基于核磁共振体系的开放量子系统中量子精密测量的实验研究

基于量子资源（例如相干、纠缠、压缩等）及其调控技术的量子精密测量有 望超越经典技术极限，以更高的精确度、灵敏度和/或空间分辨率等实现对物理量 的感知和度量。借助这些优势，量子精密测量在基础科学研究和实际应用领域都 展现出巨大的潜力。然而，在量子精密测量中起着关键作用的量子探针态对外界 环境极为敏感，导致在开放量子系统中测量精度难以达到海森堡极限（Heisenberg limit, HL）。鉴于实际的量子体系必然处于开放系统中，研究如何在开放量子系统 中接近甚至达到 HL，成为量子精密测量领域的重要内容及巨大挑战。其中存在一 些关键性问题，例如：在开放量子系统中，量子资源在测量中的优势是否依旧存在？若存在，其可能达到的精度极限是多少？我们能否通过量子控制等方法来提 升开放量子系统中的测量精度，使之逼近 HL？以及在真实噪声条件下，最大纠缠 态是否依旧是最优的探针态？如何制备最优探针态？本文将针对以上问题进行实 验研究。 首先，我们实验研究了最大纠缠态在非马尔可夫纯退相位噪声下的测量精度 极限。结果表明，尽管其测量精度极限无法达到 HL，却成功超越了标准量子极限 （standard quantum limit），达到了量子芝诺效应（quantum Zeno effect, QZE）极限。 然而，非马尔可夫纯退相位噪声难以从更加复杂的噪声机制中单独区分出来，我们 为此开发了一种噪声调控技术，它可以精确地模拟非马尔可夫纯退相位噪声。在 核磁共振（nuclear magnetic resonance, NMR）体系中，我们制备了二到七个量子比 特的最大纠缠态作为探针，通过利用体系在非马尔可夫噪声下的 QZE，最大纠缠 探针态能够提升测量精度达到 QZE 极限。这与理论预测一致，并且展示了非马尔 可夫噪声下量子精密测量的效率和潜力。

随后，我们利用量子控制来提升非马尔可夫环境中的测量精度极限，使其尽 可能的逼近 HL。常见的两种非马尔可夫噪声的描述方式可以分为噪声信道和噪声 谱。我们针对这两种描述方式设计了对应的控制增强的量子精密测量方案。在多 量子比特 NMR 量子处理器中验证了这些方案的有效性。结果表明，我们的方案可 以大幅提高参数估计的精度，使其接近 HL。

考虑到真实实验环境中噪声机制的复杂性，我们进一步研究了真实实验中的 量子精密测量。首次在实验上表明，真实实验体系中存在比最大纠缠态更有效的 量子探针态。在实验中，我们提出了一种新的协议，将高效的探针性能评估策略与闭环线路学习相结合。在七比特的 NMR 量子处理器上，我们成功搜寻到了一种 在该开放量子系统中可替代最大纠缠态的最优探针态。通过与传统的探针为最大 纠缠态的量子精密测量协议相比较，我们的协议在提升测量性能方面展现了显著 优势。本研究所提出的协议不仅具有良好的可扩展性，而且特别适用于利用量子 优势来执行的短期传感任务，为量子精密测量技术在实际应用场景中的推广提供 了强有力的支持。

综上所述，本论文通过一系列开放量子系统的量子精密测量实验，探索了在 实际量子精密测量场景中实现量子优势的可行性。我们通过结合多种量子控制技 术，成功地在开放量子系统中提升了测量精度，使之逼近理论上的 HL。这些成果 为量子精密测量在实际场景中的广泛应用开辟了道路，体现了在真实环境下利用 量子优势进行精确测量的可能性和有效性。

Quantum metrology, which utilizes quantum resources (such as coherence, entanglement, squeezing, etc.) and their control technologies, is expected to exceed the limit of classical metrology, achieving higher precision, sensitivity and/or spatial resolution in the sensing and measurement of various physical quantities.

Leveraging these advantages, quantum metrology exhibits tremendous potential in both fundamental scientific research and practical application fields. However, the quantum probe states in quantum metrology are extremely sensitive to external environments. This leads to difficulties in achieving the Heisenberg limit (HL) of measurement precision in open quantum systems. Given that practical quantum systems inevitably operate within open systems, approaching or even reaching the HL in open quantum systems has become a significant challenge for quantum metrology. There are some critical issues, for example: In open quantum systems, does the advantage of quantum resources in measurement still exist? If so, what is the precision limit? Can we enhance the measurement precision in open quantum systems through quantum control and other methods to approach the HL? And in real experimental systems, is the maximally entangled state still the optimal probe? How to prepare the optimal probe? This thesis conducts experimental researches on the aforementioned issues.

Firstly, we conduct an experimental study on the measurement precision limit of maximally entangled states in non-Markovian pure dephasing noise. The results indicate that although the precision limit of these measurements cannot reach the HL, they successfully exceed the standard quantum limit and reach the limit of the quantum Zeno effect (QZE). However, non-Markovian pure dephasing noise is difficult to distinguish from more complex noises separately. We develop a noise control technology that can accurately simulate pure dephasing noise in a nuclear magnetic resonance (NMR) system. In the experiments, we prepare maximally entangled states of up to seven qubits and studied the dynamical behavior in non-Markovian pure dephasing noise. The results showed that by utilizing the QZE in the system under non-Markovian noise, the maximally entangled states could enhance measurement precision, reaching the QZE limit. This is consistent with theoretical predictions and demonstrates the efficiency and potential of quantum metrology in non-Markovian noise.

Subsequently, we utilize quantum control to enhance the measurement precision limit in non-Markovian environments, aiming to approach the HL. The common descriptions of non-Markovian noise include noise channels and noise spectrum. We design corresponding control-enhanced quantum metrology schemes for these two descriptions and experimentally validate their effectiveness in multi-qubit NMR quantum processors. The results indicate that our schemes can significantly improve the precision of measurement, approaching the HL. Considering the complexity of noise mechanisms in experimental environments, we conduct a profound study on quantum metrology in real conditions. This is the first experimental demonstration showing the existence of quantum probe states in real systems, which are more efficient than maximally entangled states. In the experiment, we introduced a new protocol that combines efficient probe performance evaluation strategies with closed-loop circuit learning. On a seven-qubit NMR quantum processor, we successfully find an optimal probe state that can replace the maximally entangled state in open quantum systems. Compared with traditional quantum metrology protocols using maximally entangled states, our protocol demonstrates significant advantages in enhancing measurement performance. The protocol proposed in this study not only exhibits good scalability but is also particularly suitable for short-term sensing tasks using quantum advantages, providing strong support for the widespread application of quantum metrology techniques in practical scenarios. In summary, through a series of quantum metrology experiments in open quantum systems, this paper explores the feasibility of achieving quantum advantages in real quantum metrology scenarios. By combining various quantum control techniques, we successfully enhance measurement precision in open quantum systems, approaching the theoretical HL. These achievements bring the opportunities for the broad application of quantum metrology in practical scenarios, showcasing the potential and effectiveness of precise measurement using quantum advantages in real experimental systems.

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