Add `pauli_rep` properties for common static gates

[dwierichs]

Feature details

The pauli_rep property allows to represent an operator as a PauliSentence instance. Currently, it is mostly implemented for qml.X, qml.Y, qml.Z and for operator math classes. It would be great to have pauli_rep attributes for, e.g., Clifford gates (Hadamard, S, CNOT), but also for other ops. This would simplify manipulation of qml.pauli objects.

This came up while writing this demo, where we currently have to do

new_op = qml.CNOT([0, 1]) @ original_op @ qml.CNOT([0, 1])
new_op = qml.pauli_decompose(new_op.matrix())

i.e., we have to go via the dense matrix representation to obtain the new operator. With qml.CNOT.pauli_rep implemented, we could stay in the more efficient Pauli representation.

Implementation

Basically trivial, as far as I can tell.

How important would you say this feature is?

1: Not important. Would be nice to have.

Additional information

No response