Thermalisation and Controllability of Quantum Systems

在过去的十年里，我们看到了量子力学中重要的范式转变。尽管海森堡测不准原理以前被认为是一种基本噪声，但现在人们已经接受了量子力学的不确定性，以薛定谔猫为特征的例子，实际上可以非常有用地构建强大的量子计算机。尽管量子计算的基本理论已经相当发达，但该领域仍然缺乏对这些概念的实验证实。之所以很难进行实验，是因为我们试图将微小的量子物体与我们笨拙的宏观世界联系起来。在量子计算机上运行算法需要大量的控制--就像我们戴着拳击手套弹钢琴一样。我的研究是基于控制和噪声之间的关系。一般来说，控制意味着噪音，也就是对系统的干扰，但奇怪的是，我也发现噪音可以暗示控制！这些违反直觉的结果表明，更深入地了解量子力学噪声的基本形式对于构建量子计算机非常有用。在极端的情况下，我建议的方法是根本不需要外部控制，计算机就像机械时钟一样运行。所提出的研究主要涉及中间情形，其中在相关约束下最小化控制，并且以最优方式利用量子噪声。它的一个重要方面将是开发实验来测试这些概念，并在通往全量子计算机的道路上取得进展。另一个关键点将是从信息论的角度加深对噪声和量子系统弛豫的理解。虽然每个人都对温度意味着什么以及如何量化能量有一个基本的概念，但事实证明，在量子力学层面上，这些概念不再是明确定义的。我的研究将通过开发玩具模型和思维实验来澄清这些问题，从而为这一主题做出贡献。

Over the last decade we have seen an important paradigm shift in Quantum Mechanics. Whereas formerly the Heisenberg uncertainty principle was regarded as type of fundamental noise, it has now been accepted that the indecisiveness of Quantum Mechanics, with Schrdingers cat as a characteristic example, can actually be very useful to build powerful Quantum Computers.While the fundamental theory of Quantum Computation is quite developed, the field still lacks experimental confirmation of these concepts. The reason why it is so hard to perform experiments is that we are trying to connect the tiny quantum objects to our clumsy macroscopic world. One requires a large amount of control to run an algorithm on a Quantum Computer - it is as if we were playing piano with boxing gloves.My research is based on the relationship between control and noise. Generally control implies noise, i.e. the disturbance of the system, but strangly I have also found that noise can imply control! These counterintuitive results show that a deeper understanding of the fundamental forms of quantum mechanical noise is very useful to build a Quantum Computer. In the extrem case, I suggest methods where no external control is required at all, and the computer just runs like a mechanical clockwork. The proposed research is mostly concerned with the intermediate case, where the control is minimised under the relevant constraints, and the quantum noise is made use of in an optimal manner. One important aspect of it will be to develop experiments to test these concepts and to progress on the path to a full quantum computer. Another vital point will be to deepen the understanding of noise and of the relaxation of quantum systems from an information theory point of view. While everyone has a basic idea of what temperature means and how quantify energy, it turns out that on a quantum mechanical level these concepts are no longer well-defined. My research will contribute to this topic by developing toy-models and thought experiments to clarify such problems.