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Homotopy classes of loops of Clifford unitaries
September 12, 2023 @ 4:00 pm - 5:00 pm
![](https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-09.12.23-1.png)
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.