Universal resources for quantum information processing over continuous variables

我们知道经典系统可以计算，我们每天都在我们的现代电子设备中利用这一点，在现代电子设备中，经典比特信息被常规处理。类似的计算也可以在量子水平上发生：电子、光子和量子系统通常可以存储和处理信息的量子比特(Qubit)。非同寻常的事实是，量子系统可以以无与伦比的方式进行计算，比它们的经典系统要好得多，从而对我们的技术产生革命性的影响。为了使这一承诺成为现实，有必要识别能够支持量子信息处理的可控物理系统。量子信息的大部分概念最初是为有限维系统(量子比特)而发展的。然而，人们很快意识到，无限维系统--行话中的连续变量--也提供了一个有效和有前途的替代方案，最熟悉的例子是量子化谐振子的位置和动量。这个博士项目将处理后一种方法，探索连续变量系统为量子信息处理提供的可能性。在连续变量上完全(通用)的量子信息处理只有在单个非线性运算也可用的情况下，才能用所谓的线性运算来实现。虽然线性运算已经在实验上和理论上得到了充分的证明，但关于基本的非线性运算的研究却少得多。在这种情况下，博士项目将致力于从理论上彻底理解目前和不久的将来实验中可用的弱非线性运算，特别是它们如何用于连续变量系统上的量子信息技术。该项目将包括三个部分。第一部分的重点将是使用量子资源理论的创新理论方法来表征非线性。后者是一个强大的数学框架，最近已被应用于量子信息的各种背景下，包括最近连续的变量。在方案的第二部分，将调查在技术上开始实现非线性的物理环境(例如用于量子光学和光力学的超导电路)，目的是提出项目第一部分的结论的实际执行情况。第三部分涉及非线性在新兴的量子机器学习领域的应用，目的是开发策略来构建量子设备(特别是量子多模光系统)，以模仿经典神经网络在标准机器学习算法中的作用--例如用于图像识别的算法。学生将全面参与本项目所有部分的开发，从开发关于量子资源理论方法的背景理论知识到开发连续变量的量子机器学习方法。该项目的发现将有助于EPSRC量子技术主题的研究，特别是量子计算和量子光学。

We know that classical systems can compute, and we exploit this everyday in our modern electrical devices where classical bits of information are routinely processed. A similar computation can happen at the quantum level as well: electrons, photons, and quantum systems in general can store and process quantum bits (qubits) of information. The extraordinary fact is that quantum systems can compute in an unparalleled way, much better than their classical counterpart, with a consequent revolutionary impact for our technologies. To make this promise a reality, it is necessary to identify controllable physical systems able to support the processing of quantum information. Most of the concepts of quantum information were originally developed for finite dimensional systems (qubits). However it was soon realised that a valid and promising alternative is offered also by infinite dimensional systems -- continuous variables in jargon -- the most familiar examples being position and momentum of a quantised harmonic oscillator. This Ph.D. programme will deal with the latter approach, exploring the possibilities offered by continuous-variable systems for quantum information processing.Fully-fledged (universal) quantum information processing over continuous variables is achievable with so-called linear operations only provided that a single non-linear operation is also available. Whereas linear operations have been both demonstrated experimentally and fully characterised theoretically, much less has been achieved for what concerns the essential non-linear operations. In this context, the Ph.D. programme will aim at developing a thorough theoretical understanding of the weak non-linear operations available experimentally nowadays and in the near future, and in particular how they can be used for quantum information technologies over continuous-variable systems.The project will comprise three parts. The focus of the first part will be the characterisation of non-linearities using the innovative theoretical approach of quantum resource theories. The latter is a powerful mathematical framework that has been recently applied to a variety of contexts in quantum information, including recently continuous variables. In the second part of the programme, the physical settings in which non-linearities are starting to become technologically achievable (such as superconducting circuits for quantum optics and opto-mechanics) will be investigated with the aim of proposing actual implementations of the findings of the first part of the project. The third part concerns applications of non-linearities to the emergent field of quantum machine learning, with the aim of developing strategies to build quantum devices (in particular, quantum multi-mode systems of light) that mimic the role of classical neural networks in the standard machine-learning algorithms -- used for example in the context of image recognition. The student will be fully involved in the development of all the parts of this project, starting from the development of a background theoretical knowledge about the methods of quantum resource theories to the development of continuous-variable approaches to quantum machine-learning. The findings of this project will contribute to the research on the EPSRC theme of quantum technologies, with specific focus on quantum computing and quantum optics.