Homotopy Classes of Loops of Clifford Unitaries

Watch a 48-minute seminar presentation from the Topological Quantum Matter series at Harvard CMSA where UCLA researcher Roman Geiko explores the relationship between Clifford locality-preserving unitaries and stabilizer Hamiltonians through the lens of Hermitian K-theory. Discover how algebraic homotopy of modules over Laurent polynomial rings connects to the concept of linking short-range entangled stabilizer Hamiltonians via shallow Clifford circuits. Learn about the classification of homotopy classes of loops of Clifford unitaries, based on collaborative research with Yichen Hu that examines fundamental concepts in quantum computing and topological quantum matter.