Fun with Quantum Experiments and Graph Theory

Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, results of quantum experiments are perfectly computable - but often elude human logic. In this talk, we will present a hidden bridge between quantum experiments and graph theory to show how one can model and understand modern-day photonic quantum experiments. First we will explain how questions in quantum physics can be translated and answered using Graph theory, while questions in graph theory can be converted and answered in quantum experiments. Then we introduce one important perspective is that complex weights in the graph naturally describe the quantum interference which happens when many photons are involved. This quantum interference is the basis of a new special-purpose scheme of quantum computation, which can be exploited to solve Graph Theory questions that are intractable on a classical computer. In the end, our new connection between these seemingly unrelated fields also revealed new insights into quantum state generation with current photonic technology using linear optics and probabilistic sources. In general, the bridge gives us a new perspective on photonic quantum technologies and will be significant for the design of future experiments and applications in quantum information.