Simplifying the simulation of local Hamiltonian dynamics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911904097632256 |
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| author | Usui, Ayaka Sanpera, Anna Díaz, María García |
| author_facet | Usui, Ayaka Sanpera, Anna Díaz, María García |
| contents | Local Hamiltonians, $H_k$, describe non-trivial $k$-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a $k$-local Hamiltonian by a simpler one, $H_{k'}$, with $k'<k$, under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of $H_k$ and $H_{k'}$ that simulate the same physics. We also address the most realistic case of approximate simulation. There, we upper-bound the error up to which a Hamiltonian can simulate another one, regardless of their internal structure, and prove, by means of an example, that the accuracy of a $(k'=2)$-local Hamiltonian to simulate $H_{k}$ with $k>2$ increases with $k$. Finally, we propose a method to search for the $k'$-local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given $H_k$ Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simplifying the simulation of local Hamiltonian dynamics Usui, Ayaka Sanpera, Anna Díaz, María García Quantum Physics Local Hamiltonians, $H_k$, describe non-trivial $k$-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a $k$-local Hamiltonian by a simpler one, $H_{k'}$, with $k'<k$, under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of $H_k$ and $H_{k'}$ that simulate the same physics. We also address the most realistic case of approximate simulation. There, we upper-bound the error up to which a Hamiltonian can simulate another one, regardless of their internal structure, and prove, by means of an example, that the accuracy of a $(k'=2)$-local Hamiltonian to simulate $H_{k}$ with $k>2$ increases with $k$. Finally, we propose a method to search for the $k'$-local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given $H_k$ Hamiltonian. |
| title | Simplifying the simulation of local Hamiltonian dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.07054 |