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Homotopy classes of loops of Clifford unitaries

September 12, 2023 @ 4:00 pm - 5:00 pm

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.

Details

Date:
September 12, 2023
Time:
4:00 pm - 5:00 pm
Event Category:

Organizer

Jie Wang

Venue

CMSA Room G10
CMSA, 20 Garden Street
Cambridge, MA 02138 United States
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Phone:
6174967132