Reduce number of compose calls in LieTrotter synthesis (#12021)

* Reduce number of compose calls in LieTrotter synthesis

* Decompose the output

* Update lie_trotter.py

* Update lie_trotter.py

* release note

* Update release note section

---------

Co-authored-by: Max Rossmannek <oss@zurich.ibm.com>

qiskit/synthesis/evolution/lie_trotter.py

@@ -76,7 +76,6 @@ def synthesize(self, evolution):
 
         # construct the evolution circuit
         evolution_circuit = QuantumCircuit(operators[0].num_qubits)
-        first_barrier = False
 
         if not isinstance(operators, list):
             pauli_list = [(Pauli(op), np.real(coeff)) for op, coeff in operators.to_list()]
@@ -86,20 +85,14 @@ def synthesize(self, evolution):
         # if we only evolve a single Pauli we don't need to additionally wrap it
         wrap = not (len(pauli_list) == 1 and self.reps == 1)
 
-        for _ in range(self.reps):
-            for op, coeff in pauli_list:
-                # add barriers
-                if first_barrier:
-                    if self.insert_barriers:
-                        evolution_circuit.barrier()
-                else:
-                    first_barrier = True
-
-                evolution_circuit.compose(
-                    self.atomic_evolution(op, coeff * time / self.reps), wrap=wrap, inplace=True
-                )
+        for i, (op, coeff) in enumerate(pauli_list):
+            evolution_circuit.compose(
+                self.atomic_evolution(op, coeff * time / self.reps), wrap=wrap, inplace=True
+            )
+            if self.insert_barriers and i != len(pauli_list) - 1:
+                evolution_circuit.barrier()
 
-        return evolution_circuit
+        return evolution_circuit.repeat(self.reps).decompose()
 
     @property
     def settings(self) -> Dict[str, Any]:

releasenotes/notes/faster-lie-trotter-ba8f6dd84fe4cae4.yaml

@@ -0,0 +1,6 @@
+---
+features_synthesis:
+  - |
+    :meth:`.LieTrotter.synthesize` now uses :meth:`.QuantumCircuit.repeat` to generate additional reps
+    after the first. This reduces the number of :meth:`.QuantumCircuit.compose` calls by a factor of
+    ``reps`` and significantly reduces the runtime for larger operators.