Qiskit / qiskit / 11411236768

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Oxidize `UnitarySynthesis` pass (#13141)

* Inital attempt at oxidizing unitary synthesis.

* Add cacache pygates feature to accelerate

* Use sabre target to speed up preferred_direction

* Adapt code to changes in PackedInstruction

* Use target in preferred_direction

* Some cleanup

* More cleanup

* Apply inline suggestions from  Matt's code review

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>

* Apply remaining review suggestions:

 * Fix details after applying inline suggestions
 * Keep TwoQubitWeilDecomposition attributes private. Add getter.
 * Initialize new_blocks using size hint
 * Remove basis_set as it's not used if there is a target.
 * Use ref_qubits ([PhysicalQubit; 2]) instead of wire_map (IndexMap<Qubit, Physicalqubit>)
 * Define static GOODBYE_SET as suggested
 * Use ImportOnceCell for XXDecomposer and XXEmbodiments to avoid importing in a loop.
 * Set preferred_direction without making it mutable.
 * Fix check_goodbye
 * Privatize assets
 * Use the add_global_phase method instead of the private function.
 * Add qs_decomposition to imports
 * Simplify flip_bits
 * Use NormalOperation to pass around decomposer gate and params info
 * First attempt at attaching synth circuits directly
 * Second attempt at attaching synth circuits directly
 * Use edge set for coupling map
 * Avoid exposing internals from NullableIndexMap
 * Use unitary_to_gate_sequence_inner instead of optimize_1q_gates_decomposition.
 * Use concat! in long error message.

* Use dag.apply_operation_back in 1q case. Additional cleanup.

* Don't return ref to float in two qubit decomposer.

* Use PyList as input type for coupling_edges (previous approach was innefficient)

* Avoid using UnitarySynthesisReturn type, avoid intermediate dag creation in all cases except XXDecomposer.

* Refactor appending to out_dag, remove unnecesary clones.

* Cosmetic changes. Reduce indentation.

* Squash bug

* Fix clippy

* Add qsd test

* Avoid making unnecessary variables... (continued)

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