Fidelity-aware heuristic and search graph visualization

[EliasLF]

Description

Includes:

• a new fidelity-aware heuristic (+some changes to the current heuristic mapping system making it compatible with the new approach)
• a data logger (logging all search nodes and metadata in the heuristic mapper)
• a Python visualization module for visualizing search graphs after mapping
• the option to automatically split layers if the search takes too long
• iterative bidirectional routing (similar to Qiskit's SabreLayout but using QMAP's routing pass)

Currently, the fidelity-aware heuristic mapping is not yet compatible with dynamic initial layouting, lookahead or qubit teleportation. Therefore, I did not yet add an example for fidelity-aware mapping in Mapping.ipynb in the documentation. (I think advertising this feature outside the API reference only makes sense once it is more fleshed out)

Checklist:

• The pull request only contains commits that are related to it.
• I have added appropriate tests and documentation.
• I have made sure that all CI jobs on GitHub pass.
• The pull request introduces no new warnings and follows the project's style guidelines.

[codecov]

Codecov Report

Attention: 87 lines in your changes are missing coverage. Please review.

Comparison is base (07642b8) 92.3% compared to head (aebd205) 93.0%.

Additional details and impacted files

@@           Coverage Diff           @@
##            main    #384     +/-   ##
=======================================
+ Coverage   92.3%   93.0%   +0.7%     
=======================================
  Files         44      46      +2     
  Lines       4158    4875    +717     
  Branches     701     843    +142     
=======================================
+ Hits        3838    4534    +696     
- Misses       320     341     +21     

Flag	Coverage Δ
cpp	92.6% <90.7%> (+0.8%)	⬆️
python	96.0% <100.0%> (+0.1%)	⬆️

Files	Coverage Δ
include/DataLogger.hpp	100.0% <100.0%> (ø)
include/Mapper.hpp	83.8% <ø> (+19.3%)	⬆️
include/MappingResults.hpp	79.1% <100.0%> (+0.6%)	⬆️
include/configuration/Configuration.hpp	100.0% <100.0%> (ø)
include/heuristic/HeuristicMapper.hpp	98.3% <100.0%> (+0.1%)	⬆️
include/utils.hpp	80.0% <ø> (ø)
src/mqt/qmap/__init__.py	66.6% <100.0%> (+1.9%)	⬆️
src/mqt/qmap/compile.py	97.1% <100.0%> (+0.9%)	⬆️
src/utils.cpp	92.5% <100.0%> (+1.8%)	⬆️
include/configuration/InitialLayout.hpp	47.0% <0.0%> (-0.6%)	⬇️
... and 6 more

[github-advanced-security]

CodeQL found more than 10 potential problems in the proposed changes. Check the Files changed tab for more details.

[burgholzer]

Many many thanks again for this nice contribution.
As discussed, I quickly skimmed over everything again and checked the most important parts. You can find a couple of extremely small comments inline as part of this review. Most of them, you should just be able to collect in a batch and commit in bulk (if you agree with the suggestions of course).
After that, I'd be happy to merge this 🎉

[burgholzer]

I believe this is good to go, so let's get it in 🎉
Many thanks for all the work here. Looking forward to what's next!

[EliasLF]

I agree, let's merge👍
Thank you very much for the suggestions and the recent work on the Graphviz issue!