金刚石氮-空位色心电子-核自旋体系的鲁棒量子优化控制研究

近年来，量子科技因其重要而广泛的应用前景而受到人们极大的关注。金刚 石 NV 色心体系在室温下具有良好的物理性质和相干时间，这使它成为优秀的量 子信息物理载体之一。然而，想把基于 NV 色心体系的量子技术推向实际应用，还 存在一系列挑战。其中，如何在 NV 色心体系中实现高精度高鲁棒性的量子控制， 是实现其应用的关键。跟其它量子体系一样，作为真实的物理平台，各种噪声是无 法避免的，例如体系自身的自旋晶格弛豫、失谐、Rabi 误差、脉冲有限带宽引起 的误差等等。这给高精度的量子控制带来难题。想解决这些难题，除了硬件层面 上良好制备的样品和噪声尽可能低的实验平台外，操控层面基于量子控制论的理 论方法和优化技术来优化降低各种噪声的影响也是非常关键的。鲁棒性量子优化 控制作为一种实用的脉冲搜索理论，提供了一个在含有噪声时依然能保证脉冲性 能的方案。相比于其它传统的鲁棒性脉冲技术，它具有鲁棒性区域大而平滑，能 同时抵抗多种噪声等优势。本文中，我们详细介绍了量子优化控制的理论细节和 多个典型鲁棒性控制方法，以及 NV 色心体系的哈密顿量、操控、初始化与读取、 拓展性和退相干等基本知识。随后我们介绍了鲁棒性量子优化控制框架，并在单 比特的鲁棒性量子门问题上初步展示该方法的优势。最后我们将鲁棒性量子优化 控制应用到 NV 色心中的两个重要的控制问题:核自旋的间接控制和动态核极化， 分别提出了两者的鲁棒性优化方案。我们通过数值计算搜索了能同时抵抗 Rabi 误 差和失谐两种静态噪声的控制脉冲，并模拟了脉冲对噪声的抵抗性能。结果表明， 鲁棒性优化的间接控制和动态核极化相对于传统的组合脉冲方案拥有更好的鲁棒性。

Quantum science and technology have received significant attention for their essen- tial and widespread applications in recent years. Nitrogen-vacancy (NV) color centers in diamond possess excellent physical properties and long coherence time at room tempera- ture, thus constituting a unique system for experimental quantum research. However, it is challenging in bringing this system to practical applications. One important challenge is to achieve high accuracy quantum engineering of the NV color centers. In reality, there unavoidably exist various types of errors, such as spin-lattice relaxation, detuning effects, Rabi inaccuracy, pulse imperfection, etc. Apart from preparing good samples and lower- ing experimental noise level through hardware layer efforts, it is also crucial to develop roust quantum control methods and optimization techniques to reduce noise effects. Ro- bust quantum optimal control is such a pulse design and optimization framework which can be very effective in providing high robustness pulses. Compared to other conventional robust pulse techniques, it has the advantages of a large and smooth robustness region and the ability to resist multiple noise channels simultaneously. In this thesis, we first intro- duce quantum optimal control theory and several typical robust quantum control methods. then we introduce the basic knowledge of NV color center system, including Hamiltonian, manipulation, initialization and read out, expansibility and decoherence. Subsequently we introduce the robust quantum optimal control framework, and preliminarily show the ad- vantages of this method on the robust quantum control of single qubit.Finally, we apply robust quantum optimal control to two important and practical control problems in NV color center in diamond system:indirect control of nuclear spins and dynamic nuclear po- larization. We numerically search control pulses that can resist static Rabi imperfection and detuning noise and simulate their robustness performance. The results indicate that the robustness-optimized indirect control and dynamic nuclear polarization control sequence show better robustness than the conventional schemes such as those use composite pulses.

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