How efficiently can we simulate the open system dynamics of Ising models?

A near-term goal for Noisy Intermediate Scale Quantum (NISQ) devices is quantum simulation of nonequilibrium dynamics in many-body systems [Preskill Quantum 2, 79 (2018)]. While the exact unitary dynamics of a closed many-body quantum systems is generally intractable, recent work has shown that approximate simulations of NISQ devices are tractable [Zhou, et al, arXiv:2002.07730; Noh, et al, arXiv:2003.13163; Chen et al arXiv:2004.02388]. Inspired by experiments using arrays of Rydberg atoms and trapped ions, we study the quantum simulation of non-equilibrium dynamics of Ising spin chains in 1D. We assume open quantum system dynamics with local decoherence given by a Lindblad master equation, which we solve using quantum trajectories and tensor networks. We explore how decoherence and approximation using a truncated matrix product state representation effects the long range order observed in the non-equilibrium dynamics. We find that decoherence permits more aggressive truncation of matrix product states, suggesting that classical simulation of certain quantum observables may be tractable above a certain level of decoherence.