Study Of Several Problems In Asymmetric Quantum Error-correcting Codes

In recent years, quantum computing technology caused the people's attention and in-depth research because of its powerful computation ability. Especially quantum error-correcting technology has overcome the extinction of quantum coherence which brings the quantum noise, which promotes the development of quantum computer and the realization of the quantum communication. However, previous research work in quantum error-correcting codes mostly focuses on code constructions for symmetric quantum channels, i.e., phase-shift and qubit-flip errors have equal probabilities.This paper focuses on the more realistic asymmetric quantum channels, i.e., in the physical implementation scheme, phase-shift and qubit-flip errors have different probabilities, based on the classic error-correcting codes theory and quantum error-correcting codes theory to research. Specific content and innovations are as follows:1. With classical polynomial codes, a new family of asymmetric quantum error-correcting codes is given which based on the polynomial basis. A new map is constructed based on polynomial basis in the construction, then a family of codes is given which meet the conditions.2. Constructing asymmetric quantum constant cyclic codes from classical cyclic codes, then a unified method of asymmetric quantum error-correcting codes is given which based on the close contact among cyclic codes, constant cyclic codes, quasi-cyclic codes and quasi-twisted codes, unifying the construction method to the method of constructing asymmetric quantum quasi-twisted codes.3. With subsystem codes and the nature of the classic cyclic codes, a family of asymmetric subsystem codes is given which based on classical cyclic codes. And we get a unified method of constructing asymmetric subsystem codes which based on the close contact among cyclic codes, constant cyclic codes, quasi-cyclic codes and quasi-twisted codes.