Entangling Capability and Expressibility

[stroblme]

This PR resolved #47 and #37.
The implementation includes:

• random circuits are first generated with unbound parameters (parameters are only bound before conversion to qasm). This was necessary, because the implementation of measures requires parameter adjustment
• implementation of the entangling capability following https://arxiv.org/abs/1905.10876
• implementation of the expressiblity following https://arxiv.org/abs/quant-ph/0305094 as inverse of the similarity of the state integral to the Haar measure
• both implementations of the measures were inspired by https://obliviateandsurrender.github.io/blogs/expr.html
• adding of 'samples_per_parameter' option in 'data_generation.yml' to the amount of sampled parameters when calculating the measures
• adding separate folder for storing the measures, so that in case something goes wrong, we don't have to start all-over again. This will result in different data locations but should not conflict with existent installations.
• adaption of the 'data generation' pipelines to include the nodes for calculating the measures
• adaption of the 'data science' pipeline to include the measures when combining evaluation results
• implementation of corresponding visualizations. Both measures result in a single figure using the standard color scheme.
• adaption of the 'data visualization' pipeline to include the nodes for generating the plots
• docstrings for all modified methods

After some evaluations and testing:

• added caching for both, Haar integrals and statevectors of circuits for each of the sampled parameter combinations which are identified using md5 hashes
• converted performance critical operations to jax->jit
• minor performance optimizations
• sort of hacky estimate how many samples we use for the pqc based on its parameters and number of qubits
• fixes in visualization
• updated overview diag accordingly

[pep8speaks]

Hello @stroblme! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

• In the file src/quafel/pipelines/data_generation/nodes.py:

Line 476:61: E203 whitespace before ':'

Comment last updated at 2024-06-06 08:58:40 UTC

[stroblme]

Hello @stroblme! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

* In the file [`src/quafel/pipelines/data_generation/nodes.py`](https://github.com/cirKITers/Quafel/blob/a85c147f0a4db880badf25f8d7b0de72b230bf23/src/quafel/pipelines/data_generation/nodes.py):

Line 382:61: E203 whitespace before ':'

Comment last updated at 2024-03-25 14:32:37 UTC

ignoring, because E203 is not PEP compliant

[cDenius]

Although there is some randomness in the calculation, you should be able to reproduce the results from your source, correct? Have you done that?

It would be a nice way to check your implementation.

[stroblme]

Although there is some randomness in the calculation, you should be able to reproduce the results from your source, correct? Have you done that?

It would be a nice way to check your implementation.

Good point, will add that!

[stroblme]

Added some tests to verify reasonable values for expressibility and entangling capability as mentioned in #42

[cDenius]

Looks good Melvin!
Like the additions you made!
Go for it, buddy!