  Quantum technologies have shown immeasurable potential to effectively solve
several information processing tasks such as prime number factorization,
unstructured database search or complex macromolecule simulation. As a result
of such capability to solve certain problems that are not classically
tractable, quantum machines have the potential revolutionize the modern world
via applications such as drug design, process optimization, unbreakable
communications or machine learning. However, quantum information is prone to
suffer from errors caused by the so-called decoherence, which describes the
loss in coherence of quantum states associated to their interactions with the
surrounding environment. This decoherence phenomenon is present in every
quantum information task, be it transmission, processing or even storage of
quantum information. Consequently, the protection of quantum information via
quantum error correction codes (QECC) is of paramount importance to construct
fully operational quantum computers. Understanding environmental decoherence
processes and the way they are modeled is fundamental in order to construct
effective error correction methods capable of protecting quantum information.
In this thesis, the nature of decoherence is studied and mathematically
modelled; and QECCs are designed and optimized so that they exhibit better
error correction capabilities.
