I want the draw the quantum circuit of the following Hamiltonian: $$H = - 4 \times X\otimes X\otimes X\otimes X - 4\times Z\otimes Z\otimes Z \otimes Z$$. I have been able to draw the circuits of $ - X\otimes X\otimes X\otimes X$ and $- Z\otimes Z\otimes Z \otimes Z$. But adding them up using qiskit functions like compose, and combine did not give me the matrix I am looking for.
I would like to recall that when looking at $ 4 \times X\otimes X\otimes X\otimes X$ for instance, the operator $ X\otimes X\otimes X\otimes X$ will be applied $4$ times but not on the same set of qubits and the matrix should $16\times 16$. Using compose and combine function, I still obtain the $16\times 16$ matrix by its components do not add up. Instead, the gates acted on the same set of qubits.
It will be very helpful if someone can help me. Thanks