🚸 Ancillary and garbage handling

[burgholzer]

Description

This PR ensures that the way ancillary and garbage qubits are treated in QCEC is theoretically sound and removes several corresponding "TODOs" in the code.

In particular, the alternating DD checker cannot be used whenever both circuits contain ancillary qubits that are acted upon.
Up until now, this did not cause any issues since, for the predominant use case of verifying compilation results, only one of the circuits typically uses ancillary qubits.
As a solution, the default verification scheme switches to the construction checker whenever it detects that the alternating checker is not capable of handling the circuits in question.
Furthermore, the alternating checker emits an exception should it ever be configured to still run on instances it can't handle.

Last, but not least, the matrix equivalence check is slightly improved so that it does not incur an inversion and a multiplication when ancillaries are used.

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

Merging #167 (cc4abee) into main (7ea1567) will decrease coverage by 0.0%.
The diff coverage is 97.6%.

@@           Coverage Diff           @@
##            main    #167     +/-   ##
=======================================
- Coverage   98.0%   98.0%   -0.1%     
=======================================
  Files         35      35             
  Lines       1716    1736     +20     
  Branches     205     204      -1     
=======================================
+ Hits        1683    1702     +19     
- Misses        33      34      +1     

Flag	Coverage Δ
cpp	98.1% <97.6%> (-0.1%)	⬇️
python	96.8% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
include/checker/dd/DDAlternatingChecker.hpp	93.3% <ø> (ø)
src/checker/dd/DDAlternatingChecker.cpp	97.2% <94.1%> (-1.5%)	⬇️
src/EquivalenceCheckingManager.cpp	97.9% <100.0%> (+<0.1%)	⬆️
src/checker/dd/DDEquivalenceChecker.cpp	96.1% <100.0%> (ø)
test/test_equality.cpp	100.0% <100.0%> (ø)
include/EquivalenceCheckingManager.hpp	100.0% <0.0%> (ø)

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[pehamTom]

Nice that this PR finally handles the long-standing question of ancillaries.

I didn't find anything major, just a discussion and a minor remark. Other than that, LGTM.