Modeling Quantum Wavefunction Collapse via the AMDCF Memory-Driven Framework

The transition of a quantum system from a superposition state to an eigenstate (measurement) is traditionally described by instantaneous, non-unitary projection. However, simulating rapid state transitions in quantum control hardware often leads to numerical instabilities (overshoots) due to the abrupt changes in control fields. In this paper, we propose a phenomenological control algorithm based on the unified AMDCF (Adaptive Memory-Driven Coupling Framework) to smoothly drive a qubit towards a target state. We utilize a derivative-based dynamic safety valve acting as a mathematical "rate limiter" to prevent unphysical numerical divergences during the control pulse. The simulation demonstrates a bounded, smooth transition from a coherence index of C=1.0 to C=0.0, while successfully steering the target state population towards |0⟩. This study highlights the AMDCF kernel's potential as a robust numerical stabilizer in quantum control engineering, without attempting to replace standard quantum measurement theory.