# Lindbladian Simulation with Commutator Bounds

arXiv: https://arxiv.org/abs/2603.28602 · HTML: https://mlsanity.com/paper/2603.28602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [Learning the structure of open quantum systems](https://mlsanity.com/paper/2606.30358/) (2026)

## Abstract (arXiv)

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(√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.