Topological Quantum Matter Seminar
Speaker: Roman Geiko, UCLA
Title: Homotopy classes of loops of Clifford unitaries
Abstract: We study Clifford locality-preserving unitaries and stabilizer Hamiltonians by means of Hermitian K-theory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two short-range entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu. https://arxiv.org/abs/2306.09903.