In QTT open quantum systems are modelled as scattering processes, with classical external fields corresponding to the inputs and classical stochastic processes corresponding to the outputs (the fields after the measurement process). The mapping from inputs to outputs is provided by a quantum stochastic process that is set up to account for a particular measurement strategy (e.g., photon counting, homodyne / heterodyne detection, etc.). The calculated system state as a function of time is known as a quantum trajectory, and the desired density matrix as a function of time may be calculated by averaging over many simulated trajectories.