Convergence Theory - Non-linear Quantum Feedback Control Loop
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This preprint presents a hybrid classical-quantum framework for stabilizing coherence in open systems using a geometric invariant \\Phi(\\pi\*r) (r = 0.154) as a scalar potential boundary condition. The approach replaces traditional grid-based simulations with a constrained manifold projection \\Pi\_{\\mathcal{K}}, enabling efficient feedback control. The included Master Key (master.py) demonstrates: • Real-time non-commuting feedback (\\sigma\_x drive + \\sigma\_z control) • Explicit geometric projection operator pulling \\langle\\sigma\_z\\rangle toward the \\pi\*r target • Open-system decoherence handling • Clear “Valley of Convergence” in the stability map Key Results: Strong numerical evidence of a basin of attraction around the geometric invariant and effective decoherence suppression in a driven qubit. Limitations: Currently limited to a single-qubit model. The specific choice of r = 0.154 and full mathematical rigor of the surface integral / topology-dependent \\mathcal{K} require further development. Multi-qubit scaling, deeper physical justification, and experimental validation are planned for future work. Presented as an exploratory proof-of-concept in quantum control and geometric methods. Keywords: quantum coherence, feedback control, geometric invariant, open quantum systems, manifold projection, QuTiP At the bottom replace the stability map \[i,j\] with V≈d⋅Φln(d) V≈ln(d)d⋅Φ And it will fix my error. LogV also corrects my velocity issues/whipping The attached is my zenodo link for the code and rest of my paper. https://doi.org/10.5281/zenodo.20481518 I am asking for community help to prove it all wrong. Counter intuitive I know. But I have been trying for a long time to break it apart and would really appreciate help from everyone . I can define further if needed and aid in whatever way . submitted by /u/IntelligentYam8580 [link] [comments]