diff --git a/.github/CHANGELOG.md b/.github/CHANGELOG.md
index 851f9025a..10773ae50 100644
--- a/.github/CHANGELOG.md
+++ b/.github/CHANGELOG.md
@@ -53,6 +53,8 @@ which uses the old Numba code. When setting to a higher value, the new Julia cod
   [(#303)](https://github.com/XanaduAI/MrMustard/pull/303)
   [(#304)](https://github.com/XanaduAI/MrMustard/pull/304)
 
+* Changed the ``cast`` functions in the numpy and tensorflow backends to avoid ``ComplexWarning``s.
+
 ### Bug fixes
 
 * Added the missing `shape` input parameters to all methods `U` in the `gates.py` file.
diff --git a/mrmustard/math/backend_numpy.py b/mrmustard/math/backend_numpy.py
index cabf9e245..36452835d 100644
--- a/mrmustard/math/backend_numpy.py
+++ b/mrmustard/math/backend_numpy.py
@@ -43,8 +43,8 @@ class BackendNumpy(BackendBase):  # pragma: no cover
     """
 
     int32 = np.int32
-    float64 = np.float64
     float32 = np.float32
+    float64 = np.float64
     complex64 = np.complex64
     complex128 = np.complex128
 
@@ -90,6 +90,8 @@ def cast(self, array: np.array, dtype=None) -> np.array:
         if dtype is None:
             return array
 
+        if dtype not in [self.complex64, self.complex128, "complex64", "complex128"]:
+            array = self.real(array)
         return np.array(array, dtype=dtype)
 
     def clip(self, array, a_min, a_max) -> np.array:
diff --git a/mrmustard/math/backend_tensorflow.py b/mrmustard/math/backend_tensorflow.py
index 8930bf46a..8534717c6 100644
--- a/mrmustard/math/backend_tensorflow.py
+++ b/mrmustard/math/backend_tensorflow.py
@@ -42,8 +42,8 @@ class BackendTensorflow(BackendBase):  # pragma: no cover
     """
 
     int32 = tf.int32
-    float64 = tf.float64
     float32 = tf.float32
+    float64 = tf.float64
     complex64 = tf.complex64
     complex128 = tf.complex128
 
@@ -87,6 +87,9 @@ def boolean_mask(self, tensor: tf.Tensor, mask: tf.Tensor) -> Tensor:
     def cast(self, array: tf.Tensor, dtype=None) -> tf.Tensor:
         if dtype is None:
             return array
+
+        if dtype not in [self.complex64, self.complex128, "complex64", "complex128"]:
+            array = self.real(array)
         return tf.cast(array, dtype)
 
     def clip(self, array, a_min, a_max) -> tf.Tensor:
@@ -467,7 +470,9 @@ def reorder_AB_bargmann(self, A: tf.Tensor, B: tf.Tensor) -> Tuple[tf.Tensor, tf
         r"""In mrmustard.math.compactFock.compactFock~ dimensions of the Fock representation are ordered like [mode0,mode0,mode1,mode1,...]
         while in mrmustard.physics.bargmann the ordering is [mode0,mode1,...,mode0,mode1,...]. Here we reorder A and B.
         """
-        ordering = np.arange(2 * A.shape[0] // 2).reshape(2, -1).T.flatten()
+        ordering = (
+            np.arange(2 * A.shape[0] // 2).reshape(2, -1).T.flatten()
+        )  # ordering is [0,2,4,...,1,3,5,...]
         A = tf.gather(A, ordering, axis=1)
         A = tf.gather(A, ordering)
         B = tf.gather(B, ordering)