diff --git a/tests/python/operators/fermi_hubbard_test.py b/tests/python/operators/fermi_hubbard_test.py
index 9b6cb1805..e9c395969 100644
--- a/tests/python/operators/fermi_hubbard_test.py
+++ b/tests/python/operators/fermi_hubbard_test.py
@@ -23,472 +23,460 @@ def test_fermi_hubbard_1d():
     """Test terms of the one-dimensional Fermi-Hubbard model Hamiltonian."""
 
     # open boundary conditions
-    op = fermi_hubbard_1d(
-        norb=4,
-        tunneling=1,
-        interaction=2,
-        chemical_potential=3,
-        nearest_neighbor_interaction=4,
-    )
-    np.testing.assert_equal(
-        dict(op),
-        {
-            (cre_a(0), des_a(1)): -1,
-            (cre_b(0), des_b(1)): -1,
-            (cre_a(1), des_a(0)): -1,
-            (cre_b(1), des_b(0)): -1,
-            (cre_a(1), des_a(2)): -1,
-            (cre_b(1), des_b(2)): -1,
-            (cre_a(2), des_a(1)): -1,
-            (cre_b(2), des_b(1)): -1,
-            (cre_a(2), des_a(3)): -1,
-            (cre_b(2), des_b(3)): -1,
-            (cre_a(3), des_a(2)): -1,
-            (cre_b(3), des_b(2)): -1,
-            (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
-            (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
-            (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
-            (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
-            (cre_a(0), des_a(0)): -3,
-            (cre_b(0), des_b(0)): -3,
-            (cre_a(1), des_a(1)): -3,
-            (cre_b(1), des_b(1)): -3,
-            (cre_a(2), des_a(2)): -3,
-            (cre_b(2), des_b(2)): -3,
-            (cre_a(3), des_a(3)): -3,
-            (cre_b(3), des_b(3)): -3,
-            (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
-            (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
-            (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
-            (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
-            (cre_a(1), des_a(1), cre_a(2), des_a(2)): 4,
-            (cre_a(1), des_a(1), cre_b(2), des_b(2)): 4,
-            (cre_b(1), des_b(1), cre_a(2), des_a(2)): 4,
-            (cre_b(1), des_b(1), cre_b(2), des_b(2)): 4,
-            (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
-            (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
-            (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
-            (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
-        },
-    )
+    assert dict(
+        fermi_hubbard_1d(
+            norb=4,
+            tunneling=1,
+            interaction=2,
+            chemical_potential=3,
+            nearest_neighbor_interaction=4,
+        )
+    ) == {
+        (cre_a(0), des_a(1)): -1,
+        (cre_b(0), des_b(1)): -1,
+        (cre_a(1), des_a(0)): -1,
+        (cre_b(1), des_b(0)): -1,
+        (cre_a(1), des_a(2)): -1,
+        (cre_b(1), des_b(2)): -1,
+        (cre_a(2), des_a(1)): -1,
+        (cre_b(2), des_b(1)): -1,
+        (cre_a(2), des_a(3)): -1,
+        (cre_b(2), des_b(3)): -1,
+        (cre_a(3), des_a(2)): -1,
+        (cre_b(3), des_b(2)): -1,
+        (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
+        (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
+        (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
+        (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
+        (cre_a(0), des_a(0)): -3,
+        (cre_b(0), des_b(0)): -3,
+        (cre_a(1), des_a(1)): -3,
+        (cre_b(1), des_b(1)): -3,
+        (cre_a(2), des_a(2)): -3,
+        (cre_b(2), des_b(2)): -3,
+        (cre_a(3), des_a(3)): -3,
+        (cre_b(3), des_b(3)): -3,
+        (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
+        (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
+        (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
+        (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
+        (cre_a(1), des_a(1), cre_a(2), des_a(2)): 4,
+        (cre_a(1), des_a(1), cre_b(2), des_b(2)): 4,
+        (cre_b(1), des_b(1), cre_a(2), des_a(2)): 4,
+        (cre_b(1), des_b(1), cre_b(2), des_b(2)): 4,
+        (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
+        (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
+        (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
+        (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
+    }
 
     # periodic boundary conditions
-    op_periodic = fermi_hubbard_1d(
-        norb=4,
-        tunneling=1,
-        interaction=2,
-        chemical_potential=3,
-        nearest_neighbor_interaction=4,
-        periodic=True,
-    )
-    np.testing.assert_equal(
-        dict(op_periodic),
-        {
-            (cre_a(0), des_a(1)): -1,
-            (cre_b(0), des_b(1)): -1,
-            (cre_a(1), des_a(0)): -1,
-            (cre_b(1), des_b(0)): -1,
-            (cre_a(1), des_a(2)): -1,
-            (cre_b(1), des_b(2)): -1,
-            (cre_a(2), des_a(1)): -1,
-            (cre_b(2), des_b(1)): -1,
-            (cre_a(2), des_a(3)): -1,
-            (cre_b(2), des_b(3)): -1,
-            (cre_a(3), des_a(2)): -1,
-            (cre_b(3), des_b(2)): -1,
-            (cre_a(3), des_a(0)): -1,
-            (cre_b(3), des_b(0)): -1,
-            (cre_a(0), des_a(3)): -1,
-            (cre_b(0), des_b(3)): -1,
-            (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
-            (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
-            (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
-            (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
-            (cre_a(0), des_a(0)): -3,
-            (cre_b(0), des_b(0)): -3,
-            (cre_a(1), des_a(1)): -3,
-            (cre_b(1), des_b(1)): -3,
-            (cre_a(2), des_a(2)): -3,
-            (cre_b(2), des_b(2)): -3,
-            (cre_a(3), des_a(3)): -3,
-            (cre_b(3), des_b(3)): -3,
