Research On Construction Scheme For Quantum Error-correcting Code Based On Cluster State

In the fields of quantum computing and quantum information,noise tends to cause errors in information processing.Overcoming and reducing the influence of the quantum noise have become a key issue,one of effective methods against noise is the quantum error-correcting code.It has many applications in aspects of quantum computing and quantum information,such as fault-tolerant quantum computation,quantum key distribution and quantum entanglement purification.This essay proposes a construction scheme for quantum graph codes by stepwise synthesis,which is based on the construction principle of Toric code.In this scheme,firstly the entanglement of neighborhood is constructed by graph states interaction which establishes main part of stabilizer.Through the analysis of the calculation,it replenishes the omission which is not satisfied the error correction condition by implementing stabilizer operator.Thus,the stabilizer code can be acquired with the capability of correcting errors.This scheme is applied to graph states,the corresponding stabilizer code is constructed by establishing a chain-structure graph stabilizer on graph states.And the validity of the acquired code is illustrated simply.Compared with graph state,cluster state is more entangled,safer and easier for preparation.Furthermore,this scheme is applied to cluster states,the corresponding stabilizer code is constructed by establishing a single-row structure,splicing structure and plane structure on cluster states.Finally the validity of the acquired codes is illustrated.Compared with the traditional construction scheme of quantum graph code,the proposed scheme can not only reduce the complexity when obtaining a graph code by searching super graph,but also dispense with many physics model constraints.According to the further study,it discovers that this scheme is also applicable to higher dimensional space and combined with the topological law.The obtained cluster code by this scheme is characterized by strong security and high entanglement.Therefore,there are research significance and application prospect in the obtained code and this proposed scheme.