The classical simulation of open quantum systems can bridge the gap between theory and experimental results.
Current noisy simulation methods such as the quantum jump method rely on using vectors which scale exponentially as larger and larger systems are considered. Up until now, this method has not utilized the computational advantage offered by representing quantum states as Matrix Product States which are able to avoid the unwanted exponential scaling. In this work, the tensor network quantum jump method has been created by adapting the vector-based method to tensor networks. This stochastic method was then benchmarked and first applications were demonstrated. The tensor network quantum jump method was created with the intent to allow us to scale quantum noise simulations much further than previously possible in order to understand noisy, error-causing processes in the building and scaling of quantum technologies.