✨⚡🍱 new optimization pass, better application strategies, new gate profiles

[burgholzer]

Description

This PR collects a couple of smaller scale improvements.

• First, it introduces a new default optimization pass, that elides permutations (i.e., SWAPs) from circuits completely. This helps to reduce the size of the circuits and might even give rise to some further optimization potential due to the removed gates. The PR also reorganizes the sequence in which individual operations are run, which should further increase the potential for optimization.

• Secondly, it slightly optimizes the default application strategies. Both, the proportional and the gate cost application scheme, now take into account whether the single qubit gate fusion optimization has been performed. Furthermore, the proportional (default) strategy now computes the gate ratio on the fly, which is expected to yield better result in general.

• Thirdly, this PR updates the gate cost profiles for Qiskit. Due to a small bug in the test, any changes were no longer detected. This has been fixed and the gate profiles have been updated. This also includes support for 6 more (two-target) gates.

• Lastly, the PR contains some fixes for new clang-tidy warnings.

Checklist:

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

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 99.37888% with 1 lines in your changes are missing coverage. Please review.

Project coverage is 96.3%. Comparing base (3a0f498) to head (b4a306a). Report is 1 commits behind head on main.

Additional details and impacted files

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[include/EquivalenceCheckingManager.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2FEquivalenceCheckingManager.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9FcXVpdmFsZW5jZUNoZWNraW5nTWFuYWdlci5ocHA=) | `100.0% <ø> (ø)` | | | [include/checker/EquivalenceChecker.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2Fchecker%2FEquivalenceChecker.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL0VxdWl2YWxlbmNlQ2hlY2tlci5ocHA=) | `100.0% <100.0%> (ø)` | | | 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[include/checker/dd/DDEquivalenceChecker.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2Fchecker%2Fdd%2FDDEquivalenceChecker.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL2RkL0RERXF1aXZhbGVuY2VDaGVja2VyLmhwcA==) | `100.0% <ø> (ø)` | | | [include/checker/dd/DDSimulationChecker.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2Fchecker%2Fdd%2FDDSimulationChecker.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL2RkL0REU2ltdWxhdGlvbkNoZWNrZXIuaHBw) | `100.0% <ø> (ø)` | | | [include/checker/dd/TaskManager.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2Fchecker%2Fdd%2FTaskManager.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL2RkL1Rhc2tNYW5hZ2VyLmhwcA==) | `98.5% <100.0%> (+<0.1%)` | :arrow_up: | | [...dd/applicationscheme/GateCostApplicationScheme.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2Fchecker%2Fdd%2Fapplicationscheme%2FGateCostApplicationScheme.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL2RkL2FwcGxpY2F0aW9uc2NoZW1lL0dhdGVDb3N0QXBwbGljYXRpb25TY2hlbWUuaHBw) | `95.4% <100.0%> (+0.2%)` | :arrow_up: | | [...pplicationscheme/ProportionalApplicationScheme.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree&filepath=include%2Fchecker%2Fdd%2Fapplicationscheme%2FProportionalApplicationScheme.hpp&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL2RkL2FwcGxpY2F0aW9uc2NoZW1lL1Byb3BvcnRpb25hbEFwcGxpY2F0aW9uU2NoZW1lLmhwcA==) | `100.0% <100.0%> (ø)` | | | ... and [9 more](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum) | | ... and [1 file with indirect coverage changes](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/385/indirect-changes?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum)