Tensor Network Methods for the Driven-Dissipative Dynamics of Polariton Lattice Quantum Simulators

Light matter based quantum simulation platforms such as polariton lattices and circuit QED systems have recently shown the ability to support stong many-body quantum correlations. Here, the strong correlations between light-matter particles lead to highly non-classical phenomena such as photon blockade, superfluid to Mott insulator phase transitions and non-linear topological physics. Numerical methods to understand these systems in one- and two- dimensions have mostly been restricted to mean field theories which are expected to break down in the limit of strong correlations. In this work, new methods based on tensor networks are developed to simulate driven dissipative many-body systems in the strongly correlated regime. These methods are based on matrix products states (MPS) for one-dimensional systems and projected entangled pair states (PEPS) for two-dimensional systems. It is expected that these new techniques will offer valuable insight into the dynamics of strongly correlated light-matter systems.

Quantum technologies promise a transformation of the fields of measurement, communication and information processing. They present a particular opportunity since they are disruptive technologies: not only do they offer a chance for rapid growth but they also allow lesser participants in a field (such as the UK in IT) to become major players through appropriate risk-taking and manpower development. Students graduating from the InQuBATE Skills Hub will have the right mindset to work in the industries where quantum technologies will be applied, and help to break down the traditional barriers between those sectors to make this transformation happen. They will have all the necessary technical and transferable skills, plus a network of contacts with our partners, their fellow cohort members and the academic supervisors.

Our commercial partners are keen to help our students realise their potential and achieve the impact we expect of them, through the training they offer and their contributions to the centre's research. They include companies who have already developed quantum technologies to products in quantum communication (Toshiba) and optimization (D-Wave), large corporates who are investing in quantum technology because they see its potential to transform their businesses in aerospace, defence, instrumentation and internet services (Lockheed Martin, Google,) and government agencies with key national responsibilities (NPL). We want to see the best communication of our students' research, so our students will benefit from the existing training programme set up with a leading scientific publisher (Nature Publishing Group); we also want to see more of the future companies that lead this field based the UK, so we have partnered with venture capital group DFJ Esprit to judge and mentor the acceleration of our students' innovations toward the market.