Cross-resonance interactions are a promising way to implement all-microwave two-qubit gates with fixed-frequency qubits. In this work, we study the dependence of the cross-resonance interaction rate on qubit-qubit detuning and compare with a model that includes the higher levels of a transmon system. To carry out this study we employ two transmon qubits--one fixed frequency and the other flux tunable--to allow us to vary the detuning between qubits. We find that the interaction closely follows a three-level model of the transmon, thus confirming the presence of an optimal regime for cross-resonance gates.
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