Transpiler pass that converts a generic circuit to PBC (#15502)

* add a function to replace gates by Pauli rotations

* add pbc_transformation pass in rust (initial version)

* minor fix, formatting

* add python pbc transpiler pass

* add initial test

* minor fix

* formatting

* handle non param gates

* add test for non-param gates

* add UGate, handle several parameters

* minor update following PR 15434

* fix comment

* complete handling all 1-qubit gates

* add CUGate, CU3Gate

* fix test

* complete handling all 2-qubit gates

* reduce code duplication. add generate_pauli_evolution_gate function

* handle barrier and measure

* handle parameters, not only floats

* remove un-needed if-else

* enhance test

* add a test for parametrized gates

* do not panic. raise TranspilerError instead

* fix error

* improved synthesis for H, CH, ECR

* update docs

* add release notes

* fix reno

* unify U and U3

* remove with_capacity

* add PPM instead of measure, delay and reset

* remove PyGate, following PR 15277

* handle unreachable

* unify the cases of 0 and 1 parametrs. reduce code duplication

* raise error for GlobalPhaseGate

* simplify tests using get_standard_gate_name_mapping

* update tests following review

* update release notes following review

* fix comments

* fix header

* fix header

* fix header

* replace function by a table

* add check that a gate is not an instruction

* replace unreachble by panic

* handle GlobalPhaseGate

* update tests

* update docstring

* enhance and fix docs following review

* update types

* nicer handle of barrier/reset/delay

* move original_qubits outside the loop

* fix typos

* add PBC transform for the 3-qubit gates

* update comment

* update tests

* simplify RCCX

* rename pass to ConvertToPauliRotations

* remove pbc_transformation files

* formatting

* fix misprint

* replace PauliEvolutioGate by PauliProductRotationGate

* update tests to check PPR gate

* update docs to use PPR

* update release notes to use PPR

* Update crates/transpiler/src/passes/convert_to_pauli_rotations.rs

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* Update crates/transpiler/src/passes/convert_to_pauli_rotations.rs

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* Update crates/transpiler/src/passes/convert_to_pauli_rotations.rs

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* Update crates/transpiler/src/passes/convert_to_pauli_rotations.rs

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* Update crates/transpiler/src/passes/convert_to_pauli_rotations.rs

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* Update crates/transpiler/src/passes/convert_to_pauli_rotations.rs

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* Update qiskit/transpiler/passes/optimization/convert_to_pauli_rotations.py

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

* update docs and reno following review

---------

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

Author: ShellyGarion

crates/pyext/src/lib.rs

@@ -91,5 +91,6 @@ fn _accelerate(m: &Bound<PyModule>) -> PyResult<()> {
     add_submodule(m, ::qiskit_transpiler::passes::wrap_angles_mod, "wrap_angles")?;
     add_submodule(m, ::qiskit_transpiler::passes::optimize_clifford_t_mod, "optimize_clifford_t")?;
     add_submodule(m, ::qiskit_transpiler::passes::substitute_pi4_rotations_mod, "substitute_pi4_rotations")?;
+    add_submodule(m, ::qiskit_transpiler::passes::convert_to_pauli_rotations_mod, "convert_to_pauli_rotations")?;
     Ok(())
 }