Efficient simulation of non-equilibrium many-body quantum dynamics using a stochastic unraveling

Spin models are paradigmatic many-body systems, informing various phenomena, including transport, phase transitions, and entanglement dynamics. Extending to open systems can both show new effects and is crucial in the current NISQ-era of devices. We present a new technique for efficiently simulating a class of open, many-body spin models with Jordan-Wigner strings in the jump operators, despite the fact that these models cannot be mapped to free fermion master equations [1]. Many such Lindblad master equations admit an exact stochastic unraveling, with individual trajectories evolving as Gaussian fermionic states, even though the full master equation describes an interacting system. We can calculate arbitrary observables efficiently with bounded sampling complexity. Beyond simply providing a powerful numerical technique, our method can also be used to gain both qualitative and quantitative insights into the role of interactions in these models. We demonstrate a surprising connection to dissipative Z2 gauge theories that permits exact study of both 1D and 2D systems from a transverse field Ising model in a noisy longitudinal field, to the evolution of topological order in a Kitaev honeycomb subjected to depolarizing noise.



[1] A. Pocklington and A. A. Clerk PRX Quantum 6, 030349 (2025)