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Recently I've been working on a setup with two qubits and a resonator. And usually people consider the following scenarios:

  • Qubit-Qubit Interaction something like $\hat{\sigma}_X^{(a)}\hat{\sigma}_X^{(b)}$
  • Qubit-Resonator Interaction something like $\hat{\sigma}_X^{(a)}(\hat{a} +\hat{a}^\dagger)$

And combinations of them present in the same setup.

My question is about a native Qubit-Qubit-Resonator interaction term like $\hat{\sigma}_X^{(a)}\hat{\sigma}_X^{(b)}(\hat{a} +\hat{a}^\dagger)$. Is there a native way to setup such an interaction? Or any other way to set it up?

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