MPCT-τ: Geometric Quantum State Control via Multi-Path Closure Time Theory

We present a novel quantum state control method based on Multi-PathClosure Time (MPCT) theory that achieves significant quantum stateamplification through purely geometric dynamics without externalHamiltonian driving. The MPCT-τ framework demonstrates: (1) Average 2.50×(maximum 3.55×) local state probability enhancement via weak periodicmarking, (2) Observation of quantized peak spacing following n² patternswith n²=4 corresponding to n=2, (3) Natural formation of multi-peaksuperposition states with average 3.4 significant peaks in geometric mode,and (4) Non-zero entanglement entropy averaging 0.44, confirming genuinequantum correlations. The core mechanism involves emergent time scalesfrom MPCT phase closures, geometric vibrations for coherence maintenance,and weak dissipation implementing the Principle of Existence Cost (PEC). Thiswork establishes a new paradigm for low-energy geometric quantum controlwith only three core parameters, potentially revolutionizing quantumcomputation approaches.Keywords: Quantum state control, Geometric quantum computation, Multipath closure, Emergent time, Quantum amplification, n² quantization