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

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".

* Academic impact

As detailed in the "Case for support", the research will tackle the issue of reliable scalability of quantum computation (namely, the necessity of identifying a feasible approach that permits coherent and universal operations among a large number of quanta). This issue was recognised as the main obstacle to quantum computation since the very beginning of quantum information science. Thanks to recent breakthroughs, the quantum systems considered in this proposal are among the first promising to overcome this obstacle. Thus, the theoretical investigations here proposed will enhance the UK competitiveness in this promising context -- with the ultimate vision of bringing quantum computation over continuous variables into the realm of actual and scalable applications. The benefits of this for the physics community will be of great value, thus increasing the attractiveness of UK for researchers.

For more details on the academic impact see also the "Academic Beneficiaries" Annex and the "Academic Impact" section of the "Case for Support" document.

* Economic and societal impacts

By tackling some of the most relevant questions of quantum science, the proposed investigations will contribute to the UK culture at all levels as computer technologies becomes integral to all aspects of life. Also, the project has the potential to increase the general awareness and understanding of science, with a benefit for the wider public in the short term. In particular, quantum-information science exploits many fundamental aspects of quantum mechanics that fascinate the general public. This is true in particular for quantum computers, the central topic of my project. As detailed in the "Pathways to Impact" annex, I will be directly involved in this engaging process.

Besides the cultural impact, the research I planned has immense potential to contribute to UK wealth and health, twofold. On one hand, my project will foster the research on novel quantum technologies. In the long term, mastering these technologies will provide a key resource for future economic paths, thus increasing the economic competitiveness of the UK in general and its high-tech companies in particular. On the other hand, the "vision" that guides this project (that is, to obtain scalable and feasible schemes for quantum computation) is potentially of the highest transformative impact for the society as a whole. In fact, the implementation of quantum computers would allow for the processing of unprecedented amounts of information. This would permit the realisation of tasks that are inaccessible to current technologies and that indeed could remain inaccessible also in the future (unless a change in the paradigm of information processing, such as the one pursued by the quantum information community takes place). Once mastered in the laboratory, quantum computers could open unprecedented opportunities also for other researchers e.g., material scientists and chemists, and ultimately revolutionise material and drug design. The societal impact in this case will be the highest.