Non-linearity as a universal resource for quantum computation over continuous variables

量子力学是一门“不容易”的科学分支。它超越了我们日常的直觉，也挑战了我们目前对物质世界的理解。但尽管如此，量子力学还是有很多东西可以提供。我们知道经典系统可以计算，我们在日常生活中经常利用这一点：每天在我们的计算机，移动的手机和其他设备的经典电路中存储和处理大量信息。类似的计算可以发生在量子层面：电子、光子和基本粒子可以存储信息的“量子比特”，当它们相互作用时，这些量子比特可以被处理。令人兴奋的事实是，量子系统可以以一种非凡的方式进行计算，比我们现在正在学习的经典对应物要好得多。通过“破解”模糊量子世界的计算能力，我们可以建造量子计算机，以无与伦比的水平存储和处理信息。如今可能会让我们的普通计算机不知所措多年的问题，可以在眨眼之间被这些非凡的量子机器解决。这场“量子信息”革命的影响将是巨大的，深入到我们生活的每个角落。从无条件安全的通信到复杂的材料和药物工程建模，存在着大量的可能性。为了使其成为现实，有必要在自然界存在的众多量子系统中识别出那些可以控制的系统，从而为量子信息处理提供物理支持。但是大自然似乎嫉妒她的秘密--到目前为止还没有确定的领先者。这种令人兴奋的探索是我的项目的主要动机。关于“量子比特”的替代方法由所谓的“量子模式”给出。前者是只能呈现两种状态的量子系统（就像光的两种偏振态），而后者可以跨越更多的状态（可能是无限的，类似于光可以呈现的无限颜色梯度）。从历史上看，技术障碍阻碍了控制足够大的量子模式，以真正利用量子世界的计算能力。然而，关键的实验突破正在迅速改变这一局面：2011年，科学家们最多只能控制10种模式，而目前已经驯服了数千种模式！受此启发，我的提案的主要目标是设计适合这些技术的新型通用门，最终愿景是释放量子信息的全部力量。我还将评估这些门对近似误差在现实的实验平台，并介绍一个通用的框架来评估其performance.As它的设想，我的建议将在量子信息科学的前沿，它将有助于英国和世界各地的努力，发展非凡的量子机器，提供下一个“量子革命”。

Quantum mechanics is an "uneasy" branch of science. It is beyond our daily intuition and defies current comprehension of the physical world. But despite this, quantum mechanics has much to offer. We know that classical systems can compute, we exploit this routinely in our day-to-day life: a huge amount of information is stored and processed everyday in the classical electrical circuits of our computers, mobile phones and other devices. A similar computation can happen at the quantum level: electrons, photons, and elementary particles can store "quantum bits" of information, and when they interact those quantum bits can be processed. The exciting fact is that quantum systems can compute in an extraordinary way, much better than their classical counterpart as we are now learning. By "hacking" the computational power of the blurry quantum world, we can build quantum computers which store and process information at an unparalleled level. Problems that nowadays might overwhelm our ordinary computers for years could be solved in the blink of an eye by these extraordinary quantum machines. The impact of this "quantum information" revolution will be huge, reaching into every corner of our lives. From unconditionally secure communication to complex modelling for material and drug engineering-there is a huge number of possibilities.In order to make this a reality, it is necessary to identify, among the many quantum systems present in Nature, those that can be controlled thus providing the physical support for quantum information processing. But Nature seems jealous of her secrets -there is no definitive front-runner identified to-date. This exciting search is the main motivation of my project. An alternative approach with respect to "quantum bits" is given by so called "quantum modes". Whereas the former are quantum systems that can assume two states only (like two polarisation states of light), the latter can span over many more states (potentially infinite, similar to the infinite gradient of colours that light can assume). Historically, technological obstacles precluded control a number of quantum modes large enough to really exploit the computational power of the quantum world. However, crucial experimental breakthroughs are rapidly changing this scenario: in 2011 scientists were able to control only 10 modes at most, currently thousands be tamed! Inspired by this, the main objective of my proposal is to devise novel universal gates suited for these technologies, with the ultimate vision of unleashing the full power of quantum information. I will also assess these gates against approximation errors in realistic experimental platforms and introduce a general framework to evaluate their performances.As it is conceived, my proposal will be at the forefront of quantum information science and it will contribute to the UK and indeed worldwide effort to develop extraordinary quantum machines to deliver the next "quantum revolution".