# How to create a quantum circuit to implement the same operations but acting on different qubits?

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

• Can I suggest you switch notation? It might help make it clearly what you're asking for. For example, let $X_2$ be $I\otimes X\otimes I\otimes I\otimes\ldots\otimes I$, so you can write things like $X_1X_2X_3X_4$ as the operator you're talking about on the first 4 qubits. Now, what do you really mean by $4\times X\otimes X\otimes X\otimes X$? Oct 6 at 8:37
• Yeah. But the $x_i$ are the same. There are x-Pauli matrices. The initial form of the Hamiltonian is $H = -\sum_v As - \sum_p Bp$ where $As = X\otimes ^4$ and $Bp = Z\otimes^4$. In my case, The sum contains 4 elements for both operator. Oct 6 at 8:46
• Yes, but, as I understand it, the sets of 4 qubits are different for each term. This is the crucial thing that's missing from the question, and (I suspect) in what you're telling qiskit to do. Oct 6 at 9:47
• The sets of the 4 qubits are differents. That is true. While applying the operators As and Bp on them, the circuit of each will be the same I think. My concern is how to add up all the circuits without using combine and compose functions Oct 6 at 10:11
• Are you doing a Toric code(surface code) implementation? If so, you can check this answer: entangledquery.com/t/surface-code-implementation/23 Oct 15 at 23:55