Polariton and circuit QED lattices: solid-state platforms for quantum simulations of correlated and topological states

Quantum simulation-where one quantum system is emulated by another quantum system-is one of the pillars of modern quantum technologies, potentially allowing for the study of processes inaccessible to a classical computer, and even processes that do not occur in nature. In contrast to a universal quantum computer that theoretically allows for the implementation of any quantum mechanical dynamical process, powerful "quantum simulators" can be tailor-made to probe a specific class of physics problems. Quantum systems incorporating a combination of drive and dissipation- processes where energy is pumped into the system and allowed to disperse into the surrounding environment-is one such class of problems, exhibiting rich physical phenomena that is substantially more difficult to model compared to a perfectly isolated system, thus necessitating the existence of a functional quantum simulator. The aim of this PhD is to further develop and apply classical numerical methods to aid in the understanding of many-body quantum physics with drive and dissipation, as a step toward the practical realisation of useful quantum simulator. The physical systems we look at-those based on quantum mechanical objects constructed form a combination of light and matter-are particularly suited as platforms for this goal, due to their inherent drivendissipative nature, high degree of controllability and flexibility, and potential for room temperature operation. These emergent platforms have shown to host a great deal of profound and novel physics, the study of which could not only lead to the development of new materials for use in technology, but could also allow us to enter new and unexplored realms of quantum mechanics.

The first and most important impact of our Centre will be through the cross-disciplinary technical training it provides for its students. Through this training, they will have not only skills to control and exploit quantum physics in new ways, but also the background in device engineering and information science to bring these ideas to implementation and to seek out new applications. Our commercial and governmental partners tell us how important these skills are in the growing number of people they are hiring in the field of quantum technologies. In the longer term we expect our graduates to be prominent in the development of new technologies and their application to communication, information processing, and measurement science in leading university and government laboratories as well as in commercial research and development. In the shorter term we expect them to be carrying out doctoral research of the highest international quality.

Second, impact will also flow from the students' approach to enterprise and technology transfer. From the outset they will be encouraged to think about the value of intellectual property, the opportunity it provides, and the fundraising needed to support research and development. As students with this mindset come to play a prominent part in university and commercial laboratories, their common background will help to break down the traditional barriers between these sectors and deliver the promise of quantum technologies for the benefit of the UK and world economies. Concrete actions to accelerate this impact will include entrepreneurship training and an annual CDT industry day.

Third, through the participation it nucleates in the training programme and in students' research, the Centre will bring together a community of partners from industry and government laboratories. In the short term this will facilitate new collaborations and networks involving the partners and the students; in the long term it will help to ensure that the supply of highly skilled people from the CDT reaches the parts of industry that need them most.

Finally, the CDT will have a strong impact on the quantum technologies training landscape in the UK. The Centre will organise training events and workshops open to all doctoral researchers to attend. We will also collaborate with CDTs in the quantum technologies and related research areas to coordinate our efforts and maximise our joint impact. Working in consort, these CDTs will form a vibrant national training network benefitting the entire UK doctoral research community.