Optimal control for robust ion trap quantum logic

与受牛顿经典力学定律约束的宏观物体相比，遵循量子力学定律的微小物体有望从根本上更好地执行精细任务。叠加原理允许单个量子力学物体平行地沿着多个轨迹运动，这样的物体对(或更大的集合)可以相互纠缠，这样一个物体上的测量会影响其他物体的性质，即使它们相距很远。叠加原理和纠缠为精密计量学或量子计算等应用提供了基础，这些应用有望像蒸汽机或电的出现一样改变我们的技术。然而，要明确地将这些量子力学效应用于有用的应用，需要对量子对象及其与周围环境的相互作用进行极其精确的控制。囚禁离子是这方面的主要系统之一。离子的选定能级定义了量子比特，量子比特是量子计算机的基本单位，就像经典计算机由许多比特组成一样。在电场和磁场的限制下，离子可以被激光操控，离子串的集体运动使几个量子比特之间能够交换信息。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，人们就会利用这样一个事实，即任何对离子的操作都会改变它们的运动状态，以实现定义量子算法基本构件的逻辑运算。由于离子的运动很容易被其室温环境加热，因此有意引起的运动状态的变化可能伴随着不受控制的加热过程，而任何对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对囚禁离子的激光控制，在存在不需要的加热和其他实验缺陷的情况下，以高精度和稳健性实现预期的操作。在理论和实验的紧密合作中，将在一种新型的离子陷阱中开发和测试控制序列，该离子陷阱的参数可以在很大范围内变化。能够调节量子比特和运动之间相互作用的强度(Lamb-Dicke参数)和热效应的强度，将使我们能够确定以理想方式处理每种类型缺陷的控制策略。目前的大多数实验都是在量子比特和运动之间的相互作用相当弱的情况下进行的，但我们的目标是实现量子比特之间的逻辑运算，这些量子比特与运动相互作用很强。强相互作用带来的操作速度的提高增加了在有限退相干时间施加的限制内可以执行的逻辑运算的数量，因此将帮助我们从证明原理的实验转向实际应用。我们工作的直接目标是改进用于量子计算的囚禁离子的控制，但我们将开发的先进控制技术直接适用于任何类型的囚禁离子的相干操控。由于量子比特之间的强相互作用有利于快速的信息传输，但对实现几乎任何量子系统的精确操作都具有挑战性，因此，即将开发的控制技术有望在量子光学和量子电子学的其他广泛系统中得到应用。

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.