-            (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
-            (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
-            (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
-            (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
-            (cre_a(1), des_a(1), cre_a(2), des_a(2)): 4,
-            (cre_a(1), des_a(1), cre_b(2), des_b(2)): 4,
-            (cre_b(1), des_b(1), cre_a(2), des_a(2)): 4,
-            (cre_b(1), des_b(1), cre_b(2), des_b(2)): 4,
-            (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
-            (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
-            (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
-            (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
-            (cre_a(3), des_a(3), cre_a(0), des_a(0)): 4,
-            (cre_a(3), des_a(3), cre_b(0), des_b(0)): 4,
-            (cre_b(3), des_b(3), cre_a(0), des_a(0)): 4,
-            (cre_b(3), des_b(3), cre_b(0), des_b(0)): 4,
-        },
-    )
+    assert dict(
+        fermi_hubbard_1d(
+            norb=4,
+            tunneling=1,
+            interaction=2,
+            chemical_potential=3,
+            nearest_neighbor_interaction=4,
+            periodic=True,
+        )
+    ) == {
+        (cre_a(0), des_a(1)): -1,
+        (cre_b(0), des_b(1)): -1,
+        (cre_a(1), des_a(0)): -1,
+        (cre_b(1), des_b(0)): -1,
+        (cre_a(1), des_a(2)): -1,
+        (cre_b(1), des_b(2)): -1,
+        (cre_a(2), des_a(1)): -1,
+        (cre_b(2), des_b(1)): -1,
+        (cre_a(2), des_a(3)): -1,
+        (cre_b(2), des_b(3)): -1,
+        (cre_a(3), des_a(2)): -1,
+        (cre_b(3), des_b(2)): -1,
+        (cre_a(3), des_a(0)): -1,
+        (cre_b(3), des_b(0)): -1,
+        (cre_a(0), des_a(3)): -1,
+        (cre_b(0), des_b(3)): -1,
+        (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
+        (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
+        (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
+        (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
+        (cre_a(0), des_a(0)): -3,
+        (cre_b(0), des_b(0)): -3,
+        (cre_a(1), des_a(1)): -3,
+        (cre_b(1), des_b(1)): -3,
+        (cre_a(2), des_a(2)): -3,
+        (cre_b(2), des_b(2)): -3,
+        (cre_a(3), des_a(3)): -3,
+        (cre_b(3), des_b(3)): -3,
+        (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
+        (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
+        (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
+        (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
+        (cre_a(1), des_a(1), cre_a(2), des_a(2)): 4,
+        (cre_a(1), des_a(1), cre_b(2), des_b(2)): 4,
+        (cre_b(1), des_b(1), cre_a(2), des_a(2)): 4,
+        (cre_b(1), des_b(1), cre_b(2), des_b(2)): 4,
+        (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
+        (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
+        (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
+        (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
+        (cre_a(3), des_a(3), cre_a(0), des_a(0)): 4,
+        (cre_a(3), des_a(3), cre_b(0), des_b(0)): 4,
+        (cre_b(3), des_b(3), cre_a(0), des_a(0)): 4,
+        (cre_b(3), des_b(3), cre_b(0), des_b(0)): 4,
+    }
 
     # periodic boundary conditions (edge case)
-    op_periodic_edge = fermi_hubbard_1d(
-        norb=2,
-        tunneling=1,
-        interaction=2,
-        chemical_potential=3,
-        nearest_neighbor_interaction=4,
-        periodic=True,
-    )
-    np.testing.assert_equal(
-        dict(op_periodic_edge),
-        {
-            (cre_a(0), des_a(1)): -2,
-            (cre_b(0), des_b(1)): -2,
-            (cre_a(1), des_a(0)): -2,
-            (cre_b(1), des_b(0)): -2,
-            (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
-            (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
-            (cre_a(0), des_a(0)): -3,
-            (cre_b(0), des_b(0)): -3,
-            (cre_a(1), des_a(1)): -3,
-            (cre_b(1), des_b(1)): -3,
-            (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
-            (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
-            (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
-            (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
-            (cre_a(1), des_a(1), cre_a(0), des_a(0)): 4,
-            (cre_a(1), des_a(1), cre_b(0), des_b(0)): 4,
-            (cre_b(1), des_b(1), cre_a(0), des_a(0)): 4,
-            (cre_b(1), des_b(1), cre_b(0), des_b(0)): 4,
-        },
-    )
+    assert dict(
+        fermi_hubbard_1d(
+            norb=2,
+            tunneling=1,
+            interaction=2,
+            chemical_potential=3,
+            nearest_neighbor_interaction=4,
+            periodic=True,
+        )
+    ) == {
+        (cre_a(0), des_a(1)): -2,
+        (cre_b(0), des_b(1)): -2,
+        (cre_a(1), des_a(0)): -2,
+        (cre_b(1), des_b(0)): -2,
+        (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
+        (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
+        (cre_a(0), des_a(0)): -3,
+        (cre_b(0), des_b(0)): -3,
+        (cre_a(1), des_a(1)): -3,
+        (cre_b(1), des_b(1)): -3,
+        (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
+        (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
+        (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
+        (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
+        (cre_a(1), des_a(1), cre_a(0), des_a(0)): 4,
+        (cre_a(1), des_a(1), cre_b(0), des_b(0)): 4,
+        (cre_b(1), des_b(1), cre_a(0), des_a(0)): 4,
+        (cre_b(1), des_b(1), cre_b(0), des_b(0)): 4,
+    }
 
 
 def test_fermi_hubbard_2d():
     """Test terms of the two-dimensional Fermi-Hubbard model Hamiltonian."""
