Lindbladian Simulation with Commutator Bounds
This work advances simulation techniques for open quantum systems, offering better scaling for researchers in quantum computing and physics.
The authors derived commutator-based error bounds for simulating open quantum systems using Trotter decomposition, achieving O(√N) scaling in Trotter steps for locally interacting systems and applying Richardson extrapolation for polylogarithmic precision. Numerical simulations validated the improved system-size and precision scaling compared to prior methods.
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.