In two-qubit system there are $ZZ$- and $XX$-interaction between the qubits, in some papers it is described how to remove such parasitic interactions, but I didn't find the reason of why does it happen?

  • $\begingroup$ Can you add more details to your question? Like can you describe how those papers describe exactly and cite those papers here? $\endgroup$
    – narip
    Nov 11, 2022 at 5:06

1 Answer 1


This comes down very much to the physics of the individual devices. I'll describe here one relatively simple model which hopefully gives you a little bit of insight. But, as I say, it's different for each device...

Consider an optical lattice. You should basically think of a sinusoidal trapping potential. Within each minimum you could define a qubit by the presence or absence of an atom (there are better things to do, but I'm keeping it simple).

Now, whatever our best description of the wavefunction of the atom within a single potential well, that wavefunction extends outside that single well, and into the neighbouring ones. In other words, it has the possibility to tunnel from one potential well to the next. This would be described by a Hamiltonian $XX+YY$. You can even be precise about the coupling strength: simply ask what's the overlap between the wavefunction of an atom trapped in one site, with the wavefunction of an atom trapped in the next site. So, the higher you make the potential barrier between them, the smaller the overlap, and the smaller the coupling strength.

  • $\begingroup$ your description is quite good and clear, thank you) but what about ZZ-interaction and Bloch sphere? $\endgroup$
    – Curious
    Nov 15, 2022 at 7:15
  • $\begingroup$ What do you mean "ZZ-interaction and the Bloch sphere"? (i.e. what are you wanting to know?) As soon as you're talking about multi-qubit interactions, the Bloch sphere by itself isn't so helpful. Except to say that the ZZ interaction will induce some entanglement, which may be interpreted as a shortening of the Bloch vector of the individual qubits. $\endgroup$
    – DaftWullie
    Nov 15, 2022 at 7:29
  • $\begingroup$ I'd like to know some kind of physical interpretation of this interaction, for example for superconducting qubits or ion trapps. $\endgroup$
    – Curious
    Nov 15, 2022 at 17:35
  • $\begingroup$ is it possible? $\endgroup$
    – Curious
    Nov 16, 2022 at 10:44

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