We present a comprehensive theoretical study of the cross-resonance gate operation covering estimates for gate parameters and gate error as well as analyzing spectator qubits and multi-qubit frequency collisions. Starting from the Josephson nonlinearity and by accounting for the eigenstates renormalization, due to counter-rotating terms, we derive a new starting model for the cross-resonance gate with modified qubit-qubit interaction and drive matrix elements. Employing time-dependent Schrieffer-Wolff perturbation theory, we derive an effective Hamiltonian for the cross-resonance gate with estimates for the gate parameters calculated up to the fourth order in drive amplitude. The new model with renormalized eigenstates lead to 10–15 percent relative correction of the effective gate parameters compared to Kerr theory. We find that gate operation is strongly dependent on the ratio of qubit-qubit detuning and anharmonicity. In particular, we characterize five distinct regions of operation, and propose candidate parameter choices for achieving high gate speed and low coherent gate error when the cross-resonance tone is equipped with an echo pulse sequence. Furthermore, we generalize our method to include a third spectator qubit and characterize possible detrimental multi-qubit frequency collisions.

中文翻译：

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互谐振门操作的第一性原理分析

我们对跨共振门操作进行了全面的理论研究，涵盖了门参数和门误差的估计以及分析观众的量子位和多量子位频率冲突。从约瑟夫森非线性开始，并考虑到本征态的重新归一化，由于反向旋转项，我们推导了具有改进的量子位-量子位相互作用和驱动矩阵元素的交叉共振门的新起始模型。利用与时间有关的Schrieffer-Wolff微扰理论，我们推导出了有效的哈密顿量用于交叉谐振门，并估算了驱动参数，直到驱动振幅达到四阶为止。与Kerr理论相比，具有重新归一化的本征态的新模型可对有效门参数进行10％到15％的相对校正。我们发现，门操作在很大程度上取决于量子位-量子位失谐和非谐波的比率。特别是，我们表征了五个不同的操作区域，并提出了在交叉谐振音调配备回波脉冲序列时实现高栅极速度和低相干栅极误差的候选参数选择。此外，我们将我们的方法概括为包括第三个观众量子位，并描述可能有害的多量子位频率冲突。