Use pauli_rep to compute qml.matrix() whenever possible

doc/releases/changelog-dev.md

@@ -344,6 +344,10 @@
   [stim](https://github.com/quantumlib/Stim) `v1.13.0`.
   [(#5409)](https://github.com/PennyLaneAI/pennylane/pull/5409)
 
+* `qml.matrix` uses the pauli representation for matrix computation,
+  which results in faster computation of the matrix.
+  [(5392)](https://github.com/PennyLaneAI/pennylane/pull/5392)
+
 * `default.mixed` has improved support for sampling-based measurements with non-numpy interfaces.
   [(#5514)](https://github.com/PennyLaneAI/pennylane/pull/5514)
 

pennylane/ops/functions/matrix.py

@@ -211,8 +211,10 @@ def circuit():
     if isinstance(op, qml.operation.Tensor) and wire_order is not None:
         op = 1.0 * op  # convert to a Hamiltonian
 
-    if isinstance(op, qml.ops.Hamiltonian):
+    if (pr := op.pauli_rep) is not None:
+        return pr.to_mat(wire_order=wire_order or op.wires, format="csr").toarray()
 
+    if isinstance(op, qml.ops.Hamiltonian):
         return op.sparse_matrix(wire_order=wire_order).toarray()
 
     try:

tests/ops/functions/test_matrix.py

@@ -569,8 +569,8 @@ def circuit():
             qml.matrix(circuit, wire_order=wires)()
 
         with pytest.raises(
-            TransformError,
-            match=r"Wires in circuit \[0\] are inconsistent with those in wire_order \[1\]",
+            ValueError,
+            match=r"the matrix for the specified wire order because it does not contain all the Pauli sentence",
         ):
             qml.matrix(qml.PauliX(0), wire_order=[1])