Temporal Tensors and Quantum Shortcut Dynamics in a Supermaze of Multidimensional Time
Koffka Khan
TL;DR
This paper addresses how to unify multiple time dimensions, quantum shortcut dynamics, and topological state-space structure into a coherent framework for quantum and classical systems. It introduces a Temporal Tensor Formalism with a temporal manifold $\mathcal{T}$, a quantum shortcut operator framework with a shortcut Hamiltonian $H_S$, and a supermaze topology to model state-space routing. The authors show that shortcut edges can reduce the topological complexity $TC(\Gamma)$ of the state space and can generate Mpemba-like relaxation phenomena in quantum systems, while respecting quantum speed limits. The work offers a conceptual bridge between geometry, topology, and quantum control, with potential implications for quantum cloud computing and algorithmic routing, and lays out directions for solvable models and simulations.
Abstract
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.