Seminar: Julien Pinske, University of Rostock, Germany

Quantum Holonomies in Photonic Waveguide Systems

The findings of gauge theory, both Abelian and non-Abelian, apply to areas beyond the theories of fundamental interactions. A gauge potential acting on a quantum state results in an evolution that is determined by a non-Abelian geometric phase (quantum holonomy). A striking feature of these geometric and topological proposals is that nontrivial quantum information processing can be performed even in the presence of a vanishing Hamiltonian, thus leading to desirable fault-tolerance features. The seminar deals with the emergence of quantum holonomies in systems of coupled waveguides. Several proposals for their realisation in arrays of laser-written fused-silica waveguides are presented, including experimental results. I develop an operator-theoretic framework for the photon-number independent description of these optical networks. Finally, quantum holonomies will be embedded into schemes for measurement-based quantum computation, with the aim of approximating Jones polynomials.