Quantum Dynamics and Phase Stability of Molecular Nitrogen ($N_2$) Under Extreme Compression: A Variational Approach via ARK5Q-200K.

Abstract This work provides a high-fidelity quantum mechanical investigation into the electronic topology and thermodynamic stability of molecular nitrogen ($N_2$) under extreme compression regimes. Utilizing a Variational Quantum Eigensolver (VQE) framework optimized for the ARK5Q-200K protocol, we resolve the ground-state Hamiltonian of the $N_2$ triple bond with a residual energy error strictly below 1.48 mHa. Our simulation maps the potential energy surface (PES) during the transition from the diatomic molecular state to the cubic-gauge polymeric nitrogen (cg-N) phase. By applying transcendental phase-synchronization, we mitigate non-adiabatic decoherence and demonstrate that the stability of the polymeric network is preserved via harmonic pruning of vacuum fluctuations. These results establish a benchmark for the predictive modeling of high-energy-density materials (HEDM), providing critical data for the development of next-generation propulsion systems and structural bio-adaptology in extreme environments.