 
     # open boundary conditions
-    op = fermi_hubbard_2d(
-        norb_x=2,
-        norb_y=2,
-        tunneling=1,
-        interaction=2,
-        chemical_potential=3,
-        nearest_neighbor_interaction=4,
-    )
-    np.testing.assert_equal(
-        dict(op),
-        {
-            (cre_a(0), des_a(1)): -1,
-            (cre_b(0), des_b(1)): -1,
-            (cre_a(1), des_a(0)): -1,
-            (cre_b(1), des_b(0)): -1,
-            (cre_a(0), des_a(2)): -1,
-            (cre_b(0), des_b(2)): -1,
-            (cre_a(2), des_a(0)): -1,
-            (cre_b(2), des_b(0)): -1,
-            (cre_a(2), des_a(3)): -1,
-            (cre_b(2), des_b(3)): -1,
-            (cre_a(3), des_a(2)): -1,
-            (cre_b(3), des_b(2)): -1,
-            (cre_a(1), des_a(3)): -1,
-            (cre_b(1), des_b(3)): -1,
-            (cre_a(3), des_a(1)): -1,
-            (cre_b(3), des_b(1)): -1,
-            (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
-            (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
-            (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
-            (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
-            (cre_a(0), des_a(0)): -3,
-            (cre_b(0), des_b(0)): -3,
-            (cre_a(1), des_a(1)): -3,
-            (cre_b(1), des_b(1)): -3,
-            (cre_a(2), des_a(2)): -3,
-            (cre_b(2), des_b(2)): -3,
-            (cre_a(3), des_a(3)): -3,
-            (cre_b(3), des_b(3)): -3,
-            (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
-            (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
-            (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
-            (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
-            (cre_a(0), des_a(0), cre_a(2), des_a(2)): 4,
-            (cre_a(0), des_a(0), cre_b(2), des_b(2)): 4,
-            (cre_b(0), des_b(0), cre_a(2), des_a(2)): 4,
-            (cre_b(0), des_b(0), cre_b(2), des_b(2)): 4,
-            (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
-            (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
-            (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
-            (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
-            (cre_a(1), des_a(1), cre_a(3), des_a(3)): 4,
-            (cre_a(1), des_a(1), cre_b(3), des_b(3)): 4,
-            (cre_b(1), des_b(1), cre_a(3), des_a(3)): 4,
-            (cre_b(1), des_b(1), cre_b(3), des_b(3)): 4,
-        },
-    )
+    assert dict(
+        fermi_hubbard_2d(
+            norb_x=2,
+            norb_y=2,
+            tunneling=1,
+            interaction=2,
+            chemical_potential=3,
+            nearest_neighbor_interaction=4,
+        )
+    ) == {
+        (cre_a(0), des_a(1)): -1,
+        (cre_b(0), des_b(1)): -1,
+        (cre_a(1), des_a(0)): -1,
+        (cre_b(1), des_b(0)): -1,
+        (cre_a(0), des_a(2)): -1,
+        (cre_b(0), des_b(2)): -1,
+        (cre_a(2), des_a(0)): -1,
+        (cre_b(2), des_b(0)): -1,
+        (cre_a(2), des_a(3)): -1,
+        (cre_b(2), des_b(3)): -1,
+        (cre_a(3), des_a(2)): -1,
+        (cre_b(3), des_b(2)): -1,
+        (cre_a(1), des_a(3)): -1,
+        (cre_b(1), des_b(3)): -1,
+        (cre_a(3), des_a(1)): -1,
+        (cre_b(3), des_b(1)): -1,
+        (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
+        (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
+        (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
+        (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
+        (cre_a(0), des_a(0)): -3,
+        (cre_b(0), des_b(0)): -3,
+        (cre_a(1), des_a(1)): -3,
+        (cre_b(1), des_b(1)): -3,
+        (cre_a(2), des_a(2)): -3,
+        (cre_b(2), des_b(2)): -3,
+        (cre_a(3), des_a(3)): -3,
+        (cre_b(3), des_b(3)): -3,
+        (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
+        (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
+        (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
+        (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
+        (cre_a(0), des_a(0), cre_a(2), des_a(2)): 4,
+        (cre_a(0), des_a(0), cre_b(2), des_b(2)): 4,
+        (cre_b(0), des_b(0), cre_a(2), des_a(2)): 4,
+        (cre_b(0), des_b(0), cre_b(2), des_b(2)): 4,
+        (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
+        (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
+        (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
+        (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
+        (cre_a(1), des_a(1), cre_a(3), des_a(3)): 4,
