Quantum Error Correction: Theory and Experiment

在好奇心的驱使下，物理学家试图通过自然的性质来理解我们周围的世界。一旦我们有了一定的理解，我们开始能够预测具有这些性质的系统的行为，然后获得控制它们的能力。一旦实现控制，有时就有可能开发基于这些现象的技术。 其中一些不仅对我们的社会产生了深远的影响，它们还通过提供以不同规模或复杂性探索其他自然属性的能力，为这个循环的重复奠定了基础。回顾过去，火、蒸汽和电磁就是这些性质的例子。 展望未来，有许多迹象表明量子力学现象将发挥类似的作用。量子信息处理不仅为量子力学带来了新的见解，而且也为新技术带来了无与伦比的力量。这些技术的关键要求是对量子系统的精确控制。虽然物理学家在过去已经开发了一些控制方法并将其应用于一些量子系统，但它们是不可扩展的，即，随着量子比特数量的增加，所需的资源将呈指数增长。在20世纪90年代中期，随着量子纠错的发现，景观发生了巨大的变化。容错量子纠错是一种理论，只要错误率低于阈值，就允许对量子系统进行充分控制，以使用合理的资源解决问题。我的工作建立在这个理论（我帮助创建）的基础上，旨在将概念转化为实际实现。我在量子纠错方面的工作包括理论和实验研究。实现容错量子纠错需要四个元素：特定的编码，具有足够的控制，表征噪声的类型，以及提取损坏量子比特的熵。我的工作将有助于这四个领域，目标是展示多轮量子纠错，保护量子信息免受其自然噪声的影响。这项工作将包括开发新的代码，评估噪声的新方法，并使用它们尽可能多地改善量子控制，最后研究算法冷却方法，允许从一组损坏的量子比特中提取熵。我的工作将包括理论和实验研究。

Driven by curiosity, physicists try to understand the world around us through the properties of nature. Once we have a certain understanding, we begin to be able to predict the behavior of systems with these properties and then gain the ability to control them. Once control is achieved, it is sometimes possible to develop technologies based on these phenomena. Some of these not only have profound impact on our society, they also lay down the basis for this cycle to repeat itself by providing the ability to explore other natural properties at a different scale or complexity. Looking at the past, fire, steam and electro-magnetism are examples of these properties. Turning towards the future, there are many hints that quantum mechanical phenomena will play a similar role.******Quantum information processing promises not only new insight on quantum mechanics but also new technologies with unparalleled power. A critical requirement for these technologies is an exquisite control of quantum systems. Although physicists have developed some control methods and applied them to some quantum systems in the past, they were not scalable, i.e., as the number of quantum bits is increased the required resources would increase exponentially. In the mid-1990s the landscape changed dramatically with the discovery of quantum error correction. Fault-tolerant quantum error correction is a theory that allows for sufficient control of quantum systems to solve problems using reasonable resources, as long as the error rate is below a threshold. My work builds on this theory (that I have helped create) with an aim to turning concepts into practical implementations. My work in quantum error correction encompasses both theoretical and experimental investigations.******There are four elements needed to implement fault tolerant quantum error correction: a specific encoding, having sufficient control, characterizing the type of noise, and extracting entropy of corrupted qubits. My work will contribute to these four areas with the goal of demonstrating many rounds of quantum error correction that protects quantum information against its natural noise. The work will include developing new codes, new methods to assess the noise and use them to improve quantum control as much aas possible and finally work on algorithmic cooling a methods that allows to extract entropy from a set of corrupted qubits. My work will encompasses both theoretical and experimental investigations.**