Quantum Codes for Topological Quantum Computation

The book "Quantum Codes for Topological Quantum Computation" offers a structured, algebraic, and geometric approach to the classification and construction of quantum codes for topological quantum computing. It combines key concepts from linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, as well as classical and quantum coding theory. This combination enables readers to gain a deeper understanding of the development of quantum codes that are significant for topological quantum computation. The book discusses, among other topics, surface codes that operate as stabilizer codes, and the development of models for topological order using qubits distributed on the surface of a torus. Additionally, fundamental geometric and algebraic concepts are introduced that are necessary for constructing promising classes of quantum error correction codes, such as surface codes and color codes. It is aimed at advanced students in electrical engineering and mathematics who already have a foundational knowledge of linear algebra and quantum mechanics.