I built a PyTorch global optimization engine (Basin Hopping + LAPACK) that computationally refutes an 18-year-old theorem in Quantum Information Theory
Hi r/MachineLearning,
I am an independent researcher working at the intersection of AI optimization and Quantum Information Theory.
For the past 18 years, the quantum computing community has accepted the Smith-Yard (2008) "Quantum Superactivation" theorem. The proof relied on analytical approximations to evaluate the Devetak-Winter key rate ($K_{DW}$) for low-dimensional Positive Partial Transpose (PPT) states.
Instead of relying on analytical approximations, I decided to test this computationally.
I built a highly constrained global optimization engine in PyTorch. By combining Basin Hopping with exact LAPACK diagonalizations and massive NPT penalty multipliers, the optimizer exhaustively searched the 512-dimensional manifold (for $d \le 6$).
The result: The optimizer proved that the Devetak-Winter key rate is strictly bounded by $K_{DW} \le -0.68$. The supposed positive key rate is mathematically impossible in these regimes.
To verify this wasn't a finite-blocklength scaling issue, I also built a 30-qubit hybrid AI simulator using SPSA (Simultaneous Perturbation Stochastic Approximation) for the $N=15$ Joint Channel topology. Even with an omniscient noise-prediction encoder, the loss hits a strict Barren Plateau at 1.0. The math shows superactivation is physically unrealizable.
To ensure complete transparency and reproducibility, I have open-sourced the entire PyTorch codebase, the Stinespring purification logic, and the optimization pipeline.
GitHub Repo: https://github.com/lizbeth307/quantum-superactivation-refutation Preprint (Zenodo): https://doi.org/10.5281/zenodo.20189708
I have prepared a formal manuscript detailing the methodology, but as an independent researcher, I currently lack the institutional affiliation required to submit to the quant-ph category on arXiv. If any established researchers here find this PyTorch implementation sound, I would be incredibly grateful for an arXiv endorsement (Endorsement code: QU8THF).
I would love for the ML/Optimization community to tear my code apart and tell me if you see any flaws in the PyTorch pipeline. Thanks for reading!