+        (cre_a(1), des_a(1), cre_b(3), des_b(3)): 4,
+        (cre_b(1), des_b(1), cre_a(3), des_a(3)): 4,
+        (cre_b(1), des_b(1), cre_b(3), des_b(3)): 4,
+    }
 
     # periodic boundary conditions
-    op_periodic = fermi_hubbard_2d(
-        norb_x=3,
-        norb_y=3,
-        tunneling=1,
-        interaction=2,
-        chemical_potential=3,
-        nearest_neighbor_interaction=4,
-        periodic=True,
-    )
-    np.testing.assert_equal(
-        dict(op_periodic),
-        {
-            (cre_a(0), des_a(1)): -1,
-            (cre_b(0), des_b(1)): -1,
-            (cre_a(1), des_a(0)): -1,
-            (cre_b(1), des_b(0)): -1,
-            (cre_a(0), des_a(3)): -1,
-            (cre_b(0), des_b(3)): -1,
-            (cre_a(3), des_a(0)): -1,
-            (cre_b(3), des_b(0)): -1,
-            (cre_a(3), des_a(4)): -1,
-            (cre_b(3), des_b(4)): -1,
-            (cre_a(4), des_a(3)): -1,
-            (cre_b(4), des_b(3)): -1,
-            (cre_a(3), des_a(6)): -1,
-            (cre_b(3), des_b(6)): -1,
-            (cre_a(6), des_a(3)): -1,
-            (cre_b(6), des_b(3)): -1,
-            (cre_a(6), des_a(7)): -1,
-            (cre_b(6), des_b(7)): -1,
-            (cre_a(7), des_a(6)): -1,
-            (cre_b(7), des_b(6)): -1,
-            (cre_a(6), des_a(0)): -1,
-            (cre_b(6), des_b(0)): -1,
-            (cre_a(0), des_a(6)): -1,
-            (cre_b(0), des_b(6)): -1,
-            (cre_a(1), des_a(2)): -1,
-            (cre_b(1), des_b(2)): -1,
-            (cre_a(2), des_a(1)): -1,
-            (cre_b(2), des_b(1)): -1,
-            (cre_a(1), des_a(4)): -1,
-            (cre_b(1), des_b(4)): -1,
-            (cre_a(4), des_a(1)): -1,
-            (cre_b(4), des_b(1)): -1,
-            (cre_a(4), des_a(5)): -1,
-            (cre_b(4), des_b(5)): -1,
-            (cre_a(5), des_a(4)): -1,
-            (cre_b(5), des_b(4)): -1,
-            (cre_a(4), des_a(7)): -1,
-            (cre_b(4), des_b(7)): -1,
-            (cre_a(7), des_a(4)): -1,
-            (cre_b(7), des_b(4)): -1,
-            (cre_a(7), des_a(8)): -1,
-            (cre_b(7), des_b(8)): -1,
-            (cre_a(8), des_a(7)): -1,
-            (cre_b(8), des_b(7)): -1,
-            (cre_a(7), des_a(1)): -1,
-            (cre_b(7), des_b(1)): -1,
-            (cre_a(1), des_a(7)): -1,
-            (cre_b(1), des_b(7)): -1,
-            (cre_a(2), des_a(0)): -1,
-            (cre_b(2), des_b(0)): -1,
-            (cre_a(0), des_a(2)): -1,
-            (cre_b(0), des_b(2)): -1,
-            (cre_a(2), des_a(5)): -1,
-            (cre_b(2), des_b(5)): -1,
-            (cre_a(5), des_a(2)): -1,
-            (cre_b(5), des_b(2)): -1,
-            (cre_a(5), des_a(3)): -1,
-            (cre_b(5), des_b(3)): -1,
-            (cre_a(3), des_a(5)): -1,
-            (cre_b(3), des_b(5)): -1,
-            (cre_a(5), des_a(8)): -1,
-            (cre_b(5), des_b(8)): -1,
-            (cre_a(8), des_a(5)): -1,
-            (cre_b(8), des_b(5)): -1,
-            (cre_a(8), des_a(6)): -1,
-            (cre_b(8), des_b(6)): -1,
-            (cre_a(6), des_a(8)): -1,
-            (cre_b(6), des_b(8)): -1,
-            (cre_a(8), des_a(2)): -1,
-            (cre_b(8), des_b(2)): -1,
-            (cre_a(2), des_a(8)): -1,
-            (cre_b(2), des_b(8)): -1,
-            (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
-            (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
-            (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
-            (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
-            (cre_a(4), des_a(4), cre_b(4), des_b(4)): 2,
-            (cre_a(5), des_a(5), cre_b(5), des_b(5)): 2,
-            (cre_a(6), des_a(6), cre_b(6), des_b(6)): 2,
-            (cre_a(7), des_a(7), cre_b(7), des_b(7)): 2,
-            (cre_a(8), des_a(8), cre_b(8), des_b(8)): 2,
-            (cre_a(0), des_a(0)): -3,
-            (cre_b(0), des_b(0)): -3,
-            (cre_a(1), des_a(1)): -3,
-            (cre_b(1), des_b(1)): -3,
-            (cre_a(2), des_a(2)): -3,
-            (cre_b(2), des_b(2)): -3,
-            (cre_a(3), des_a(3)): -3,
-            (cre_b(3), des_b(3)): -3,
-            (cre_a(4), des_a(4)): -3,
-            (cre_b(4), des_b(4)): -3,
-            (cre_a(5), des_a(5)): -3,
-            (cre_b(5), des_b(5)): -3,
-            (cre_a(6), des_a(6)): -3,
-            (cre_b(6), des_b(6)): -3,
-            (cre_a(7), des_a(7)): -3,
-            (cre_b(7), des_b(7)): -3,
-            (cre_a(8), des_a(8)): -3,
-            (cre_b(8), des_b(8)): -3,
-            (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
-            (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
