Graph-Theoretical Approaches for Digital Discoveries in Quantum Optics

Abstract

We present a theoretical study that investigates the applicability of a graph theoretical approach to realize various quantum experiments. Crucially, we may represent quantum optical experiments involving tabletop optical elements in terms of highly interpretable, coloured, weighted multi-graphs. We introduce the formalism behind this approach; then through the digital discovery framework PyTheus, we uncover over 100 different quantum experiments which realizes complex, novel quantum states. Towards enhancing our interpretation of the AI-based framework's solutions, we also leverage eXplainable-AI (XAI) techniques from computer vision to investigate what a trained neural network learns about quantum experiments. Crucially, we find that we are able to conceptualize the learned strategies which the neural network applies to optimize for a target quantum property, and discover how the network conceives of its solution. We conclude by presenting an experimental proposal which yields realizable solutions that, for the first time, solves high-dimensional variants of a quantum retrodiction puzzle known as the Mean King's Problem. We, therefore, present a case study which investigates the potential for new scientific discoveries through a joint collaboration between human and artificial intelligence.