✨ Partial equivalence checking

[reb-ddm]

Description

Added a flag checkPartialEquivalence in order to decide whether to check for total equivalence or for partial equivalence. Two circuits are partially equivalent if, for each possible initial input state, they have the same probability for each measurement outcome. Therefore the state of not measured qubits (= garbage qubits), or phases are ignored.

The Construction Checker and the Simulation Checker implement this by reducing the contribution of garbage qubits in the matrix/vector representation of the circuit. Additionally, all weights in the DD representation are set to their magnitude, such that different phases don't influence the result.

The Alternating Checker implements it by checking that the resulting matrix representation is equal to a diagonal matrix, modulo garbage qubits (instead of checking that it is equal to the identity matrix).

For more information, there is documentation in the file PartialEquivalence.ipynb.

An additional feature are the automatically generated benchmarks for partial equivalence. The function generatePartiallyEquivalentCircuits generates pairs of circuits which are partially equivalent, following the method described in the paper Partial Equivalence Checking of Quantum Circuits in Section VI. B.

Fixes issue #155

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

All modified and coverable lines are covered by tests ✅

Project coverage is 96.4%. Comparing base (a46794a) to head (faf7d2e).

Additional details and impacted files

@@           Coverage Diff           @@
##            main    #375     +/-   ##
=======================================
+ Coverage   96.2%   96.4%   +0.1%     
=======================================
  Files         34      34             
  Lines       1753    1763     +10     
  Branches     215     217      +2     
=======================================
+ Hits        1688    1701     +13     
+ Misses        65      62      -3     

Flag	Coverage Δ
cpp	96.2% <100.0%> (+0.2%)	⬆️
python	97.2% <100.0%> (+<0.1%)	⬆️

Files	Coverage Δ
include/Configuration.hpp	96.4% <100.0%> (+<0.1%)	⬆️
include/EquivalenceCheckingManager.hpp	100.0% <100.0%> (ø)
include/checker/dd/TaskManager.hpp	98.4% <100.0%> (ø)
src/EquivalenceCheckingManager.cpp	94.3% <100.0%> (+<0.1%)	⬆️
src/checker/dd/DDAlternatingChecker.cpp	92.0% <100.0%> (+0.2%)	⬆️
src/checker/dd/DDEquivalenceChecker.cpp	92.8% <100.0%> (+0.9%)	⬆️
src/mqt/qcec/configuration.py	100.0% <100.0%> (ø)

... and 1 file with indirect coverage changes

[burgholzer]

Hey @reb-ddm 👋🏼

Many thanks for all the work here! I took the liberty to rework some bits and pieces, but overall this is looking great and ready to merge. Once CI is all-green here, I'll start by merging the mqt-core PR and changing back the submodule pointers from the fork to the main repository. After that, this should be good to go 🎉

[burgholzer]

Really nice how little change was required here to enable support for partial equivalence checking! 🎉
This is now also ready to merge ✅

The C++ linter (unfortunately) fails on all PRs from forks due to missing permissions. But this can be safely ignored.
I'll admin-merge once all checks have run through.