** This is a weekly seminar with research talks from local condensed matter theory students and postdocs, aimed at a broad quantum audience. Everyone is welcome! If you're interested in presenting at a future seminar, please send a message to This email address is being protected from spambots. You need JavaScript enabled to view it.. **  Time: Thursday, April 30 - 4:00-5:00pm Location:  ATL 3100A and Virtual Via Zoom: https://umd.zoom.us/j/94978519761  Speaker: Chris Fechisin, UMD Title: A Clifford hierarchy stabilizer formalism (with applications to twisted quantum doubles) Abstract: We introduce a stabilizer formalism based on the Clifford hierarchy, which generalizes the Pauli stabilizer formalism by combining Pauli-$X$ operators with diagonal operators drawn from a fixed level of the Clifford hierarchy on prime-dimensional qudits. This yields a natural class of beyond-Pauli stabilizer models, including many twisted quantum double phases. Using this framework and focusing on a minimal example, we construct a logical qudit and an explicit level-three transversal logical gate. Together, these results provide a concrete stabilizer framework for topological codes beyond Pauli stabilizer models and enable the construction of logical gates.