基于快速Jacket变换的量子纠错码

Quantum error-correction codes based on fast Jacket transform

受到基于Pauli矩阵的快速Jacket变换的启发,提出一种利用分块Jacket矩阵简化量子纠错码编码方案的方法。与已有的量子纠错码构造法相比,在构造量子Jacket码的稳定子的时候,不需要检验经典纠错码的自对偶条件,因此,它能促使高效地利用由分块Jacket矩阵产生的Pauli矩阵群的Abelian子群直接生成辛内积为零的独立向量,在此基础上构造出码长较大、参数较好的量子纠错码。该量子Jacket码具有构造快速、纠错行为渐进好的优点。

Motivated by the fast block Jacket transform based on Pauli matrices,this paper showed how block Jacket matrix could simplify the coding theory of quantum error-correction.Quantum Jacket codes（QJCs） did not require the dual-containing constraint necessary for standard quantum error-correction codes（QECCs）,thus allowing to construct quantum codes of large block length with efficiency.These QJCs were generated from some Abelian subgroups of Pauli group that were composed of different rows of the yielded block Jacket matrix,and had advantages of being fast constructed with asymptotically good behaviors.