Computation of Green's function by local variational quantum compilation
Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum comp...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-08-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.033070 |
| _version_ | 1797210435820191744 |
|---|---|
| author | Shota Kanasugi Shoichiro Tsutsui Yuya O. Nakagawa Kazunori Maruyama Hirotaka Oshima Shintaro Sato |
| author_facet | Shota Kanasugi Shoichiro Tsutsui Yuya O. Nakagawa Kazunori Maruyama Hirotaka Oshima Shintaro Sato |
| author_sort | Shota Kanasugi |
| collection | DOAJ |
| description | Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to 4×4 sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition. |
| first_indexed | 2024-04-24T10:10:33Z |
| format | Article |
| id | doaj.art-48b37446daad497a9100ad1334283f03 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:33Z |
| publishDate | 2023-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-48b37446daad497a9100ad1334283f032024-04-12T17:32:55ZengAmerican Physical SocietyPhysical Review Research2643-15642023-08-015303307010.1103/PhysRevResearch.5.033070Computation of Green's function by local variational quantum compilationShota KanasugiShoichiro TsutsuiYuya O. NakagawaKazunori MaruyamaHirotaka OshimaShintaro SatoComputation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to 4×4 sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition.http://doi.org/10.1103/PhysRevResearch.5.033070 |
| spellingShingle | Shota Kanasugi Shoichiro Tsutsui Yuya O. Nakagawa Kazunori Maruyama Hirotaka Oshima Shintaro Sato Computation of Green's function by local variational quantum compilation Physical Review Research |
| title | Computation of Green's function by local variational quantum compilation |
| title_full | Computation of Green's function by local variational quantum compilation |
| title_fullStr | Computation of Green's function by local variational quantum compilation |
| title_full_unstemmed | Computation of Green's function by local variational quantum compilation |
| title_short | Computation of Green's function by local variational quantum compilation |
| title_sort | computation of green s function by local variational quantum compilation |
| url | http://doi.org/10.1103/PhysRevResearch.5.033070 |
| work_keys_str_mv | AT shotakanasugi computationofgreensfunctionbylocalvariationalquantumcompilation AT shoichirotsutsui computationofgreensfunctionbylocalvariationalquantumcompilation AT yuyaonakagawa computationofgreensfunctionbylocalvariationalquantumcompilation AT kazunorimaruyama computationofgreensfunctionbylocalvariationalquantumcompilation AT hirotakaoshima computationofgreensfunctionbylocalvariationalquantumcompilation AT shintarosato computationofgreensfunctionbylocalvariationalquantumcompilation |