Quantum Algorithm Zoo: Fast Quantum Algorithm for Numerical Gradient Estimation

[amir-naveh]

In this issue, we will create an implementation of the following paper: Fast Quantum Algorithm for Numerical Gradient Estimation.
This tutorial should follow the structure of the Deutsch Jozsa algorithm implementationl.
Once finished, the implementation will be added to the Quantum Algorithm Zoo, and of course credit will be given to the implementor.

To complete this issue, follow these steps:

1. Read the following paper: Fast Quantum Algorithm for Numerical Gradient Estimation.
2. Create a new jupyter notebook (.ipynb file). Use any jupyter editor (e.g. jupyter lab, google colab, etc).
3. Use Classiq's SDK to create a simple implementation of the paper, and showcase the results. If you have any implementation questions or challenges, the Classiq team will assist you, either on Github or in our slack community. Follow the Deutsch Jozsa algorithm implementation example for the structure of the notebook.
4. Create a short mathematical explanation of the work. Jupyter notebooks support markdown cells, which can contain LaTeX. You can view the source or the superposition notebook to see how this is done. Chat GPT is an excellent LaTeX assistant.
5. After creating the notebook, make sure you insert the write_qmod(model, "bell_state.qmod") line. Run the notebook, and you will automatically generate the .qmod file for this example.
6. Make sure the notebook looks well, does not have any typos / mistakes, and is running properly.
7. Follow the contribution guidelines to open a pull request. Submit the tutorial to the directory: classiq-library/community/advanced_examples/natural_gradient_estimation

If you have any questions or comments, you can ask them here in the issue, or in our slack community, and the Classiq team will be happy to assist.

Happy quantum coding!