The combination of quantum materials into electrochemical systems provides a novel procedure in advanced energy storage technology. This study focused on the use of magic-angle twisted bilayer graphene (MATBG); a material known for its unconventional superconductivity and superfluid stiffness scaling at cryogenic temperatures suitable for enhancing battery interfaces under room temperature conditions. By exploiting the quantum capacitance of MATBG and incorporating it in an adapted Poisson-Nernst-Planck (PNP) theoretical framework, this study achieved substantial and remarkable improvements in interfacial energetics and charge-transfer kinetics. Explicitly, the modified PNP model showed a 50% reduction in interfacial potential gradients (from 8.2×10³ mol/m⁴ to 2.7×10³ mol/m⁴) and a 60% decrease in charge-transfer resistance (R_ct), as confirmed by Nyquist plot analysis. Experimentally, MATBG-integrated battery cells display a threefold increase in exchange current density (j₀) compared to normal or conventional cells, along with a substantial reduction in voltage hysteresis (0.07 V vs. 0.22 V in control systems) during cycling. These improvements are linked to the unique electronic characteristic of MATBG, which facilitates efficient redistribution of charges and eradicates kinetic problems at the electrode-electrolyte interface. These findings highlight and present the potential of MATBG as a high-performance quantum-electrochemical interface, which enables high-rate battery operation with improved energy stability and efficiency. This work bridges quantum material physics with practical electrochemistry and also opens a novel technique for designing next-generation energy storage systems that leverage quantum-engineered interfaces.