Stabilizer formalism for quantum error correction and its subsystem generalization
Ching-Wei Teng · The Atrium (University of Guelph) · 2007
One of the fundamental barriers to continued advances in quantum computing, quantum cryptography, and quantum communication is the basic problem of controlling and maintaining features of quantum systems as, they evolve in time. The common ground for these investigations is "quantum error correction." One of the most important approaches to quantum error correction is the "stabilizer formalism." In this thesis we give the basics of quantum computing, stabilizer formalism and quantum error correction, and eventually show that the stabilizer formalism can be generalized to subsystems through operator algebras. Key aspects of the analysis include Pauli groups, completely positive maps and quantum channels, and operators on Hilbert space.