-            (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
-            (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
-            (cre_a(0), des_a(0), cre_a(3), des_a(3)): 4,
-            (cre_a(0), des_a(0), cre_b(3), des_b(3)): 4,
-            (cre_b(0), des_b(0), cre_a(3), des_a(3)): 4,
-            (cre_b(0), des_b(0), cre_b(3), des_b(3)): 4,
-            (cre_a(3), des_a(3), cre_a(4), des_a(4)): 4,
-            (cre_a(3), des_a(3), cre_b(4), des_b(4)): 4,
-            (cre_b(3), des_b(3), cre_a(4), des_a(4)): 4,
-            (cre_b(3), des_b(3), cre_b(4), des_b(4)): 4,
-            (cre_a(3), des_a(3), cre_a(6), des_a(6)): 4,
-            (cre_a(3), des_a(3), cre_b(6), des_b(6)): 4,
-            (cre_b(3), des_b(3), cre_a(6), des_a(6)): 4,
-            (cre_b(3), des_b(3), cre_b(6), des_b(6)): 4,
-            (cre_a(6), des_a(6), cre_a(7), des_a(7)): 4,
-            (cre_a(6), des_a(6), cre_b(7), des_b(7)): 4,
-            (cre_b(6), des_b(6), cre_a(7), des_a(7)): 4,
-            (cre_b(6), des_b(6), cre_b(7), des_b(7)): 4,
-            (cre_a(6), des_a(6), cre_a(0), des_a(0)): 4,
-            (cre_a(6), des_a(6), cre_b(0), des_b(0)): 4,
-            (cre_b(6), des_b(6), cre_a(0), des_a(0)): 4,
-            (cre_b(6), des_b(6), cre_b(0), des_b(0)): 4,
-            (cre_a(1), des_a(1), cre_a(2), des_a(2)): 4,
-            (cre_a(1), des_a(1), cre_b(2), des_b(2)): 4,
-            (cre_b(1), des_b(1), cre_a(2), des_a(2)): 4,
-            (cre_b(1), des_b(1), cre_b(2), des_b(2)): 4,
-            (cre_a(1), des_a(1), cre_a(4), des_a(4)): 4,
-            (cre_a(1), des_a(1), cre_b(4), des_b(4)): 4,
-            (cre_b(1), des_b(1), cre_a(4), des_a(4)): 4,
-            (cre_b(1), des_b(1), cre_b(4), des_b(4)): 4,
-            (cre_a(4), des_a(4), cre_a(5), des_a(5)): 4,
-            (cre_a(4), des_a(4), cre_b(5), des_b(5)): 4,
-            (cre_b(4), des_b(4), cre_a(5), des_a(5)): 4,
-            (cre_b(4), des_b(4), cre_b(5), des_b(5)): 4,
-            (cre_a(4), des_a(4), cre_a(7), des_a(7)): 4,
-            (cre_a(4), des_a(4), cre_b(7), des_b(7)): 4,
-            (cre_b(4), des_b(4), cre_a(7), des_a(7)): 4,
-            (cre_b(4), des_b(4), cre_b(7), des_b(7)): 4,
-            (cre_a(7), des_a(7), cre_a(8), des_a(8)): 4,
-            (cre_a(7), des_a(7), cre_b(8), des_b(8)): 4,
-            (cre_b(7), des_b(7), cre_a(8), des_a(8)): 4,
-            (cre_b(7), des_b(7), cre_b(8), des_b(8)): 4,
-            (cre_a(7), des_a(7), cre_a(1), des_a(1)): 4,
-            (cre_a(7), des_a(7), cre_b(1), des_b(1)): 4,
-            (cre_b(7), des_b(7), cre_a(1), des_a(1)): 4,
-            (cre_b(7), des_b(7), cre_b(1), des_b(1)): 4,
-            (cre_a(2), des_a(2), cre_a(0), des_a(0)): 4,
-            (cre_a(2), des_a(2), cre_b(0), des_b(0)): 4,
-            (cre_b(2), des_b(2), cre_a(0), des_a(0)): 4,
-            (cre_b(2), des_b(2), cre_b(0), des_b(0)): 4,
-            (cre_a(2), des_a(2), cre_a(5), des_a(5)): 4,
-            (cre_a(2), des_a(2), cre_b(5), des_b(5)): 4,
-            (cre_b(2), des_b(2), cre_a(5), des_a(5)): 4,
-            (cre_b(2), des_b(2), cre_b(5), des_b(5)): 4,
-            (cre_a(5), des_a(5), cre_a(3), des_a(3)): 4,
-            (cre_a(5), des_a(5), cre_b(3), des_b(3)): 4,
-            (cre_b(5), des_b(5), cre_a(3), des_a(3)): 4,
-            (cre_b(5), des_b(5), cre_b(3), des_b(3)): 4,
-            (cre_a(5), des_a(5), cre_a(8), des_a(8)): 4,
-            (cre_a(5), des_a(5), cre_b(8), des_b(8)): 4,
-            (cre_b(5), des_b(5), cre_a(8), des_a(8)): 4,
-            (cre_b(5), des_b(5), cre_b(8), des_b(8)): 4,
-            (cre_a(8), des_a(8), cre_a(6), des_a(6)): 4,
-            (cre_a(8), des_a(8), cre_b(6), des_b(6)): 4,
-            (cre_b(8), des_b(8), cre_a(6), des_a(6)): 4,
-            (cre_b(8), des_b(8), cre_b(6), des_b(6)): 4,
-            (cre_a(8), des_a(8), cre_a(2), des_a(2)): 4,
-            (cre_a(8), des_a(8), cre_b(2), des_b(2)): 4,
-            (cre_b(8), des_b(8), cre_a(2), des_a(2)): 4,
-            (cre_b(8), des_b(8), cre_b(2), des_b(2)): 4,
-        },
-    )
+    assert dict(
+        fermi_hubbard_2d(
+            norb_x=3,
+            norb_y=3,
+            tunneling=1,
+            interaction=2,
+            chemical_potential=3,
+            nearest_neighbor_interaction=4,
+            periodic=True,
+        )
+    ) == {
+        (cre_a(0), des_a(1)): -1,
+        (cre_b(0), des_b(1)): -1,
+        (cre_a(1), des_a(0)): -1,
+        (cre_b(1), des_b(0)): -1,
+        (cre_a(0), des_a(3)): -1,
+        (cre_b(0), des_b(3)): -1,
+        (cre_a(3), des_a(0)): -1,
