基于多项式基的非对称量子纠错码的构造

Construction of Asymmetric Quantum Error-correcting Codes Based on Polynomial Basis

量子纠错码在量子计算和量子通信中起着至关重要的作用。文中区别于之前关于量子纠错码的研究,之前大多关于量子纠错码的研究都在对称的量子信道上,所谓对称的量子信道是指量子比特翻转的错误概率与量子相位翻转的错误概率相等的信道。文中的研究侧重在非对称的量子信道上,所谓非对称性体现在量子相位翻转的错误概率与量子比特翻转的错误概率不相等,前者大于后者,利用经典多项式码,基于多项式基构造映射,满足了构造定理的条件,从而构造了一类非对称量子纠错码。

Quantum error-correcting codes play a very important role in both quantum computation and quantum communication, h is dif- ferent from the previous research work in quantum error-correcting codes that focuses on code constructions for symmetric quantum chan- nels ,the so-called symmetric quantum channel is the channel that phase-shift and qubit-flip errors have equal probabilities. It focuses on the asymmetric quantum channels ,the so-called asymmetric quantum channel is the channel that phase-shift and qubit-flip errors have different probabilities, and the former is greater than the later. By the classical polynomial codes, obtained the correct codes to meet the theorem＇s conditions,and a family of asynmmetric quantum error-correcting codes is obtained based on the polynomial basis.