| Paper Abstract and Keywords |
| Presentation |
2018-11-26 13:30
[Poster Presentation]
Subspace-search variational quantum eigensolver for excited states
Ken M Nakanishi (Univ. Tokyo), Kosuke Mitarai (Osaka Univ.), Keisuke Fujii (Kyoto Univ.) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of near-term quantum computers. The original work [Peruzzo et al.; textit{Nat. Commun.}; textbf{5}, 4213 (2014)] focused only on finding a ground state, whereas the excited states can also induce interesting phenomena in molecules and materials. Calculating excited states is, in general, a more difficult task than finding ground states for classical computers. To extend the framework to excited states, we here propose an algorithm, the subspace-search variational quantum eigensolver (SSVQE). This algorithm searches a low energy subspace by supplying orthogonal input states to the variational ansatz and relies on the unitarity of transformations to ensure the orthogonality of output states. The $k$-th excited state is obtained as the highest energy state in the low energy subspace. The proposed algorithm consists only of two parameter optimization procedures and does not employ any ancilla qubits. The disuse of the ancilla qubits is a great improvement from the existing proposals for excited states, which have utilized the swap test, making our proposal a truly near-term quantum algorithm. We further generalize the SSVQE to obtain all excited states up to the $k$-th by only single optimization procedure. From numerical simulations, we verify the proposed algorithms. This work greatly extends the applicable domain of the VQE to excited states and their related properties like a transition amplitude without sacrificing any feasibility of it. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
NISQ / VQE / Excited state / Quantum algorithm / / / / |
| Reference Info. |
IEICE Tech. Rep. |
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| Conference Information |
| Committee |
QIT |
| Conference Date |
2018-11-26 - 2018-11-27 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
The University of Tokyo |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
Quantum Information |
| Paper Information |
| Registration To |
QIT |
| Conference Code |
2018-11-QIT |
| Language |
Japanese |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
Subspace-search variational quantum eigensolver for excited states |
| Sub Title (in English) |
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NISQ |
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VQE |
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Excited state |
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Quantum algorithm |
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| 1st Author's Name |
Ken M Nakanishi |
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The University of Tokyo (Univ. Tokyo) |
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Kosuke Mitarai |
| 2nd Author's Affiliation |
Osaka University (Osaka Univ.) |
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Keisuke Fujii |
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Kyoto University (Kyoto Univ.) |
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| Date Time |
2018-11-26 13:30:00 |
| Presentation Time |
120 minutes |
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QIT |
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