An introduction to quantum error correcting codes - Nunes, Daniel Filipe Vilhena (2024)
This dissertation serves as the starting point for more in-depth work regarding quantum coding theory. In it the bridge between quantum mechanics and information, and coding theory was built. After a short description of the birth of classical information theory and quantum computation, the needed coding theory concepts are introduced with emphasis on linear codes. Concepts such as the generator matrix and parity-check matrix are described, with these being needed for the comprehension of the quantum codes that follow. The quantum component starts with the description of the fundamental behind quantum mechanics derived from its postulates. The needed basis of quantum information theory follows, with the description of its fundamental unit (qubit), the quantum logic gates paradigm and the main theorems. Finally, quantum codes are introduced, namely stabilizer codes which possess direct parallelisms with the linear codes. The focus in the description of the quantum codes is not in listing them nor describing individual codes in detail, but in the mathematical tools needed for the understanding and development of new quantum error correcting codes.