Large-scale stochastic simulation of open quantum systems

Understanding interactions between quantum systems and their environments is crucial for developing stable quantum technologies and accurate physical models. Yet, simulating open quantum systems with non-unitary dynamics remains computationally demanding. We introduce the tensor jump method (TJM), a scalable and embarrassingly parallel algorithm for stochastically simulating large-scale open quantum systems governed by Lindbladians. The TJM extends the Monte Carlo wave function (MCWF) approach to matrix product states, employs a dynamic time-dependent variational principle (TDVP) to minimize evolution errors, and introduces a sampling MPS to reduce timestep dependence. This method scales efficiently, ensuring convergence to Lindbladian dynamics independent of system size, as demonstrated both rigorously and numerically. We showcase its utility by simulating XXX Heisenberg models with up to a thousand spins on a consumer-grade CPU. The TJM represents a significant advance in open quantum system simulation, enabling exploration of dissipative many-body dynamics and the design of more stable quantum hardware.