add energy_fluctuation test into hamiltonian tests

tests/test_hamiltonians.py

@@ -423,3 +423,18 @@ def construct_hamiltonian():
 
     backend.assert_allclose(H.exp(0.5), target_matrix)
     backend.assert_allclose(H1.exp(0.5), target_matrix)
+
+
+def test_hamiltonian_energy_fluctuation(backend):
+    """Test energy fluctuation."""
+    # define hamiltonian
+    ham = hamiltonians.XXZ(nqubits=2, backend=backend)
+    # take ground state and zero state
+    ground_state = ham.ground_state()
+    zero_state = np.ones(2**2) / np.sqrt(2**2)
+    # collect energy fluctuations
+    gs_energy_fluctuation = ham.energy_fluctuation(ground_state)
+    zs_energy_fluctuation = ham.energy_fluctuation(zero_state)
+
+    assert np.isclose(gs_energy_fluctuation, 0, atol=1e-5)
+    assert gs_energy_fluctuation < zs_energy_fluctuation