fix #8992 (#8998) (#9000)

(cherry picked from commit be1e697)

Co-authored-by: Ikko Hamamura <ikkoham@users.noreply.github.com>

qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py

@@ -112,7 +112,7 @@ def __init__(self, data, coeffs=None, *, ignore_pauli_phase=False, copy=True):
 
         pauli_list = PauliList(data.copy() if copy and hasattr(data, "copy") else data)
 
-        dtype = coeffs.dtype if isinstance(coeffs, np.ndarray) else complex
+        dtype = object if isinstance(coeffs, np.ndarray) and coeffs.dtype == object else complex
 
         if coeffs is None:
             coeffs = np.ones(pauli_list.size, dtype=dtype)

releasenotes/notes/fix-sparse-pauli-real-63c31d87801671b1.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fix :meth:`.SparsePauliOp.dot` between operators with real coefficients.
+    To fix this, the dtype that :class:`SparsePauliOp` can take is restricted to
+    ``np.complex128`` and ``object``.

test/python/quantum_info/operators/symplectic/test_sparse_pauli_op.py

@@ -940,6 +940,13 @@ def commutes(left: Pauli, right: Pauli) -> bool:
                 )
             )
 
+    def test_dot_real(self):
+        """Test dot for real coefficiets."""
+        x = SparsePauliOp("X", np.array([1]))
+        y = SparsePauliOp("Y", np.array([1]))
+        iz = SparsePauliOp("Z", 1j)
+        self.assertEqual(x.dot(y), iz)
+
 
 if __name__ == "__main__":
     unittest.main()