  The quantum stabilizer formalism was originally introduced to describe
quantum error correction codes more conveniently and now are also playing an
important role in many other fields, e.g., quantum computing and quantum
foundation. In this dissertation, we first introduce relevant background and
necessary basic knowledge, then introduce the definition of quantum stabilizer
and its application in quantum system evolution and measurement. Finally, we
try to extend the quantum stabilizer formalism to qubit-qutrit and
qubit-ququart systems which not defined before, and further define quantum
stabilizers of arbitrary composite systems.
