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Add DAG-based variants of transpiler pass functions in C API (#15614)

* Add DAG-based variants of transpiler pass functions in C API (Qiskit#15576)

* Move complicated passes to qkdag_complicated_passes branch

Remove DAG-based variants for basis_translator, commutative_cancellation,
consolidate_blocks, inverse_cancellation, sabre_layout, unitary_synthesis,
and vf2 passes from this branch. These will be submitted as separate PRs
for individual review.

This branch now only contains the straightforward
passes: ElidePermutation, CheckGateDirection, GateDirection,
Optimize1qGatesDecomposition, RemoveDiagonalGatesBeforeMeasure,
RemoveIdentityEquivalent, and Split2QUnitaries.

* Remove cbinding optional feature from cext.

* Changes needed after merge with main.

* Deleted not needed functions.

* Applied modifications on ElidePermutations, as discussed in the comments.

* Apply suggestion from @eliarbel

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Apply suggestions from code review

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Applied proposed changes ingate_direction.rs

* Added proposed changes in passes.

* Change the check logic to use qk_dag_* functions in all the newly added DAG-variant test functions

* Update crates/cext/src/transpiler/passes/elide_permutations.rs

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Update crates/cext/src/transpiler/passes/elide_permutations.rs

This pass does not change the structure of the DAG in terms of qubits and registers, so we should be able to use this (and omit num_input_qubits).

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Update crates/cext/src/transpiler/passes/gate_direction.rs

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Update crates/cext/src/transpiler/passes/gate_direction.rs

Co-authored-by: Eli Arbel <46826214+eliarbel@users.noreply.github.com>

* Apply... (continued)

100454 of 114558 relevant lines covered (87.69%)

1144718.75 hits per line

Source Files on job 22657913054.1