Research On Nice Error Bases And Quantum Stabilizer Code

Quantum information technology is the combination of classical information technology and quantum mechanics.in recent years, quantum computation and quantum communication technology has developed quickly. Compared with the classical information technology, because of the character of entanglement and no-cloning, makes quantum information has an incomparable advantage in many aspect. The development of quantum information technology will make qualitative changes on the research of information technology.In the field of quantum information science, one of the main factors to restricting it’s development is quantum noise. For the errors by quantum noise, an important solution is quantum error correcting code, quantum error correcting code currently is widely used in the fields of quantum computation and quantum communication. The most important class of code in quantum error correcting code is quantum stabilizer code, and nice error bases is the bases to construct the quantum stabilizer code. Therefore the research of quantum stabilizer code through nice error bases is an important direction of research on quantum error correcting code, this paper main works as follows:1. Research on the construction and basic error correcting principle of quantum error correcting codes. Analysis the error correcting principle of quantum stabilizer code and various kinds of the construct method of stabilizer based on Pauli matrix.2. Based on research quantum stabilizer code, in order to study the construction of ternary quantum stabilizer code, we study the theory of non-binary nice error bases, and construct the nice error bases in three-dimensional Hilbert space. The error bases we construct can be used to the research on ternary quantum stabilizer codes. Based on the theory of nice error bases prove that the error bases we construct is nice, the error bases we construct can be used to the research on ternary quantum stabilizer codes.3. Based on the nice error bases we construct and the construct method of stabilizer in quantum CSS code, we construct a stabilizer of quantum CSS code in three-dimensional Hilbert space. Based on the error correcting principle of non-binary quantum stabilizer code, we study the error correcting of the stabilizer.