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

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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".