Simulating NISQ dynamics using quantum trajectories with few jumps

We present results on the efficiency of classically simulating the dynamics of open quantum many-body systems using a combination of quantum trajectories and 1D tensor network methods. Using Monte Carlo wavefunctions, the unraveling of the master equation gives rise to an ensemble of stochastic quantum trajectories conditioned on potential measurement outcomes (jumps). These trajectories must then be averaged over with appropriate jump statistics to obtain the system's density operator. The averaging is usually done in a stochastic manner until a sufficient sampling error is reached. Here we instead propose a deterministic method of sampling trajectories that avoids the computational overhead of stochastic trajectory sampling, is suitable for simulations of noisy intermediate-scale quantum (NISQ) devices, and has an easily computable sampling error. The usual object of interest in simulations of NISQ many-body dynamics is expectation values of local observables – e.g., one- or two-body correlation functions. These expectation values of local observables are regarded as being more robust to decoherence than other quantities less accessible to NISQ devices, and we conjecture that this robustness to decoherence implies the existence of a model solvable with classical efficiency. We apply our trajectory sampling method to demonstrate the efficiency of classical simulations of open quantum many-body dynamics, in support of this conjecture.