Fig. 5: Convergence of the TJM with increasing bond dimension χ = {2, 4, 8} for a 30-site noisy XXX Heisenberg model with parameters J = h = 1 and a domain-wall initial state (wall at site 15).
From: Large-scale stochastic simulation of open quantum systems
The noise model includes local relaxation and excitation channels σ± with equal strength γ± = 0.1. a–d Site-resolved magnetization 〈Z[i]〉 over time, compared against a reference simulation using an MPO with bond dimension capped at D = 400. e–h Time evolution of 〈Z[i]〉 for selected sites i = 1, 5, 10, 15, showing quantitative agreement between TJM and MPO as χ increases. All simulations use a timestep δt = 0.1, and TJM is averaged over N = 100 trajectories. While the MPO simulation requires over 24 h, the TJM runs complete in under 5 min. This highlights the ability of TJM to efficiently and accurately reproduce both global and local dynamics at modest bond dimension, making it a practical tool for rapid prototyping of noisy quantum dynamics.
