Complexity of Quantum Processes: Simulating and Learning Multi-time Physics

Nothing in nature exists in isolation. Every atom, molecule and quantum system is shaped by the world around it. These constant interactions can create surprisingly intricate patterns of behaviour -- past events my impact future behaviour. This thesis explores the complexity of these quantum systems, showing that their evolving relationship with the environment can be too rich for ordinary computers to describe. By developing new ways to study this complexity, the thesis reveals that quantum computers themselves may hold the key to understanding this hidden structure -- and to uncovering how the quantum world truly behaves over time.