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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.02966 |
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| _version_ | 1866909160367456256 |
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| author | Sharma, Kunal Tran, Minh C. |
| author_facet | Sharma, Kunal Tran, Minh C. |
| contents | We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian $A$ under a small geometrically local perturbation $αB$. In certain regimes, the algorithm achieves the optimal scaling and outperforms the state-of-the-art algorithms. By moving into the interaction frame of $A$ and classically computing the Magnus expansion of the interaction-picture Hamiltonian, our algorithm bypasses the need for ancillary qubits. In analyzing its performance, we develop a framework to capture the quasi-locality of the Magnus operators, leading to a tightened bound for the error of the Magnus truncation. The Lieb-Robinson bound also guarantees the efficiency of computing the Magnus operators and of their subsequent decomposition into elementary quantum gates. These features make our algorithm appealing for near-term and early-fault-tolerant simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion Sharma, Kunal Tran, Minh C. Quantum Physics We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian $A$ under a small geometrically local perturbation $αB$. In certain regimes, the algorithm achieves the optimal scaling and outperforms the state-of-the-art algorithms. By moving into the interaction frame of $A$ and classically computing the Magnus expansion of the interaction-picture Hamiltonian, our algorithm bypasses the need for ancillary qubits. In analyzing its performance, we develop a framework to capture the quasi-locality of the Magnus operators, leading to a tightened bound for the error of the Magnus truncation. The Lieb-Robinson bound also guarantees the efficiency of computing the Magnus operators and of their subsequent decomposition into elementary quantum gates. These features make our algorithm appealing for near-term and early-fault-tolerant simulations. |
| title | Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.02966 |