Constructing quantum error correcting code via logic function  

作　　者：ZHONG ShuQin, MA Zhi & XU YaJie Zhengzhou Institute of Information Engineering, University of Information Engineering of China, Zhengzhou 450002, China 

出　　处：《Science China(Information Sciences)》2010年第3期515-523,共9页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 60403004);the Outstanding Youth Foundation of Henan Province (Grant No. 0612000500)

摘　　要：We present a systematic way to construct p-ary quantum error correcting codes using logic functions. As a consequence, for a given function with APC distance d′ 2, we can construct quantum codes with parameters （（n, K, d））p and gain a lower bound of K for all 2 d d′. The basic states of the constructed quantum codes can be stated and the sufficient conditions for saturating quantum Singleton bound are also discussed. We give quantum codes [[5, 1, 3]]p with p prime, [[6, 0, 4]], [[6, 2, 3]]p with p 〉 2 prime and [[2n, 2n - 2, 2]] as examples constructed in this way.We present a systematic way to construct p-ary quantum error correcting codes using logic functions. As a consequence, for a given function with APC distance d′ 2, we can construct quantum codes with parameters （（n, K, d））p and gain a lower bound of K for all 2 d d′. The basic states of the constructed quantum codes can be stated and the sufficient conditions for saturating quantum Singleton bound are also discussed. We give quantum codes [[5, 1, 3]]p with p prime, [[6, 0, 4]], [[6, 2, 3]]p with p 〉 2 prime and [[2n, 2n - 2, 2]] as examples constructed in this way.

关 键 词：quantum error-correcting code logic states APC distance 

分 类 号：TN911.22[电子电信—通信与信息系统] TN791[电子电信—信息与通信工程]