Quantum Complexity of Clique Homology

Explore the intersection of topology and quantum mechanics in this 44-minute lecture by Robbie King from Caltech. Delve into the complexity theory behind determining the presence of holes in topological spaces, and discover how this problem relates to QMA (Quantum Merlin Arthur) complexity. Examine the implications for quantum algorithms, supersymmetric quantum mechanics, and quantum PCPs (Probabilistically Checkable Proofs). Gain insights into the quantum hardness proof, focusing on the application of spectral sequences, a tool from algebraic topology. Uncover the unexpected quantum mechanical structures within this seemingly classical topological problem, bridging the gap between quantum complexity theory and topology.