Fault-Tolerant Circuits from Twisted Quantum Doubles - Quantum Error Correction Beyond Stabilizer and Clifford

Watch a technical conference presentation from TQC 2024 exploring the development of fault-tolerant quantum circuits based on twisted quantum doubles. Dive into Andreas Bauer's research proposing a family of explicit fault-tolerant geometrically local circuits that can realize any abelian non-chiral topological phase. Learn how these circuits connect to discrete fixed-point path integrals and the abelian Dijkgraaf-Witten state sum, building upon the qudit toric code architecture while incorporating non-Pauli phase gates. Examine the practical implementation of the double-semion phase requiring just 12 controlled-S gates alongside 8 controlled-X gates per spacetime unit cell. Understand the proof of fault tolerance for 1-form symmetric fixed-point circuits under various noise models, including local and non-Pauli noise. Discover a novel combinatorial approach for defining higher cup products on arbitrary cellulation, with implications for twisted gauge theory research.