Optimal control for robust ion trap quantum logic

遵循量子力学定律的微小物体比受牛顿经典力学定律约束的宏观物体更有希望完成复杂的任务。叠加原理允许单个量子力学对象平行地遵循多个轨迹，并且这些对象的成对（或更大的集合）可以相互纠缠，这样对一个对象的测量就会影响其他对象的属性，即使它们相距很远。叠加原理和纠缠为精密计量或量子计算等应用提供了基础，这些应用有望彻底改变我们的技术，就像蒸汽机或电力的出现在过去所做的那样。然而，要明确利用这些量子力学效应进行有用的应用，就需要对量子物体及其与周围环境的相互作用进行极其精确的控制。在这种情况下，捕获离子是主要的系统之一。离子的选定能级定义了量子位，量子位是量子计算机的基本单位，就像经典计算机由许多位组成一样。受电场和磁场捕获场的限制，离子可以用激光束操纵，离子串的集体运动使几个量子位之间的信息交换成为可能。为了高精度地工作，通常需要将离子冷却到接近绝对零度的温度。一旦达到这样的温度，人们就可以利用离子的任何操作都会改变它们的运动状态这一事实，从而实现定义量子算法基本构建块的逻辑运算。由于离子的运动很容易被其室温环境加热，因此有意诱导的运动状态变化可以伴随着不受控制的加热过程，并且任何偏离运动状态的期望变化都会导致正在实施的操作的准确性降低。本项目的目标是开发和实验实现激光控制捕获离子，在存在不期望的加热和其他实验缺陷的情况下，以高精度和鲁棒性实现所需的操作。在理论和实验之间的紧密合作中，控制序列将在一种新型离子阱中开发和测试，其参数可以在很大范围内变化。调整量子比特与运动之间相互作用强度（Lamb-Dicke参数）和热效应强度的能力，将使我们能够确定以理想方式处理每种不完美类型的控制策略。目前的大多数实验都是在量子比特和运动之间相当弱的相互作用下进行的，但我们的目标是实现与运动强烈相互作用的量子比特之间的逻辑运算。随着强交互而增加的操作速度增加了可以在有限退相干时间限制内实现的逻辑操作的数量，因此将帮助我们从原理证明实验转向实际应用。我们工作的直接目标是改善量子计算中捕获离子的控制，但我们将开发的先进控制技术直接适用于任何类型的捕获离子的相干操作。由于量子位之间的强相互作用有利于快速信息传输，但对于在本质上任何量子系统中实现精确操作具有挑战性，因此预计将开发的控制技术将在量子光学和量子电子学的广泛其他系统中找到应用。

Minuscule objects that follow the laws of quantum mechanics have the promise of carrying out delicate tasks fundamentally better than macroscopic objects that are bound by the laws of Newtonian classical mechanics. The superposition principle permits individual quantum mechanical objects to follow multiple trajectories in parallel, and pairs (or larger collections) of such objects can be entangled with each other, such that a measurement on one object affects the properties of the other objects even if they are far apart. The superposition principle and entanglement provide the basis for applications like precision metrology or quantum computation that are expected to revolutionise our technology, just like the steam engine or the advent of electricity has done in the past.The explicit utilisation of these quantum mechanical effects for useful applications, however, requires extremely accurate control over quantum objects and their interaction with their surroundings. Trapped ions are one of the leading systems in this context. Selected energy levels of an ion define a qubit, which is the elementary unit of a quantum computer, just like a classical computer is comprised of many bits. Confined by electric and magnetic trapping fields, ions can be manipulated with laser beams, and the collective motion of strings of ions enables the exchange of information between several qubits. For this to work with high accuracy it is typically required to cool the ions to a temperature close to absolute zero. Once such a temperature has been reached, one makes use of the fact that any manipulation of the ions changes their motional state in order to implement logical operations that define the elementary building blocks of a quantum algorithm.Since the ions' motion is easily heated by its room-temperature environment, the intentionally induced changes in the motional state can be accompanied by uncontrolled heating processes, and any deviation from the desired change in motional state results in reduced accuracy of the operations being implemented. The goal of the present project is the development and experimental implementation of laser control of trapped ions that achieves desired operations with high accuracy and robustness in the presence of undesired heating and other experimental imperfections.In a strong collaboration between theory and experiment, control sequences will be developed and tested in a novel ion trap whose parameters can be varied over a wide range. The ability to tune the strength of the interaction between qubits and motion (the Lamb-Dicke parameter) and the strength of thermal effects will allow us to identify the control strategies that deal with each type of imperfection in an ideal fashion. Most current experiments are conducted with a rather weak interaction between qubits and motion, but we aim at the realisation of logical operations between qubits that interact strongly with the motion. The increased manipulation speed that comes with the strong interaction increases the number of logical operations that can be implemented within the limits imposed by finite decoherence time, and as such will help us to move from proof-of-principle experiments to a practical application.The immediate goal of our work is the improvement in the control of trapped ions for quantum computing, but the advanced control techniques we will develop directly apply to any type of coherent manipulation of trapped ions. Since strong interactions between qubits are beneficial for fast information transfer but challenging for the implementation of accurate manipulations in essentially any quantum system, the control techniques to be developed are expected to find application in a broad range of other systems in quantum optics and quantum electronics.