| Paper Abstract and Keywords |
| Presentation |
2023-12-17 17:30
How to Map Linear Differential Equations to Schr"{o}dinger Equations via Carleman and Koopman-von Neumann Embeddings for Quantum Algorithms
Yuki Ito (Osaka Univ.), Yu Tanaka (Sony Group), Keisuke Fujii (Osaka Univ./RIKEN) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
Solving differential equations with large degrees of freedom is an important task for scientific and industrial applications. In order to solve such differential equations on a quantum computer, it is necessary to embed classical variables into a quantum state. While the Carleman and Koopman-von Neumann embeddings have been investigated so far, the class of problems that can be mapped to the Schr{"o}dinger equation is not well understood even for linear differential equations. In this work, we investigate the conditions for linear differential equations to be mapped to the Schr{"o}dinger equation and solved on a quantum computer. Interestingly, we find that these conditions are identical for both Carleman and Koopman-von Neumann embeddings. We also compute the computational complexity associated with estimating the expected values of an observable. This is done by assuming a state preparation oracle, block encoding of the mapped Hamiltonian via either Carleman or Koopman-von Neumann embedding, and block encoding of the observable. These results are important in the construction of quantum algorithms for solving differential equations of large-degree-of-freedom. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
linear differential equation / Carleman embedding / Koopman-von Neumann embedding / / / / / |
| Reference Info. |
IEICE Tech. Rep. |
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| Conference Information |
| Committee |
QIT |
| Conference Date |
2023-12-17 - 2023-12-19 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
OIST |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
Quantum Information |
| Paper Information |
| Registration To |
QIT |
| Conference Code |
2023-12-QIT |
| Language |
Japanese |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
How to Map Linear Differential Equations to Schr"{o}dinger Equations via Carleman and Koopman-von Neumann Embeddings for Quantum Algorithms |
| Sub Title (in English) |
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| Keyword(1) |
linear differential equation |
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Carleman embedding |
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Koopman-von Neumann embedding |
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| 1st Author's Name |
Yuki Ito |
| 1st Author's Affiliation |
Osaka University (Osaka Univ.) |
| 2nd Author's Name |
Yu Tanaka |
| 2nd Author's Affiliation |
Sony Group Corporation (Sony Group) |
| 3rd Author's Name |
Keisuke Fujii |
| 3rd Author's Affiliation |
Osaka University/RIKEN Center for Quantum Computing (Osaka Univ./RIKEN) |
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| Speaker |
Author-1 |
| Date Time |
2023-12-17 17:30:00 |
| Presentation Time |
120 minutes |
| Registration for |
QIT |
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vol. |
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