Lindbladian Simulation with Commutator Bounds
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911553806139392 |
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| author | Wang, Xinzhao Zhou, Shuo Wang, Xiaoyang Zheng, Yi-Cong Zhang, Shengyu Li, Tongyang |
| author_facet | Wang, Xinzhao Zhou, Shuo Wang, Xiaoyang Zheng, Yi-Cong Zhang, Shengyu Li, Tongyang |
| contents | Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested commutators of the summands, such a relationship remains poorly understood for Lindbladian dynamics. In this Letter, we derive commutator-based Trotter error bounds for Lindbladian simulation, yielding an $O(\sqrt{N})$ scaling in the number of Trotter steps for locally interacting systems on $N$ sites. When estimating observable averages, we apply Richardson extrapolation to achieve polylogarithmic precision while maintaining the commutator scaling. To bound the extrapolation remainder, we develop a general truncation bound for the Baker-Campbell-Hausdorff expansion that bypasses common convergence issues in physically relevant systems. For local Lindbladians, our results demonstrate that the Trotter-based methods outperform prior simulation techniques in system-size scaling while requiring only $O(1)$ ancillas. Numerical simulations further validate the predicted system-size and precision scaling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lindbladian Simulation with Commutator Bounds Wang, Xinzhao Zhou, Shuo Wang, Xiaoyang Zheng, Yi-Cong Zhang, Shengyu Li, Tongyang Quantum Physics Data Structures and Algorithms Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested commutators of the summands, such a relationship remains poorly understood for Lindbladian dynamics. In this Letter, we derive commutator-based Trotter error bounds for Lindbladian simulation, yielding an $O(\sqrt{N})$ scaling in the number of Trotter steps for locally interacting systems on $N$ sites. When estimating observable averages, we apply Richardson extrapolation to achieve polylogarithmic precision while maintaining the commutator scaling. To bound the extrapolation remainder, we develop a general truncation bound for the Baker-Campbell-Hausdorff expansion that bypasses common convergence issues in physically relevant systems. For local Lindbladians, our results demonstrate that the Trotter-based methods outperform prior simulation techniques in system-size scaling while requiring only $O(1)$ ancillas. Numerical simulations further validate the predicted system-size and precision scaling. |
| title | Lindbladian Simulation with Commutator Bounds |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2603.28602 |