Why Quantum Natural Gradients Fail experiments 

Description
This repository contains code and experiments developed for our research paper on the Flat Earth Paradox, 
including tests of our DFS QNG optimizer, as well as analyses of noise behavior, Hessian variance, and retraction scaling in quantum-inspired models.

Folders

- Dually Flat QNG: Experiments of of our proposed QNG optimizers.
- Plots: Generated visualizations and graphs.
- QNG-Noise: Experiments and results on noisy quantum models
- RH-Variance: Experiments of Hessian variance calculations and results.
- Retraction Scaling: Experiments of Retraction error scaling.

Usage
Run the scripts in each folder to reproduce experiments and generate plots.

Notes
Results may vary depending on parameters and noise settings.

Requirements
- Python 3.x
- pip

Installation
Run the following command in your terminal:
- pip install pennylane pennylane-lightning pennylane-lightning[gpu] torch

If using Jupyter Notebook (optional)
- !pip install pennylane pennylane-lightning pennylane-lightning[gpu] torch