We develop a theoretical framework that unifies concepts of multiple time dimensions, quantum shortcut dynamics, and complex topological structures ('supermazes') to explore novel phenomena in quantum and classical systems. In particular, we introduce a Temporal Tensor Formalism to describe multidimensional time, define Quantum Shortcut Operators that enact near-instantaneous state transitions, and incorporate these into a supermaze topological model inspired by labyrinthine geometry and network complexity. We show how this framework can give rise to surprising effects such as anomalous thermodynamic relaxation (analogous to the Mpemba effect) in quantum systems. Theoretical implications for quantum computing (including quantum cloud networks) are discussed, and connections are drawn to established mathematical paradoxes and physical principles. learn more on arXiv