Lindbladian Simulation with Commutator Bounds

• URL: http://arxiv.org/abs/2603.28602v1
• Date: Mon, 30 Mar 2026 15:51:50 GMT
• Title: Lindbladian Simulation with Commutator Bounds
• Abstract summary: We derive commutator-based Trotter error bounds for Lindbladian simulation.<n>We apply Richardson extrapolation to achieve polylogarithmic precision while maintaining the commutator scaling.<n>For local Lindbladians, our results demonstrate that the Trotter-based methods outperform prior simulation techniques in system-size scaling.
• Score: 25.02796052598981
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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