✨ Stripping DDs of their identity

[burgholzer]

Description

This PR pulls in the changes from cda-tum/mqt-core#358, which considerably changes the way matrix decision diagrams are represented. Particularly, any node resembling the identity is now eliminated and only implicitly represented. This further compacts the representation of quantum gates and makes the identity the most compact it can be---a single terminal node. The overall performance improvements are still to be evaluated. Surprisingly few changes were needed to make this work in QCEC.

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

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 96.3%. Comparing base (da135b9) to head (fb1f97d). Report is 1 commits behind head on main.

Additional details and impacted files

[](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum) ```diff @@ Coverage Diff @@ ## main #377 +/- ## ======================================= + Coverage 96.2% 96.3% +0.1% ======================================= Files 34 34 Lines 1766 1765 -1 Branches 217 218 +1 ======================================= + Hits 1700 1701 +1 + Misses 66 64 -2 ``` | [Flag](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum) | Coverage Δ | | |---|---|---| | [cpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum) | `96.1% <100.0%> (+0.1%)` | :arrow_up: | | [python](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum) | `97.2% <ø> (ø)` | | | [Files](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377?dropdown=coverage&src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum) | Coverage Δ | | |---|---|---| | [include/checker/dd/DDConstructionChecker.hpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-aW5jbHVkZS9jaGVja2VyL2RkL0REQ29uc3RydWN0aW9uQ2hlY2tlci5ocHA=) | `83.3% <100.0%> (ø)` | | | [src/checker/dd/DDAlternatingChecker.cpp](https://app.codecov.io/gh/cda-tum/mqt-qcec/pull/377?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cda-tum#diff-c3JjL2NoZWNrZXIvZGQvRERBbHRlcm5hdGluZ0NoZWNrZXIuY3Bw) | `92.0% <100.0%> (+2.5%)` | :arrow_up: |