Fast-forwardability of Jordan-Wigner-transformed Fermion models based on Cartan decomposition
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913683026739200 |
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| author | Hidaka, Yuichiro Tsutsui, Shoichiro Kanasugi, Shota Matsumoto, Norifumi Maruyama, Kazunori Oshima, Hirotaka |
| author_facet | Hidaka, Yuichiro Tsutsui, Shoichiro Kanasugi, Shota Matsumoto, Norifumi Maruyama, Kazunori Oshima, Hirotaka |
| contents | We study the Hamiltonian algebra of Jordan-Wigner-transformed interacting fermion models and its fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that the qubit models obtained by the Jordan-Wigner transformation of these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast-forwardability of Jordan-Wigner-transformed Fermion models based on Cartan decomposition Hidaka, Yuichiro Tsutsui, Shoichiro Kanasugi, Shota Matsumoto, Norifumi Maruyama, Kazunori Oshima, Hirotaka Quantum Physics We study the Hamiltonian algebra of Jordan-Wigner-transformed interacting fermion models and its fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that the qubit models obtained by the Jordan-Wigner transformation of these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method. |
| title | Fast-forwardability of Jordan-Wigner-transformed Fermion models based on Cartan decomposition |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.04620 |