Quantum technologies are at the point where hundreds of noisy components can be controlled and combined to achieve remarkable feats. While exciting, the real challenge lies in overcoming the conceptual and technological difficulties that stand in the way of robust large-scale computation. With this shift comes a strong need for supporting simulation tools to characterize physical noise at several levels of the design process. This issue is exacerbated by the growing size of realistic devices, which causes conventional tools to either become intractable or necessarily discard much of the inherent quantum nature of the system. In this proposed research project, we aim to remedy this by developing tensor-network based approximate simulation tools that accurately characterize, capture and exploit realistic quantum noise in near-term devices and protocols. Building on techniques for approximate time-evolution, we will design simulation tools for dissipative pulse-level dynamics in quantum devices. On a higher level, these results will be used to characterize and exploit noise at the device-level. Finally, novel approaches to circuit-level simulations will be designed for validating experiments at the highest level. These tools would be invaluable in the development of larger quantum devices, since they facilitate a synergy between device and protocol design by establishing a direct link between the physical device properties and the resulting optimal protocol performance.