论文标题
跨谐门操作的第一原理分析
First-principles analysis of cross-resonance gate operation
论文作者
论文摘要
我们提出了一项综合的理论研究，涵盖了栅极参数和门误差的估计以及分析观众矩阵和多数频率碰撞的估计。我们首先重新审视Magesan等人之后的有效哈密顿模型的推导。 （Arxiv：1804.04073）。 Transmon Qubits通常被建模为弱的Anharmonic Kerr振荡器。 Kerr理论仅考虑量子频率的重归化，而采用数字状态为裸量子汉密尔顿的特征状态。从约瑟夫森的非线性开始，并通过对征量术语进行考虑，由于反向旋转术语，我们为具有修改的Qubit-qubit-qubit交互和驱动矩阵元素的跨谐振门提供了一个新的起始模型。采用时间依赖性的Schrieffer-Wolff扰动理论，我们为交叉谐音门提供了有效的哈密顿量，其估计的栅极参数计算出的驱动振幅中的第四阶。与KERR理论相比，具有重新归一化征收特征状态的新模型导致有效门参数的相对校正10-15％。我们发现，栅极操作很大程度上取决于Qubit Qubit的失沟和非谐度的比率。特别是，我们表征了五个不同的操作区域，并提出了候选参数选择，以实现高门速度和低相干栅极误差，当时交叉共振音调配备了回声脉冲序列。此外，我们将方法推广到包括第三个观众固定量，并表征可能有害的多Quit频率碰撞。
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. We start by revisiting the derivation of effective Hamiltonian models following Magesan et al. (arXiv:1804.04073). Transmon qubits are commonly modeled as a weakly anharmonic Kerr oscillator. Kerr theory only accounts for qubit frequency renormalization, while adopting number states as the eigenstates of the bare qubit Hamiltonian. 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.
