Ryohei Kobayashi, speaking in the Institute for Advanced Study's High Energy Theory Seminar, argues that quantum error-correcting codes can escape a long-standing limitation on their logical gates by moving beyond ordinary Pauli stabilizer codes. He opens with the Bravyi-Konig bound, which forces any transversal non-Clifford gate in a Pauli stabilizer code, such as a surface or color code, to require three spatial dimensions if the code is to support universal computation. Kobayashi then introduces what he calls Clifford-hierarchy stabilizer codes, a broader non-Pauli class, and presents constructions where a 2D version admits a transversal T gate and a 3D non-Clifford version admits a transversal square-root-of-T gate. He connects these transversal gates to automorphism symmetries of twisted gauge theory and shows the resulting codes realize non-Abelian topological order. The talk is aimed at researchers in quantum information and mathematical physics already familiar with stabilizer formalism and topological order, walking through the gauge-theoretic reasoning behind each construction.