Geometric Amplification in Quantum Networks: The MPCT-τ Protocol for Selective State Enhancement

This paper introduces the MPCT-τ (Multi-Path Closure with adaptive Time-constant) protocol, a novel geometric approach for selective amplification of tar-get states in quantum networks. By leveraging geometric phase closure relationscombined with adaptive time-scale feedback and weak marking perturbations, weachieve significant amplification of specific quantum states. Numerical simulationsdemonstrate an average amplification factor of 7.44× for target states in 12-nodenetworks, substantially outperforming pure geometric evolution (0.94×). The sys-tem exhibits controllable entanglement entropy (ranging from 0.000 to 0.690) andshows promising scaling behavior with network size. The protocol operates throughthree interconnected mechanisms: (1) geometric phase closure enhancement viatriangular loops, (2) adaptive τ feedback based on closure errors, and (3) weaksymmetry-breaking marking. Our results provide a new paradigm for geomet-ric approaches to quantum state manipulation and offer potential applications inquantum-enhanced computation, state preparation, and quantum sensing.