Precise and efficient characterization of entangled multi-qubit quantum states and quantum gates with trapped ions

量子物理，特别是纠缠可以用于安全通信、精确测量、物理系统的有效模拟和快速量子算法。此外，纠缠是一个有趣的现象，因为它区分了量子世界和经典世界。迄今为止，研究纠缠最成功的物理系统是被捕获的原子离子。在本项目中，我们在理论和实验的密切合作下，开发了实验检测和表征多粒子纠缠量子态和多粒子量子门的方法。这些方法将应用于研究多部纠缠态和多量子位量子门，这些量子门是利用被困原子离子之间的磁梯度诱导耦合（MAGIC）实现的。MAGIC在多个离子之间创建远程耦合。它允许使用射频辐射实现多量子位量子门，并且不需要将捕获的离子冷却到其运动基态。对于量子信息的实验实现来说，高精度地重复进行状态制备、状态操纵（量子门）和状态检测是至关重要的。然而，量子态和门的有效表征仍然具有挑战性，因为大多数方法对于多粒子态需要大量的资源，或者只适用于特殊情况。我们将研究系统和统计误差如何影响实验量子门，并将开发有效的工具来表征这种门的性能。Toffoli门是量子算法的通用构建模块，将利用基于MAGIC的多量子位耦合进行实验实现，并将采用这些新方法进行表征。此外，我们将开发新的纠缠准则，可以有效地应用于实验。它们将用于首次实现的N个捕获离子（N在3到9之间）的纠缠加权图态的实验检测和表征。此外，超精细量子比特的状态选择检测将被研究。首先，完整的检测过程将被准确地描述，然后它将被数值模拟。最后，在理论与实验的密切互动中对其进行改进，以获得尽可能高的检测保真度。在这个项目中获得的见解将适用于量子信息科学中包含许多其他物理系统的许多其他实验。

Quantum physics and particularly entanglement may serve for secure communication, precise measurements, efficient simulations of physical systems and fast quantum algorithms. Furthermore, entanglement is an intriguing phenomenon, since it discriminates the quantum world from the classical world. To date the most successful physical system for investigating entanglement are trapped atomic ions. In this project we develop methods to experimentally detect and characterize multi-particle entangled quantum states and multi-particle quantum gates in a close cooperation between theory and experiment. These methods will be applied to investigate multipartite entangled states and multi-qubit quantum gates realized using magnetic gradient induced coupling (MAGIC) between trapped atomic ions. MAGIC creates long range coupling between multiple ions. It allows for the realization of multi-qubit quantum gates using radio frequency radiation and does not require cooling trapped ions to their motional ground state. For the experimental realization of quantum information it is crucial to reproducibly carry out state preparation, state manipulation (quantum gates), and state detection with high accuracy. However, the efficient characterization of quantum states and gates is still challenging because most of the methods require prohibitively large resources for many-particle states or are only applicable to special cases. We will investigate how systematic and statistical errors affect experimental quantum gates and will develop efficient tools to characterize the performance of such gates. Toffoli gates, universal building blocks for quantum algorithms, will be experimentally implemented taking advantage of multi-qubit coupling based on MAGIC and will be characterized employing these novel methods. In addition, we will develop new entanglement criteria that can be applied efficiently in an experiment. They will be used to experimentally detect and characterize entangled weighted graph states of N trapped ions (with N between 3 and 9) that will be realized for the first time. Furthermore, state selective detection of hyperfine qubits will be investigated. First the complete detection process will be described exactly and then it will be numerically simulated. Finally it will be improved in close interaction between theory and experiment to obtain the highest possible detection fidelity. The insight gained in this project will be applicable to numerous other experiments in quantum information science encompassing many other physical systems.