♻️ improve implementation of Clifford+T compilation

Signed-off-by: burgholzer <[email protected]>

src/mqt/bench/qiskit_helper.py

@@ -11,8 +11,6 @@
     from .devices import Device, Gateset
 
 from qiskit import transpile
-from qiskit.synthesis import generate_basic_approximations
-from qiskit.transpiler.passes import SolovayKitaev
 
 from .utils import get_openqasm_gates, save_as_qasm
 
@@ -191,12 +189,28 @@ def get_native_gates_level(
         return True
 
     if gateset.gateset_name == "clifford+t":
-        gateset_without_cx = gateset.gates.copy()
-        gateset_without_cx.remove("cx")
-        approx = generate_basic_approximations(gateset_without_cx, depth=3)
-        skd = SolovayKitaev(recursion_degree=2, basic_approximations=approx)
-        compiled_without_architecture = skd(qc.decompose(reps=3).remove_final_measurements(inplace=False))
-        compiled_without_architecture.measure_all()
+        from qiskit.converters import circuit_to_dag, dag_to_circuit  # noqa: PLC0415
+        from qiskit.transpiler.passes.synthesis import SolovayKitaev  # noqa: PLC0415
+
+        # Transpile the circuit to single- and two-qubit gates including rotations
+        compiled_for_sk = transpile(
+            qc,
+            basis_gates=[*gateset.gates, "rx", "ry", "rz"],
+            optimization_level=opt_level,
+            seed_transpiler=10,
+        )
+        # Synthesize the rotations to Clifford+T gates
+        # Measurements are removed and added back after the synthesis to avoid errors in the Solovay-Kitaev pass
+        pass_ = SolovayKitaev()
+        new_qc = dag_to_circuit(pass_.run(circuit_to_dag(compiled_for_sk.remove_final_measurements(inplace=False))))
+        new_qc.measure_all()
+        # Transpile once more to remove unnecessary gates and optimize the circuit
+        compiled_without_architecture = transpile(
+            new_qc,
+            basis_gates=gateset.gates,
+            optimization_level=opt_level,
+            seed_transpiler=10,
+        )
     else:
         compiled_without_architecture = transpile(
             qc, basis_gates=gateset.gates, optimization_level=opt_level, seed_transpiler=10