Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.10412 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912447838814208 |
|---|---|
| author | Bishop, Gino Bagrets, Dmitry Wilhelm, Frank K. |
| author_facet | Bishop, Gino Bagrets, Dmitry Wilhelm, Frank K. |
| contents | In the framework of the hybrid quantum-classical variational cluster approach (VCA) to strongly correlated electron systems one of the goals of a quantum subroutine is to find single-particle correlation functions of lattice fermions in polynomial time. Previous works suggested to use variants of the Hadamard test for this purpose, which requires an implementation of controlled single-particle fermionic operators. However, for a number of locality-preserving mappings to encode fermions into qubits, a direct construction of such operators is not possible. In this work, we propose a new quantum algorithm, which uses an analog of the Kubo formula adapted to a quantum circuit simulating the Hubbard model. It allows to access the Green's function of a cluster directly using only bilinears of fermionic operators and circumvents the usage of the Hadamard test. We test our new algorithm in practice by using open-access simulators of noisy IBM superconducting chips. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10412 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model Bishop, Gino Bagrets, Dmitry Wilhelm, Frank K. Quantum Physics Strongly Correlated Electrons In the framework of the hybrid quantum-classical variational cluster approach (VCA) to strongly correlated electron systems one of the goals of a quantum subroutine is to find single-particle correlation functions of lattice fermions in polynomial time. Previous works suggested to use variants of the Hadamard test for this purpose, which requires an implementation of controlled single-particle fermionic operators. However, for a number of locality-preserving mappings to encode fermions into qubits, a direct construction of such operators is not possible. In this work, we propose a new quantum algorithm, which uses an analog of the Kubo formula adapted to a quantum circuit simulating the Hubbard model. It allows to access the Green's function of a cluster directly using only bilinears of fermionic operators and circumvents the usage of the Hadamard test. We test our new algorithm in practice by using open-access simulators of noisy IBM superconducting chips. |
| title | Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.10412 |