AI 中文总结
研究半导体自旋量子比特中核自旋噪声的缓慢漂移，扩展簇相关展开技术并结合量子与经典方法，通过多种实验数据验证，证明反作用效应，定量预测补偿奥弗豪泽场缓慢漂移的益处，可显著提升有效\(T_2^*\)。
AI 中文摘要
核自旋浴的动力学产生磁噪声，这是静电定义量子点中电子自旋量子比特退相干的关键因素。本文扩展了簇相关展开（CCE）技术，该技术虽能预测不同设置下固态量子比特的相干时间，但限于较短时间尺度。我们将其扩展以纳入簇动力学的随机处理，从而能在更长时间尺度上有效预测缓慢漂移的奥弗豪泽场。此方法结合量子演化与经典速率矩阵，可在广泛时间范围内模拟，如从拉姆齐实验的遍历性\(T_2^*\)的长时间收敛。我们的方法通过多种硅自旋量子比特系统的实验数据验证，展示了模拟与测量在\(T_2^*\)与平均时间、自相关函数以及功率谱密度形式的拉姆齐实验中的高度一致性。此外，通过建模和实验证明了显著的反作用效应，即核自旋浴的动力学取决于电子自旋占据时间表。最后，我们的建模定量预测了在量子比特操作中补偿奥弗豪泽场缓慢漂移的益处。研究结果表明，在某些感兴趣的场景下，补偿过去测量的奥弗豪泽旋转\(\Delta t\)导致的有效\(T_2^*\)（为清晰起见记为\(\tilde{T}_2^*(\Delta t)\)），如果每100毫秒重新表征奥弗豪泽旋转，可比遍历性\(T_2^*\)大一个或两个数量级；即\(\tilde{T}_2^*(\Delta t = 100~{\rm ms})\)可比\(T_2^*\)大10到100倍。
英文摘要
The dynamics of a nuclear spin bath generates magnetic noise that is a key contributor to the decoherence of electron spin qubits in electrostatically-defined quantum dots. In this paper, we extend the cluster correlation expansion (CCE) technique, which has proven useful for predicting solid-state qubit coherence times across various settings but is limited to shorter time scales, to incorporate stochastic treatments of cluster dynamics in order to efficiently predict slow drifting Overhauser fields over longer time scales. This approach combines quantum evolution with classical rate matrices to enable simulation across a wide range of temporal regimes required to simulate, for example, the long-time convergence of the ergodic $T_2^*$ from Ramsey experiments. Our methodology is validated against experimental data from various silicon spin qubit systems, demonstrating a strong agreement between simulation and measurement of Ramsey experiments presented in the form of $T_2^*$ versus averaging time, autocorrelation functions, as well as power spectral densities. Furthermore, we demonstrate significant back-action effects through modeling and experiment; specifically, the dynamics of the nuclear spin bath depends upon the electron spin occupation schedule. Finally, our modeling quantitatively predicts the benefits from compensating for the slow drift of Overhauser fields in qubit operations. Our findings indicate that compensating for an Overhauser rotation measured $Δt$ in the past results in an effective $T_2^*$, which we denote $\tilde{T}_2^*(Δt)$ for clarity, under certain scenarios of interest, can be one or two orders of magnitude larger than the ergodic $T_2^*$ if the Overhauser rotation is re-characterized every 100 milliseconds; that is, $\tilde{T}_2^*(Δt = 100~{\rm ms})$ can be $10$ to $100$ times larger than $T_2^*$.
