Homotopy classes of loops of Clifford unitaries

09/12/2023 4:00 pm - 5:00 pm
Jie Wang
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

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.