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1st Author's Name |
Ryu Hayakawa |
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Kyoto University (Kyoto Univ.) |
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Tomoyuki Morimae |
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Kyoto University (Kyoto Univ.) |
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Suguru Tamaki |
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University of Hyogo (Hyogo Univ.) |
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Date Time |
2019-11-19 11:50:00 |
Presentation Time |
20 minutes |
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QIT |
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