Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
Ground-state preparation is an important task in quantum computation. The probabilistic imaginary-time evolution (PITE) method is a promising candidate for preparing the ground state of the Hamiltonian, which comprises a single ancilla qubit and forward- and backward-controlled real-time evolution o...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-10-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043048 |
| _version_ | 1797210412346769408 |
|---|---|
| author | Hirofumi Nishi Koki Hamada Yusuke Nishiya Taichi Kosugi Yu-ichiro Matsushita |
| author_facet | Hirofumi Nishi Koki Hamada Yusuke Nishiya Taichi Kosugi Yu-ichiro Matsushita |
| author_sort | Hirofumi Nishi |
| collection | DOAJ |
| description | Ground-state preparation is an important task in quantum computation. The probabilistic imaginary-time evolution (PITE) method is a promising candidate for preparing the ground state of the Hamiltonian, which comprises a single ancilla qubit and forward- and backward-controlled real-time evolution operators. The ground state preparation is a challenging task even in the quantum computation, classified as complexity-class quantum Merlin-Arthur. However, optimal parameters for PITE could potentially enhance the computational efficiency to a certain degree. In this paper, we analyze the computational costs of the PITE method for both linear and exponential scheduling of the imaginary-time step size for reducing the computational cost. First, we analytically discuss an error defined as the closeness between the states acted on by exact and approximate imaginary-time evolution operators. The optimal imaginary-time step size and rate of change of imaginary time are also discussed. Subsequently, the analytical discussion is validated using numerical simulations for a one-dimensional Heisenberg chain. From the results, we find that linear scheduling works well in the case of unknown eigenvalues of the Hamiltonian. For a wide range of eigenstates, the linear scheduling returns smaller errors on average. However, the linearity of the scheduling causes problems for some specific energy regions of eigenstates. To avoid these problems, incorporating a certain level of nonlinearity into the scheduling, such as by inclusion of an exponential character, is preferable for reducing the computational costs of the PITE method. The findings of this paper can make a significant contribute to the field of ground-state preparation of many-body Hamiltonians on quantum computers. |
| first_indexed | 2024-04-24T10:10:11Z |
| format | Article |
| id | doaj.art-f26a5023be1d41a6b6d8dc7ce8485351 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:11Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-f26a5023be1d41a6b6d8dc7ce84853512024-04-12T17:35:07ZengAmerican Physical SocietyPhysical Review Research2643-15642023-10-015404304810.1103/PhysRevResearch.5.043048Optimal scheduling in probabilistic imaginary-time evolution on a quantum computerHirofumi NishiKoki HamadaYusuke NishiyaTaichi KosugiYu-ichiro MatsushitaGround-state preparation is an important task in quantum computation. The probabilistic imaginary-time evolution (PITE) method is a promising candidate for preparing the ground state of the Hamiltonian, which comprises a single ancilla qubit and forward- and backward-controlled real-time evolution operators. The ground state preparation is a challenging task even in the quantum computation, classified as complexity-class quantum Merlin-Arthur. However, optimal parameters for PITE could potentially enhance the computational efficiency to a certain degree. In this paper, we analyze the computational costs of the PITE method for both linear and exponential scheduling of the imaginary-time step size for reducing the computational cost. First, we analytically discuss an error defined as the closeness between the states acted on by exact and approximate imaginary-time evolution operators. The optimal imaginary-time step size and rate of change of imaginary time are also discussed. Subsequently, the analytical discussion is validated using numerical simulations for a one-dimensional Heisenberg chain. From the results, we find that linear scheduling works well in the case of unknown eigenvalues of the Hamiltonian. For a wide range of eigenstates, the linear scheduling returns smaller errors on average. However, the linearity of the scheduling causes problems for some specific energy regions of eigenstates. To avoid these problems, incorporating a certain level of nonlinearity into the scheduling, such as by inclusion of an exponential character, is preferable for reducing the computational costs of the PITE method. The findings of this paper can make a significant contribute to the field of ground-state preparation of many-body Hamiltonians on quantum computers.http://doi.org/10.1103/PhysRevResearch.5.043048 |
| spellingShingle | Hirofumi Nishi Koki Hamada Yusuke Nishiya Taichi Kosugi Yu-ichiro Matsushita Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer Physical Review Research |
| title | Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer |
| title_full | Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer |
| title_fullStr | Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer |
| title_full_unstemmed | Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer |
| title_short | Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer |
| title_sort | optimal scheduling in probabilistic imaginary time evolution on a quantum computer |
| url | http://doi.org/10.1103/PhysRevResearch.5.043048 |
| work_keys_str_mv | AT hirofuminishi optimalschedulinginprobabilisticimaginarytimeevolutiononaquantumcomputer AT kokihamada optimalschedulinginprobabilisticimaginarytimeevolutiononaquantumcomputer AT yusukenishiya optimalschedulinginprobabilisticimaginarytimeevolutiononaquantumcomputer AT taichikosugi optimalschedulinginprobabilisticimaginarytimeevolutiononaquantumcomputer AT yuichiromatsushita optimalschedulinginprobabilisticimaginarytimeevolutiononaquantumcomputer |