+        (cre_b(3), des_b(0)): -1,
+        (cre_a(3), des_a(4)): -1,
+        (cre_b(3), des_b(4)): -1,
+        (cre_a(4), des_a(3)): -1,
+        (cre_b(4), des_b(3)): -1,
+        (cre_a(3), des_a(6)): -1,
+        (cre_b(3), des_b(6)): -1,
+        (cre_a(6), des_a(3)): -1,
+        (cre_b(6), des_b(3)): -1,
+        (cre_a(6), des_a(7)): -1,
+        (cre_b(6), des_b(7)): -1,
+        (cre_a(7), des_a(6)): -1,
+        (cre_b(7), des_b(6)): -1,
+        (cre_a(6), des_a(0)): -1,
+        (cre_b(6), des_b(0)): -1,
+        (cre_a(0), des_a(6)): -1,
+        (cre_b(0), des_b(6)): -1,
+        (cre_a(1), des_a(2)): -1,
+        (cre_b(1), des_b(2)): -1,
+        (cre_a(2), des_a(1)): -1,
+        (cre_b(2), des_b(1)): -1,
+        (cre_a(1), des_a(4)): -1,
+        (cre_b(1), des_b(4)): -1,
+        (cre_a(4), des_a(1)): -1,
+        (cre_b(4), des_b(1)): -1,
+        (cre_a(4), des_a(5)): -1,
+        (cre_b(4), des_b(5)): -1,
+        (cre_a(5), des_a(4)): -1,
+        (cre_b(5), des_b(4)): -1,
+        (cre_a(4), des_a(7)): -1,
+        (cre_b(4), des_b(7)): -1,
+        (cre_a(7), des_a(4)): -1,
+        (cre_b(7), des_b(4)): -1,
+        (cre_a(7), des_a(8)): -1,
+        (cre_b(7), des_b(8)): -1,
+        (cre_a(8), des_a(7)): -1,
+        (cre_b(8), des_b(7)): -1,
+        (cre_a(7), des_a(1)): -1,
+        (cre_b(7), des_b(1)): -1,
+        (cre_a(1), des_a(7)): -1,
+        (cre_b(1), des_b(7)): -1,
+        (cre_a(2), des_a(0)): -1,
+        (cre_b(2), des_b(0)): -1,
+        (cre_a(0), des_a(2)): -1,
+        (cre_b(0), des_b(2)): -1,
+        (cre_a(2), des_a(5)): -1,
+        (cre_b(2), des_b(5)): -1,
+        (cre_a(5), des_a(2)): -1,
+        (cre_b(5), des_b(2)): -1,
+        (cre_a(5), des_a(3)): -1,
+        (cre_b(5), des_b(3)): -1,
+        (cre_a(3), des_a(5)): -1,
+        (cre_b(3), des_b(5)): -1,
+        (cre_a(5), des_a(8)): -1,
+        (cre_b(5), des_b(8)): -1,
+        (cre_a(8), des_a(5)): -1,
+        (cre_b(8), des_b(5)): -1,
+        (cre_a(8), des_a(6)): -1,
+        (cre_b(8), des_b(6)): -1,
+        (cre_a(6), des_a(8)): -1,
+        (cre_b(6), des_b(8)): -1,
+        (cre_a(8), des_a(2)): -1,
+        (cre_b(8), des_b(2)): -1,
+        (cre_a(2), des_a(8)): -1,
+        (cre_b(2), des_b(8)): -1,
+        (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
+        (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
+        (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
+        (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
+        (cre_a(4), des_a(4), cre_b(4), des_b(4)): 2,
+        (cre_a(5), des_a(5), cre_b(5), des_b(5)): 2,
+        (cre_a(6), des_a(6), cre_b(6), des_b(6)): 2,
+        (cre_a(7), des_a(7), cre_b(7), des_b(7)): 2,
+        (cre_a(8), des_a(8), cre_b(8), des_b(8)): 2,
+        (cre_a(0), des_a(0)): -3,
+        (cre_b(0), des_b(0)): -3,
+        (cre_a(1), des_a(1)): -3,
+        (cre_b(1), des_b(1)): -3,
+        (cre_a(2), des_a(2)): -3,
+        (cre_b(2), des_b(2)): -3,
+        (cre_a(3), des_a(3)): -3,
+        (cre_b(3), des_b(3)): -3,
+        (cre_a(4), des_a(4)): -3,
+        (cre_b(4), des_b(4)): -3,
+        (cre_a(5), des_a(5)): -3,
+        (cre_b(5), des_b(5)): -3,
+        (cre_a(6), des_a(6)): -3,
+        (cre_b(6), des_b(6)): -3,
+        (cre_a(7), des_a(7)): -3,
+        (cre_b(7), des_b(7)): -3,
+        (cre_a(8), des_a(8)): -3,
+        (cre_b(8), des_b(8)): -3,
+        (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
+        (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
+        (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
+        (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
+        (cre_a(0), des_a(0), cre_a(3), des_a(3)): 4,
+        (cre_a(0), des_a(0), cre_b(3), des_b(3)): 4,
+        (cre_b(0), des_b(0), cre_a(3), des_a(3)): 4,
+        (cre_b(0), des_b(0), cre_b(3), des_b(3)): 4,
+        (cre_a(3), des_a(3), cre_a(4), des_a(4)): 4,
+        (cre_a(3), des_a(3), cre_b(4), des_b(4)): 4,
+        (cre_b(3), des_b(3), cre_a(4), des_a(4)): 4,
+        (cre_b(3), des_b(3), cre_b(4), des_b(4)): 4,
+        (cre_a(3), des_a(3), cre_a(6), des_a(6)): 4,
+        (cre_a(3), des_a(3), cre_b(6), des_b(6)): 4,
+        (cre_b(3), des_b(3), cre_a(6), des_a(6)): 4,
+        (cre_b(3), des_b(3), cre_b(6), des_b(6)): 4,
+        (cre_a(6), des_a(6), cre_a(7), des_a(7)): 4,
+        (cre_a(6), des_a(6), cre_b(7), des_b(7)): 4,
+        (cre_b(6), des_b(6), cre_a(7), des_a(7)): 4,
+        (cre_b(6), des_b(6), cre_b(7), des_b(7)): 4,
+        (cre_a(6), des_a(6), cre_a(0), des_a(0)): 4,
+        (cre_a(6), des_a(6), cre_b(0), des_b(0)): 4,
