[Code together] Add matrix form to Grover Operator

pennylane/templates/subroutines/grover.py

@@ -17,7 +17,9 @@
 import pennylane as qml
 from pennylane.operation import AnyWires, Operation
 from pennylane.ops import Hadamard, PauliZ, MultiControlledX
-
+import numpy as np
+import itertools
+import functools
 
 class GroverOperator(Operation):
     r"""Performs the Grover Diffusion Operator.
@@ -107,6 +109,17 @@ def __init__(self, wires=None, work_wires=None, do_queue=True, id=None):
         self.work_wires = work_wires
         super().__init__(wires=wires, do_queue=do_queue, id=id)
 
+
+    def __getMultiControlledX(self):
+        ctrl_str = "0" * (len(self.wires) - 1)
+        return  MultiControlledX(
+            control_values=ctrl_str,
+            control_wires=self.wires[:-1],
+            wires=self.wires[-1],
+            work_wires=self.work_wires,
+            )
+
+
     def expand(self):
         ctrl_str = "0" * (len(self.wires) - 1)
 
@@ -115,15 +128,47 @@ def expand(self):
                 Hadamard(wire)
 
             PauliZ(self.wires[-1])
-            MultiControlledX(
-                control_values=ctrl_str,
-                control_wires=self.wires[:-1],
-                wires=self.wires[-1],
-                work_wires=self.work_wires,
-            )
+            self.__getMultiControlledX()
             PauliZ(self.wires[-1])
 
             for wire in self.wires[:-1]:
                 Hadamard(wire)
 
         return tape
+
+
+    def _matrix1(self):
+        """ Matrix representation of the Grover diffusion operator """
+        nbr_wires = len(self.wires)
+
+        # state |0>
+        state_0 = [1, 0]
+
+        s1 = Hadamard.matrix @ state_0
+
+        # uniform superposition state
+        s = functools.reduce(np.kron, list(itertools.repeat(s1, nbr_wires)))
+
+        # Grover diffusion operator
+        G = 2*np.outer(s,s) - np.identity(2**nbr_wires)
+        return G
+
+
+    def _matrix(self):
+        """ Matrix representation of the Grover diffusion operator """
+
+        nbr_wires = len(self.wires)
+
+        oplist = list(itertools.repeat(Hadamard.matrix, nbr_wires-1))
+        oplist.append(PauliZ.matrix)
+
+        CX = self.__getMultiControlledX()
+
+        CX = CX.matrix
+
+
+        M =  functools.reduce(np.kron, oplist)
+        G = M @ CX @ M
+
+
+        return G