Fig. 4: Convergence benchmarks of the TJM.
From: Large-scale stochastic simulation of open quantum systems
a Error in the local observable 〈X[5]〉 at time Jt = 1 as a function of the number of trajectories N, for several time step sizes δt. Each point represents the average over 1000 batches. Dotted lines show the corresponding first-order Trotterization results for comparison. The shaded region indicates the standard deviation for δt = 0.1. The error follows the predicted scaling \(\sim C/\sqrt{N}\), with C ≈ 0.1, demonstrating that the second-order Trotter scheme yields low time-step errors such that N dominates over δt in determining convergence. b Convergence of the two-site correlator 〈X[i]X[i+1]〉 over time Jt ∈ [0, 10] at fixed δt = 0.1, shown as a function of trajectory number N and bond dimension χ. Each panel displays the local observable error, averaged over 1000 batches of N trajectories. The colormap is centered at an error threshold ϵ = 10−2: blue indicates lower error, red higher. While increasing N significantly improves global accuracy, a larger bond dimension is still required to resolve localized dynamical features.
