🐛 [NA] Dropped Global Hadamard Gate

System and Environment Information

MAC OS 15.6.1
MQT QMAP 3.4.0dev@9c84575

Bug Description

When compiling a circuit with a global Hadamard Gate, this is dropped and does not exist in the resulting output.

Steps to Reproduce

Run the following contract:

from qiskit import QuantumCircuit
from mqt.core import load
from mqt.qmap.na.zoned import RoutingAgnosticCompiler, RoutingAwareCompiler
from mqt.qmap.na.zoned import ZonedNeutralAtomArchitecture

def global_h(num_qubits):
    """:returns: a global ry gate"""
    qc = QuantumCircuit(num_qubits)
    qc.h(range(num_qubits))
    return qc.to_gate(label="H")

qc = QuantumCircuit(5)
qc.append(global_h(5), range(5))

circ = load(qc)

arch = ZonedNeutralAtomArchitecture.from_json_string("""{
   "name": "Architecture with one entanglement and one storage zone",
   "operation_duration": {"rydberg_gate": 0.36, "single_qubit_gate": 52, "atom_transfer": 15},
   "operation_fidelity": {"rydberg_gate": 0.995, "single_qubit_gate": 0.9997, "atom_transfer": 0.999},
   "qubit_spec": {"T": 1.5e6},
   "storage_zones": [{
     "zone_id": 0,
     "slms": [{"id": 0, "site_separation": [3, 3], "r": 20, "c": 100, "location": [0, 0]}],
     "offset": [0, 0],
     "dimension": [297, 57]
   }],
   "entanglement_zones": [{
     "zone_id": 0,
     "slms": [
       {"id": 1, "site_separation": [12, 10], "r": 7, "c": 20, "location": [35, 67]},
       {"id": 2, "site_separation": [12, 10], "r": 7, "c": 20, "location": [37, 67]}
     ],
     "offset": [35, 67],
     "dimension": [230, 60]
   }],
   "aods": [{"id": 0, "site_separation": 2, "r": 100, "c": 100}],
   "rydberg_range": [[[30, 62], [270, 132]]]
 }""")

compiler = RoutingAwareCompiler(arch)

code = compiler.compile(circ)
print(code)

Got naviz:

atom (0.000, 57.000) atom0
atom (3.000, 57.000) atom1
atom (6.000, 57.000) atom2
atom (9.000, 57.000) atom3
atom (12.000, 57.000) atom4

Start with the Python reproduction using load, ZonedNeutralAtomArchitecture, RoutingAwareCompiler, and compiler.compile; inspect why the global_h gate is absent from the generated output. Compare the compiled result with the input circuit and confirm that the resulting naviz output represents the five-qubit global Hadamard operation.