Fix an error in MottonenStatePreparation with qml.math.cast (#1400)

* qml.math.cast

* Add test and update changelog.

* Typo.

* Import torch change.

* Update pennylane/templates/state_preparations/mottonen.py

Co-authored-by: antalszava <antalszava@gmail.com>

* Update tests/templates/test_state_preparations/test_mottonen_state_prep.py

Co-authored-by: antalszava <antalszava@gmail.com>

* Update tests/templates/test_state_preparations/test_mottonen_state_prep.py

Co-authored-by: antalszava <antalszava@gmail.com>

* Update tests/templates/test_state_preparations/test_mottonen_state_prep.py

Co-authored-by: antalszava <antalszava@gmail.com>

* Update .github/CHANGELOG.md

Co-authored-by: antalszava <antalszava@gmail.com>

* Update tests/templates/test_state_preparations/test_mottonen_state_prep.py

Co-authored-by: antalszava <antalszava@gmail.com>

* Tensor to array.

Co-authored-by: Romain Moyard <rmoyard@gmail.com>

Author: antalszava

.github/CHANGELOG.md

@@ -505,7 +505,7 @@ random_mat2 = rng.standard_normal(3, requires_grad=False)
   ```
 
   ```pycon
-  >>> tape = tape.expand(depth=2)
+  >>> tape = tape.expand(depth=1)
   >>> print(tape.draw(wire_order=Wires(all_wires)))
    c0: ──────────────╭C──────────────────────╭C──────────┤
    c1: ──────────────├C──────────────────────├C──────────┤
@@ -577,14 +577,18 @@ random_mat2 = rng.standard_normal(3, requires_grad=False)
 
 <h3>Bug fixes</h3>
 
+* Fixes a bug with `qml.math.cast` where the `MottonenStatePreparation` operation expected
+  a float type instead of double.
+  [(#1400)](https://github.com/XanaduAI/pennylane/pull/1400)
+
 * Fixes a bug where a copy of `qml.ControlledQubitUnitary` was non-functional as it did not have all the necessary information.
 [(#1411)](https://github.com/PennyLaneAI/pennylane/pull/1411)
 
 * Warns when adjoint or reversible differentiation specified or called on a device with finite shots.
-[(#1406)](https://github.com/PennyLaneAI/pennylane/pull/1406)
+  [(#1406)](https://github.com/PennyLaneAI/pennylane/pull/1406)
 
 * Fixes the differentiability of the operations `IsingXX` and `IsingZZ` for Autograd, Jax and Tensorflow.
-[(#1390)](https://github.com/PennyLaneAI/pennylane/pull/1390)
+  [(#1390)](https://github.com/PennyLaneAI/pennylane/pull/1390)
 
 * Fixes a bug where multiple identical Hamiltonian terms will produce a
   different result with ``optimize=True`` using ``ExpvalCost``.
@@ -595,7 +599,7 @@ random_mat2 = rng.standard_normal(3, requires_grad=False)
   [(#1392)](https://github.com/XanaduAI/pennylane/pull/1392)
 
 * Fixes floating point errors with `diff_method="finite-diff"` and `order=1` when parameters are `float32`.
-[(#1381)](https://github.com/PennyLaneAI/pennylane/pull/1381)
+  [(#1381)](https://github.com/PennyLaneAI/pennylane/pull/1381)
 
 * Fixes a bug where `qml.ctrl` would fail to transform gates that had no
   control defined and no decomposition defined.

pennylane/templates/state_preparations/mottonen.py

@@ -203,6 +203,10 @@ def _get_alpha_y(a, n, k):
     with np.errstate(divide="ignore", invalid="ignore"):
         division = numerator / denominator
 
+    # Cast the numerator and denominator to ensure compatibility with interfaces
+    division = qml.math.cast(division, np.float64)
+    denominator = qml.math.cast(denominator, np.float64)
+
     division = qml.math.where(denominator != 0.0, division, 0.0)
 
     return 2 * qml.math.arcsin(qml.math.sqrt(division))

tests/templates/test_state_preparations/test_mottonen_state_prep.py

@@ -18,6 +18,8 @@
 import numpy as np
 import pennylane as qml
 from pennylane import numpy as pnp
+
+torch = pytest.importorskip("torch", minversion="1.3")
 from pennylane.templates.state_preparations.mottonen import gray_code, _get_alpha_y
 
 
@@ -342,3 +344,31 @@ def circuit(state_vector):
             return qml.expval(qml.PauliZ(0))
 
         qml.grad(circuit)(state_vector)
+
+
+class TestCasting:
+    """Test that the Mottonen state preparation ensures the compatibility with
+    interfaces by using casting'"""
+
+    @pytest.mark.parametrize(
+        "inputs, expected",
+        [
+            (
+                torch.tensor([0.0, 0.7, 0.7, 0.0], requires_grad=True),
+                [0.0, 0.5, 0.5, 0.0],
+            ),
+            (torch.tensor([0.1, 0.0, 0.0, 0.1], requires_grad=True), [0.5, 0.0, 0.0, 0.5]),
+        ],
+    )
+    def test_scalar_torch(self, inputs, expected):
+        """Test that MottonenStatePreparation can be correctly used with the Torch interface."""
+        dev = qml.device("default.qubit", wires=2)
+
+        @qml.qnode(dev, interface="torch")
+        def circuit(inputs):
+            qml.templates.MottonenStatePreparation(inputs, wires=[0, 1])
+            return qml.probs(wires=[0, 1])
+
+        inputs = inputs / torch.linalg.norm(inputs)
+        res = circuit(inputs)
+        assert np.allclose(res.detach().numpy(), expected, atol=1e-6, rtol=0)