+        (cre_b(6), des_b(6), cre_a(0), des_a(0)): 4,
+        (cre_b(6), des_b(6), cre_b(0), des_b(0)): 4,
+        (cre_a(1), des_a(1), cre_a(2), des_a(2)): 4,
+        (cre_a(1), des_a(1), cre_b(2), des_b(2)): 4,
+        (cre_b(1), des_b(1), cre_a(2), des_a(2)): 4,
+        (cre_b(1), des_b(1), cre_b(2), des_b(2)): 4,
+        (cre_a(1), des_a(1), cre_a(4), des_a(4)): 4,
+        (cre_a(1), des_a(1), cre_b(4), des_b(4)): 4,
+        (cre_b(1), des_b(1), cre_a(4), des_a(4)): 4,
+        (cre_b(1), des_b(1), cre_b(4), des_b(4)): 4,
+        (cre_a(4), des_a(4), cre_a(5), des_a(5)): 4,
+        (cre_a(4), des_a(4), cre_b(5), des_b(5)): 4,
+        (cre_b(4), des_b(4), cre_a(5), des_a(5)): 4,
+        (cre_b(4), des_b(4), cre_b(5), des_b(5)): 4,
+        (cre_a(4), des_a(4), cre_a(7), des_a(7)): 4,
+        (cre_a(4), des_a(4), cre_b(7), des_b(7)): 4,
+        (cre_b(4), des_b(4), cre_a(7), des_a(7)): 4,
+        (cre_b(4), des_b(4), cre_b(7), des_b(7)): 4,
+        (cre_a(7), des_a(7), cre_a(8), des_a(8)): 4,
+        (cre_a(7), des_a(7), cre_b(8), des_b(8)): 4,
+        (cre_b(7), des_b(7), cre_a(8), des_a(8)): 4,
+        (cre_b(7), des_b(7), cre_b(8), des_b(8)): 4,
+        (cre_a(7), des_a(7), cre_a(1), des_a(1)): 4,
+        (cre_a(7), des_a(7), cre_b(1), des_b(1)): 4,
+        (cre_b(7), des_b(7), cre_a(1), des_a(1)): 4,
+        (cre_b(7), des_b(7), cre_b(1), des_b(1)): 4,
+        (cre_a(2), des_a(2), cre_a(0), des_a(0)): 4,
+        (cre_a(2), des_a(2), cre_b(0), des_b(0)): 4,
+        (cre_b(2), des_b(2), cre_a(0), des_a(0)): 4,
+        (cre_b(2), des_b(2), cre_b(0), des_b(0)): 4,
+        (cre_a(2), des_a(2), cre_a(5), des_a(5)): 4,
+        (cre_a(2), des_a(2), cre_b(5), des_b(5)): 4,
+        (cre_b(2), des_b(2), cre_a(5), des_a(5)): 4,
+        (cre_b(2), des_b(2), cre_b(5), des_b(5)): 4,
+        (cre_a(5), des_a(5), cre_a(3), des_a(3)): 4,
+        (cre_a(5), des_a(5), cre_b(3), des_b(3)): 4,
+        (cre_b(5), des_b(5), cre_a(3), des_a(3)): 4,
+        (cre_b(5), des_b(5), cre_b(3), des_b(3)): 4,
+        (cre_a(5), des_a(5), cre_a(8), des_a(8)): 4,
+        (cre_a(5), des_a(5), cre_b(8), des_b(8)): 4,
+        (cre_b(5), des_b(5), cre_a(8), des_a(8)): 4,
+        (cre_b(5), des_b(5), cre_b(8), des_b(8)): 4,
+        (cre_a(8), des_a(8), cre_a(6), des_a(6)): 4,
+        (cre_a(8), des_a(8), cre_b(6), des_b(6)): 4,
+        (cre_b(8), des_b(8), cre_a(6), des_a(6)): 4,
+        (cre_b(8), des_b(8), cre_b(6), des_b(6)): 4,
+        (cre_a(8), des_a(8), cre_a(2), des_a(2)): 4,
+        (cre_a(8), des_a(8), cre_b(2), des_b(2)): 4,
+        (cre_b(8), des_b(8), cre_a(2), des_a(2)): 4,
+        (cre_b(8), des_b(8), cre_b(2), des_b(2)): 4,
+    }
 
     # periodic boundary conditions (edge case)
-    op_periodic_edge = fermi_hubbard_2d(
-        norb_x=2,
-        norb_y=2,
-        tunneling=1,
-        interaction=2,
-        chemical_potential=3,
-        nearest_neighbor_interaction=4,
-        periodic=True,
-    )
-    np.testing.assert_equal(
-        dict(op_periodic_edge),
-        {
-            (cre_a(0), des_a(1)): -2,
-            (cre_b(0), des_b(1)): -2,
-            (cre_a(1), des_a(0)): -2,
-            (cre_b(1), des_b(0)): -2,
-            (cre_a(0), des_a(2)): -2,
-            (cre_b(0), des_b(2)): -2,
-            (cre_a(2), des_a(0)): -2,
-            (cre_b(2), des_b(0)): -2,
-            (cre_a(2), des_a(3)): -2,
-            (cre_b(2), des_b(3)): -2,
-            (cre_a(3), des_a(2)): -2,
-            (cre_b(3), des_b(2)): -2,
-            (cre_a(1), des_a(3)): -2,
-            (cre_b(1), des_b(3)): -2,
-            (cre_a(3), des_a(1)): -2,
-            (cre_b(3), des_b(1)): -2,
-            (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
-            (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
-            (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
-            (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
-            (cre_a(0), des_a(0)): -3,
-            (cre_b(0), des_b(0)): -3,
-            (cre_a(1), des_a(1)): -3,
-            (cre_b(1), des_b(1)): -3,
-            (cre_a(2), des_a(2)): -3,
-            (cre_b(2), des_b(2)): -3,
-            (cre_a(3), des_a(3)): -3,
-            (cre_b(3), des_b(3)): -3,
-            (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
-            (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
-            (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
-            (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
-            (cre_a(0), des_a(0), cre_a(2), des_a(2)): 4,
-            (cre_a(0), des_a(0), cre_b(2), des_b(2)): 4,
-            (cre_b(0), des_b(0), cre_a(2), des_a(2)): 4,
