Building Quantum Codes from Quantum Lego

Explore quantum error correcting codes through a comprehensive quantum seminar that introduces a novel Quantum Lego framework for design and analysis. Learn how this universal framework enables the creation of both stabilizer and non-stabilizer codes on qubits or qudits through simple lego block combinations. Discover how this innovative method leads to new quantum codes with transversal non-Clifford gates and opens possibilities for automated code design using machine learning. Examine the role of weight enumerator polynomials in determining code properties, including rate and distance, while understanding their application in optimal decoders. Master the tensor network method for computing general weight enumerator polynomials, which offers improved efficiency over existing algorithms. Conclude with an exploration of XP stabilizer codes featuring non-abelian stabilizer groups, presented by Virginia Tech Assistant Professor Charles Cao, whose expertise spans quantum information theory and quantum gravity with emphasis on quantum error correction and AdS/CFT correspondence.