Geometric Properties of Quantum States Representing Directed Graphs on Quantum Computer

Explore the geometric properties of multi-qubit states represented by directed graphs in this 32-minute seminar from the HyperComplex Seminar series. Delve into the relationship between graph structure and quantum state properties, focusing on curvature and torsion. Learn how curvature is determined by weighted vertex degrees and edge products forming squares in the graph, while torsion relates to edge products creating triangles. Examine the results of quantum calculations performed on IBM's quantum computer for a chain-like graph state, comparing them to theoretical predictions. Investigate quantum states represented by directed networks and their geometric measure of entanglement, calculated both analytically and using the AerSimulator. Discover the connection between a qubit's entanglement measure and the weights of incoming and outgoing arcs, as well as vertex degrees in the corresponding graph. Gain insights into cutting-edge research at the intersection of quantum computing, graph theory, and geometry.