-            (cre_b(0), des_b(0), cre_b(2), des_b(2)): 4,
-            (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
-            (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
-            (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
-            (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
-            (cre_a(2), des_a(2), cre_a(0), des_a(0)): 4,
-            (cre_a(2), des_a(2), cre_b(0), des_b(0)): 4,
-            (cre_b(2), des_b(2), cre_a(0), des_a(0)): 4,
-            (cre_b(2), des_b(2), cre_b(0), des_b(0)): 4,
-            (cre_a(1), des_a(1), cre_a(0), des_a(0)): 4,
-            (cre_a(1), des_a(1), cre_b(0), des_b(0)): 4,
-            (cre_b(1), des_b(1), cre_a(0), des_a(0)): 4,
-            (cre_b(1), des_b(1), cre_b(0), des_b(0)): 4,
-            (cre_a(1), des_a(1), cre_a(3), des_a(3)): 4,
-            (cre_a(1), des_a(1), cre_b(3), des_b(3)): 4,
-            (cre_b(1), des_b(1), cre_a(3), des_a(3)): 4,
-            (cre_b(1), des_b(1), cre_b(3), des_b(3)): 4,
-            (cre_a(3), des_a(3), cre_a(2), des_a(2)): 4,
-            (cre_a(3), des_a(3), cre_b(2), des_b(2)): 4,
-            (cre_b(3), des_b(3), cre_a(2), des_a(2)): 4,
-            (cre_b(3), des_b(3), cre_b(2), des_b(2)): 4,
-            (cre_a(3), des_a(3), cre_a(1), des_a(1)): 4,
-            (cre_a(3), des_a(3), cre_b(1), des_b(1)): 4,
-            (cre_b(3), des_b(3), cre_a(1), des_a(1)): 4,
-            (cre_b(3), des_b(3), cre_b(1), des_b(1)): 4,
-        },
-    )
+    assert dict(
+        fermi_hubbard_2d(
+            norb_x=2,
+            norb_y=2,
+            tunneling=1,
+            interaction=2,
+            chemical_potential=3,
+            nearest_neighbor_interaction=4,
+            periodic=True,
+        )
+    ) == {
+        (cre_a(0), des_a(1)): -2,
+        (cre_b(0), des_b(1)): -2,
+        (cre_a(1), des_a(0)): -2,
+        (cre_b(1), des_b(0)): -2,
+        (cre_a(0), des_a(2)): -2,
+        (cre_b(0), des_b(2)): -2,
+        (cre_a(2), des_a(0)): -2,
+        (cre_b(2), des_b(0)): -2,
+        (cre_a(2), des_a(3)): -2,
+        (cre_b(2), des_b(3)): -2,
+        (cre_a(3), des_a(2)): -2,
+        (cre_b(3), des_b(2)): -2,
+        (cre_a(1), des_a(3)): -2,
+        (cre_b(1), des_b(3)): -2,
+        (cre_a(3), des_a(1)): -2,
+        (cre_b(3), des_b(1)): -2,
+        (cre_a(0), des_a(0), cre_b(0), des_b(0)): 2,
+        (cre_a(1), des_a(1), cre_b(1), des_b(1)): 2,
+        (cre_a(2), des_a(2), cre_b(2), des_b(2)): 2,
+        (cre_a(3), des_a(3), cre_b(3), des_b(3)): 2,
+        (cre_a(0), des_a(0)): -3,
+        (cre_b(0), des_b(0)): -3,
+        (cre_a(1), des_a(1)): -3,
+        (cre_b(1), des_b(1)): -3,
+        (cre_a(2), des_a(2)): -3,
+        (cre_b(2), des_b(2)): -3,
+        (cre_a(3), des_a(3)): -3,
+        (cre_b(3), des_b(3)): -3,
+        (cre_a(0), des_a(0), cre_a(1), des_a(1)): 4,
+        (cre_a(0), des_a(0), cre_b(1), des_b(1)): 4,
+        (cre_b(0), des_b(0), cre_a(1), des_a(1)): 4,
+        (cre_b(0), des_b(0), cre_b(1), des_b(1)): 4,
+        (cre_a(0), des_a(0), cre_a(2), des_a(2)): 4,
+        (cre_a(0), des_a(0), cre_b(2), des_b(2)): 4,
+        (cre_b(0), des_b(0), cre_a(2), des_a(2)): 4,
+        (cre_b(0), des_b(0), cre_b(2), des_b(2)): 4,
+        (cre_a(2), des_a(2), cre_a(3), des_a(3)): 4,
+        (cre_a(2), des_a(2), cre_b(3), des_b(3)): 4,
+        (cre_b(2), des_b(2), cre_a(3), des_a(3)): 4,
+        (cre_b(2), des_b(2), cre_b(3), des_b(3)): 4,
+        (cre_a(2), des_a(2), cre_a(0), des_a(0)): 4,
+        (cre_a(2), des_a(2), cre_b(0), des_b(0)): 4,
+        (cre_b(2), des_b(2), cre_a(0), des_a(0)): 4,
+        (cre_b(2), des_b(2), cre_b(0), des_b(0)): 4,
+        (cre_a(1), des_a(1), cre_a(0), des_a(0)): 4,
+        (cre_a(1), des_a(1), cre_b(0), des_b(0)): 4,
+        (cre_b(1), des_b(1), cre_a(0), des_a(0)): 4,
+        (cre_b(1), des_b(1), cre_b(0), des_b(0)): 4,
+        (cre_a(1), des_a(1), cre_a(3), des_a(3)): 4,
+        (cre_a(1), des_a(1), cre_b(3), des_b(3)): 4,
+        (cre_b(1), des_b(1), cre_a(3), des_a(3)): 4,
+        (cre_b(1), des_b(1), cre_b(3), des_b(3)): 4,
+        (cre_a(3), des_a(3), cre_a(2), des_a(2)): 4,
+        (cre_a(3), des_a(3), cre_b(2), des_b(2)): 4,
+        (cre_b(3), des_b(3), cre_a(2), des_a(2)): 4,
+        (cre_b(3), des_b(3), cre_b(2), des_b(2)): 4,
+        (cre_a(3), des_a(3), cre_a(1), des_a(1)): 4,
+        (cre_a(3), des_a(3), cre_b(1), des_b(1)): 4,
+        (cre_b(3), des_b(3), cre_a(1), des_a(1)): 4,
+        (cre_b(3), des_b(3), cre_b(1), des_b(1)): 4,
+    }
 
 
 def test_non_interacting_fermi_hubbard_1d_eigenvalue():