Add check that decomposition includes qsd2q gates before optimizing them

Co-authored-by: jsmallz333 <[email protected]>

qiskit/quantum_info/synthesis/qsd.py

@@ -237,6 +237,8 @@ def _apply_a2(circ):
         instr, _, _ = instr_context
         if instr.name == "qsd2q":
             ind2q.append(i)
+    if not ind2q:
+        return ccirc
     # rolling over diagonals
     ind2 = None  # lint
     for ind1, ind2 in zip(ind2q[0:-1:], ind2q[1::]):

test/python/quantum_info/test_synthesis.py

@@ -1542,12 +1542,20 @@ def test_opt_a1a2(self, nqubits):
             ccirc.count_ops().get("cx"), (23 / 48) * 4**nqubits - (3 / 2) * 2**nqubits + 4 / 3
         )
 
+    # 10036
     def test_1q_decomposition(self):
         """Test decomposition of single qubit matrix"""
         mat = np.array([[0, 1], [1, 0]])
         circ = self.qsd(mat)
         self.assertEqual(Operator(mat), Operator(circ))
 
+    # 10036
+    def test_2q_with_no_qsd2q(self):
+        """Test decomposition of unitary whose decomposition is all "u" and "cx"."""
+        mat = CXGate().to_matrix()
+        circ = self.qsd(mat)
+        self.assertEqual(Operator(mat), Operator(circ))
+
 
 class TestTwoQubitDecomposeUpToDiagonal(QiskitTestCase):
     """test TwoQubitDecomposeUpToDiagonal class"""