diff --git a/qiskit/synthesis/evolution/qdrift.py b/qiskit/synthesis/evolution/qdrift.py
index 6642a68b8db6..968d15f87bce 100644
--- a/qiskit/synthesis/evolution/qdrift.py
+++ b/qiskit/synthesis/evolution/qdrift.py
@@ -83,8 +83,6 @@ def synthesize(self, evolution):
             size=(num_gates,),
             p=weights / lambd,
         )
-        # Update the coefficients of sampled_ops
-        self.sampled_ops = [(op, evolution_time) for op, coeff in self.sampled_ops]
 
         # pylint: disable=cyclic-import
         from qiskit.circuit.library.pauli_evolution import PauliEvolutionGate
@@ -94,7 +92,7 @@ def synthesize(self, evolution):
             insert_barriers=self.insert_barriers, atomic_evolution=self.atomic_evolution
         )
         evolution_circuit = PauliEvolutionGate(
-            sum(SparsePauliOp(op) for op, coeff in self.sampled_ops),
+            sum(SparsePauliOp(np.sign(coeff) * op) for op, coeff in self.sampled_ops),
             time=evolution_time,
             synthesis=lie_trotter,
         ).definition
diff --git a/releasenotes/notes/fix-qdrift-evolution-bceb9c4f182ab0f5.yaml b/releasenotes/notes/fix-qdrift-evolution-bceb9c4f182ab0f5.yaml
new file mode 100644
index 000000000000..a86869a4e540
--- /dev/null
+++ b/releasenotes/notes/fix-qdrift-evolution-bceb9c4f182ab0f5.yaml
@@ -0,0 +1,3 @@
+fixes:
+  - |
+    Fix incorrect implemention of `qDRIFT`, negative coeffients of the Hamiltonian are now added back whereas they were always forced to be positive.
diff --git a/test/python/circuit/library/test_evolution_gate.py b/test/python/circuit/library/test_evolution_gate.py
index e407cf0341d9..88b0529ca7c2 100644
--- a/test/python/circuit/library/test_evolution_gate.py
+++ b/test/python/circuit/library/test_evolution_gate.py
@@ -155,17 +155,25 @@ def test_qdrift_manual(self, op, time, reps, sampled_ops):
 
     def test_qdrift_evolution(self):
         """Test QDrift on an example."""
-        op = 0.1 * (Z ^ Z) + (X ^ I) + (I ^ X) + 0.2 * (X ^ X)
+        op = 0.1 * (Z ^ Z) - 3.2 * (X ^ I) - 1.0 * (I ^ X) + 0.2 * (X ^ X)
         reps = 20
-        qdrift = PauliEvolutionGate(
-            op, time=0.5 / reps, synthesis=QDrift(reps=reps, seed=self.seed)
-        ).definition
-        exact = scipy.linalg.expm(-0.5j * op.to_matrix()).dot(np.eye(4)[0, :])
+        time = 0.12
+        num_samples = 300
+        qdrift_energy = []
 
         def energy(evo):
             return Statevector(evo).expectation_value(op.to_matrix())
 
-        self.assertAlmostEqual(energy(exact), energy(qdrift), places=2)
+        for i in range(num_samples):
+            qdrift = PauliEvolutionGate(
+                op, time=time, synthesis=QDrift(reps=reps, seed=self.seed + i)
+            ).definition
+
+            qdrift_energy.append(energy(qdrift))
+
+        exact = scipy.linalg.expm(-1j * time * op.to_matrix()).dot(np.eye(4)[0, :])
+
+        self.assertAlmostEqual(energy(exact), np.average(qdrift_energy), places=2)
 
     def test_passing_grouped_paulis(self):
         """Test passing a list of already grouped Paulis."""