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Cross-resonance interactions are a promising way to implement all-microwavetwo-qubit gates with fixed-frequency qubits. In this work, we study thedependence of the cross-resonance interaction rate on qubit-qubit detuning andcompare with a model that includes the higher levels of a transmon system. Tocarry out this study we employ two transmon qubits--one fixed frequency and theother flux tunable--to allow us to vary the detuning between qubits. We findthat the interaction closely follows a three-level model of the transmon, thusconfirming the presence of an optimal regime for cross-resonance gates.

Cross-resonance interactions between superconducting qubits with variable detuning