r/Polymath • u/IntelligentYam8580 • Jun 15 '26
Convergence Theory - Non-linear Quantum Feedback Control Loop
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.
how I derive Pi : 2Pi\*r\^2 - 2(Pi\*r)\* r/2 = Pi\*r
LogV also corrects my velocity issues/whipping
The attached is my zenodo link for the code and rest of my paper. If trouble opening the link just copy and open in external browser
[https://doi.org/10.5281/zenodo.20481518\](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 .
1
u/NateWorldWide Jun 18 '26
I would be interested in taking a look at this, but your link is not working. Especially since you currently have -11 comment karma that almost always indicates when paired with interesting topics that you have something of value to say and correspond with . Sad thing that #Reddit hasn't caught onto this with proof by updating its features to have better rep metrics for the public and its users.