A quantum stabilizer code associated with cluster states
Dan Song, Zhengwen Cao, Shuanghao Zhang, Jie Feng, Yan Li, Geng Chai · 2017
We present a construction scheme for quantum error-correcting code of cluster states, which is a similar method of splicing stepwise as the Toric code. The stabilizer codes space can be founded by a Hamiltonian, which is constructed with a finite abelian group. A principal code space is set up by the entanglement among cluster state particles. Then a complete stabilizer code matrix can be found by supplement of computing analysis which satisfies the error-correcting conditions. This allows a simple verification for 1 - error correcting property in any dimension. Furthermore, we can obtain a suitable quantum stabilizer code.