STUDY ON CONSTRUCTIONS OF QUANTUM ERROR CORRECTION CODES

Abstract

Quantum computation is proven to give us effective solutions for difficult problems such as factoring large integer numbers in polynomial time, searching in un-ordered database, increasing the security of cryptography protocol; these tasks are difficult or less effective in classical computation. However, the effect of noise and imperfect environment in a quantum channel can affect the performance of quantum computation. Therefore, quantum error correction codes (QECC) is proposed to achieve the fault-tolerant quantum computation.

In this thesis, I study the design of QECCs and provide several contributions to quantum stabilizer code construction. I use stabilizer formalism to explain the quantum error correction codes as quantum stabilizer codes. The quantum stabilizer codes allow to remove and detect the errors by the group of quantum operators. In addition, quantum stabilizer codes can be constructed from binary or qua-ternary codes. So, our methods are using the combinatoric such as circulant, different sets, self-orthogonal, self-dual with Hermitian inner product, trace inner product to construct suitable classical codes; then, I investigate outstanding quantum stabilizer codes.