| Paper Abstract and Keywords |
| Presentation |
2022-12-08 16:45
Improved Hardness Results for the Guided Local Hamiltonian Problem
Ryu Hayakawa (Kyoto Univ.), Francois Le Gall (Nagoya Univ.), Sevag Gharibian (Paderborn University), Tomoyuki Morimae (Kyoto Univ.) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding state has overlap (inverse-polynomially) close to $1/sqrt{2}$ with a ground state.
In this paper, we optimally improve both the locality and the overlap parameter: we show that the BQP-completeness persists even with 2-local Hamiltonians, and even when the guiding state has overlap (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. This makes a further step towards establishing practical quantum advantage in quantum chemistry. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
Quantum Computing / Quantum advantage / Hamiltonian complexity / Quantum chemistry / / / / |
| Reference Info. |
IEICE Tech. Rep. |
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| Conference Information |
| Committee |
QIT |
| Conference Date |
2022-12-08 - 2022-12-09 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
Keio Univ. |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
Quantum Information |
| Paper Information |
| Registration To |
QIT |
| Conference Code |
2022-12-QIT |
| Language |
Japanese |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
Improved Hardness Results for the Guided Local Hamiltonian Problem |
| Sub Title (in English) |
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| Keyword(1) |
Quantum Computing |
| Keyword(2) |
Quantum advantage |
| Keyword(3) |
Hamiltonian complexity |
| Keyword(4) |
Quantum chemistry |
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| 1st Author's Name |
Ryu Hayakawa |
| 1st Author's Affiliation |
Kyoto University (Kyoto Univ.) |
| 2nd Author's Name |
Francois Le Gall |
| 2nd Author's Affiliation |
Nagoya University (Nagoya Univ.) |
| 3rd Author's Name |
Sevag Gharibian |
| 3rd Author's Affiliation |
Paderborn University (Paderborn University) |
| 4th Author's Name |
Tomoyuki Morimae |
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Kyoto University (Kyoto Univ.) |
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| Speaker |
Author-1 |
| Date Time |
2022-12-08 16:45:00 |
| Presentation Time |
15 minutes |
| Registration for |
QIT |
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vol. |
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