Update block encoding demo (#1080)

Update the demo on block encoding with matrix access oracles to:

1. Add the newly implemented `qml.FABLE` to the demo.
2. Correct an equation to allow block encoding `2 x 2` matrices.

demonstrations/tutorial_block_encoding.metadata.json

@@ -12,7 +12,7 @@
         }
     ],
     "dateOfPublication": "2023-11-28T00:00:00+00:00",
-    "dateOfLastModification": "2024-01-01T00:00:00+00:00",
+    "dateOfLastModification": "2024-04-26T00:00:00+00:00",
     "categories": [
         "Quantum Computing",
         "Algorithms"

demonstrations/tutorial_block_encoding.py

@@ -79,7 +79,10 @@
 be obtained with the :func:`~.pennylane.templates.state_preparations.mottonen.compute_theta`
 function of PennyLane.
 
-Let's now construct the FABLE block encoding circuit for a structured matrix.
+The :class:`~.pennylane.FABLE` circuit is implemented in PennyLane and
+can be easily used to block encode matrices of any given shape. Here, we manually construct the
+circuit for a structured :math:`4 \times 4` matrix.
+.
 """
 
 import pennylane as qml
@@ -116,7 +119,7 @@
 # Finally, we obtain the control wires for the C-NOT gates and a wire map that we later use to
 # translate the control wires into the wire registers we prepared.
 
-code = gray_code(2*np.sqrt(len(A)))
+code = gray_code(2 * np.log2(len(A)))
 n_selections = len(code)
 
 control_wires = [int(np.log2(int(code[i], 2) ^ int(code[(i + 1) %
@@ -173,7 +176,9 @@ def circuit():
 ##############################################################################
 # You can easily confirm that the circuit block encodes the original matrix defined above. Note that
 # the dimension of :math:`A` should be :math:`2^n` where :math:`n` is an integer. For matrices with
-# an arbitrary size, we can add zeros to reach the correct dimension.
+# an arbitrary size, we can add zeros to reach the correct dimension. The padding will be
+# automatically applied in :class:`~.pennylane.FABLE` implemented in
+# PennyLane.
 #
 # The interesting point about the FABLE method is that we can eliminate those rotation gates that
 # have an angle smaller than a defined threshold. This leaves a sequence of C-NOT gates that in