Purifying a high-temperature ensemble of quantum particles toward a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is active feedback, which stabilizes the system at a chosen target state. This alternative, if realized, offers additional control capabilities for the design of quantum states. Here we present a feedback algorithm applied to a quantum system, which is capable of stabilizing the collective state of an ensemble from its maximum entropy state to the limit of single quantum fluctuations. Our algorithmic approach maximizes the rate of state purification given the system’s physical constants; thus it remains the optimal feedback approach even in the presence of dissipation and disorder. We test experimentally the robustness of this feedback on the highly inhomogeneous nuclear-spin ensemble of a semiconductor quantum dot, reducing nuclear-spin fluctuations 83-fold, down to 5.7(2) spin macrostates. Simulations demonstrate that without system-specific inhomogeneities, our algorithm can purify the system down to single-spin fluctuations. Further, we exploit our algorithmic approach to tailor nontrivial nuclear-spin distributions that go beyond simple polarization, including weighted bimodality and latticed multistability. This control is a precursor toward quantum-correlated macrostates, which an extended version of our algorithm could generate in homogeneous systems.

中文翻译：

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通过量子算法反馈优化自旋系综

将高温量子粒子集合提纯到已知状态是利用量子多体效应的关键要求。将系统带入其基态的被动冷却的替代方法是主动反馈，它将系统稳定在选定的目标状态。如果实现这一替代方案，将为量子态的设计提供额外的控制能力。在这里，我们提出了一种应用于量子系统的反馈算法，该算法能够将集合的集体状态从其最大熵状态稳定到单量子涨落的极限。在给定系统物理常数的情况下，我们的算法方法可以最大限度地提高状态净化率；因此，即使存在耗散和无序，它仍然是最佳反馈方法。我们通过实验测试了这种反馈对半导体量子点的高度不均匀核自旋系综的鲁棒性，将核自旋波动减少了 83 倍，降至 5.7(2) 自旋宏观状态。模拟表明，没有系统特定的不均匀性，我们的算法可以将系统净化到单自旋波动。此外，我们利用我们的算法方法来定制超越简单极化的非平凡核自旋分布，包括加权双峰和晶格多稳定性。这种控制是量子相关宏观状态的前兆，我们算法的扩展版本可以在同构系统中生成。模拟表明，没有系统特定的不均匀性，我们的算法可以将系统净化到单自旋波动。此外，我们利用我们的算法方法来定制超越简单极化的非平凡核自旋分布，包括加权双峰和晶格多稳定性。这种控制是量子相关宏观状态的前兆，我们算法的扩展版本可以在同构系统中生成。模拟表明，没有系统特定的不均匀性，我们的算法可以将系统净化到单自旋波动。此外，我们利用我们的算法方法来定制超越简单极化的非平凡核自旋分布，包括加权双峰和晶格多稳定性。这种控制是量子相关宏观状态的前兆，我们算法的扩展版本可以在同构系统中生成。