The project aims to provide the first method for characterising dynamics of a quantum system immersed in a complex surrounding; such as a quantum computer interacting with an environment that remembers the computer's past. There are no known methods for battling the affects of the environment on the computer when two are intertwined. The project is anticipated to develop tools to combats such adverse effects. The project aims to uncover new physics of complex dynamics and enable investigations of unexplored physical phenomena in the laboratory, like an antenna of photosynthetic systems that use complex surrounding for efficient and fast energy transport. The project is expected to help the effort to build new and improved quantum machines.