An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut

Watch a 29-minute conference talk from the 19th Theory of Quantum Computation, Communication and Cryptography Conference (TQC 2024) exploring the development of semidefinite programming relaxations for the Quantum Max Cut problem. Delve into a novel approach that leverages SU(2) symmetry and the Navascues-Pironio-Acin hierarchy to approximate extremal energy states of local Hamiltonians. Learn about the convergence properties of this hierarchy, examine analytical proofs and computational results across various graph families, and understand the connections between SDP approaches and frustration-freeness in condensed matter physics. Discover how SDP algorithms can effectively compute physical quantities and capture features of Heisenberg-type statistical mechanics models beyond frustration-free regions. Presented at OIST, Japan, this talk represents cutting-edge research in quantum physics and complexity theory, supported by leading quantum computing organizations including JPMorganChase, Google Quantum AI, and Quantinuum.