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Explore advanced quantum error correction through this high energy theory seminar that examines the relationship between automorphism symmetries in gauge theory and Clifford-hierarchy stabilizer codes. Learn how the Bravyi-König bound constrains transversal logical gates in traditional Pauli stabilizer codes like surface codes and color codes, particularly the requirement for three spatial dimensions to implement non-Clifford gates transversally for quantum universality. Discover how these fundamental limitations can be overcome by extending beyond Pauli stabilizers to a broader class of non-Pauli stabilizer codes known as Clifford hierarchy stabilizer codes. Examine specific constructions demonstrating that certain 2D Clifford stabilizer codes can admit transversal T gates, while 3D non-Clifford stabilizer codes enable transversal sqrt{T} gates. Understand how these transversal gates correspond to automorphism symmetries of twisted gauge theory and how the resulting codes realize non-Abelian topological order, providing new pathways for fault-tolerant quantum computation.
