diff --git a/pennylane/ops/qubit/non_parametric_ops.py b/pennylane/ops/qubit/non_parametric_ops.py
index b4e0d8407dc..7d447399f5c 100644
--- a/pennylane/ops/qubit/non_parametric_ops.py
+++ b/pennylane/ops/qubit/non_parametric_ops.py
@@ -77,6 +77,10 @@ def __repr__(self) -> str:
     def name(self) -> str:
         return "Hadamard"
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({qml.pauli.PauliWord({self.wires[0]: 'X'}) : INV_SQRT2, qml.pauli.PauliWord({self.wires[0]: 'Z'}) : INV_SQRT2})
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
@@ -815,6 +819,10 @@ class S(Operation):
 
     batch_size = None
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({qml.pauli.PauliWord({self.wires[0]: 'I'}) : 0.5 + 0.5j, qml.pauli.PauliWord({self.wires[0]: 'Z'}) : 0.5 - 0.5j})
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
@@ -927,6 +935,10 @@ class T(Operation):
 
     batch_size = None
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({qml.pauli.PauliWord({self.wires[0]: 'I'}) : (0.5 + 0.5 * INV_SQRT2 * (1 + 1.j)), qml.pauli.PauliWord({self.wires[0]: 'Z'}) : (0.5 - 0.5 * INV_SQRT2 * (1 + 1.j))})
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
@@ -1037,6 +1049,10 @@ class SX(Operation):
 
     basis = "X"
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({qml.pauli.PauliWord({self.wires[0]: 'I'}) : (0.5 + 0.5j), qml.pauli.PauliWord({self.wires[0]: 'X'}) : (0.5 - 0.5j)})
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
@@ -1152,6 +1168,13 @@ class SWAP(Operation):
 
     batch_size = None
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({ qml.pauli.PauliWord({self.wires[0]: 'I', self.wires[1]: 'I'}) : 0.5,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'X', self.wires[1]: 'X'}) : 0.5,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Y', self.wires[1]: 'Y'}) : 0.5,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Z', self.wires[1]: 'Z'}) : 0.5 })
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
@@ -1243,6 +1266,11 @@ class ECR(Operation):
 
     batch_size = None
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({ qml.pauli.PauliWord({self.wires[0]: 'X', self.wires[1]: 'I'}) :   INV_SQRT2,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Y', self.wires[1]: 'X'}) : - INV_SQRT2 })
+
     @staticmethod
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
         r"""Representation of the operator as a canonical matrix in the computational basis (static method).
@@ -1371,6 +1399,13 @@ class ISWAP(Operation):
 
     batch_size = None
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({ qml.pauli.PauliWord({self.wires[0]: 'I', self.wires[1]: 'I'}) : 0.5,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'X', self.wires[1]: 'X'}) : 0.5j,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Y', self.wires[1]: 'Y'}) : 0.5j,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Z', self.wires[1]: 'Z'}) : 0.5 })
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
@@ -1488,6 +1523,13 @@ class SISWAP(Operation):
 
     batch_size = None
 
+    def __init__(self, wires: WiresLike, id: Optional[str] = None):
+        super().__init__(wires=wires, id=id)
+        self._pauli_rep = qml.pauli.PauliSentence({ qml.pauli.PauliWord({self.wires[0]: 'I', self.wires[1]: 'I'}) : 0.5 + 0.5 * INV_SQRT2,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'X', self.wires[1]: 'X'}) : 0.5j * INV_SQRT2,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Y', self.wires[1]: 'Y'}) : 0.5j * INV_SQRT2,
+                                                    qml.pauli.PauliWord({self.wires[0]: 'Z', self.wires[1]: 'Z'}) : 0.5 - 0.5 * INV_SQRT2 })
+
     @staticmethod
     @lru_cache()
     def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