Construction of non-CSS quantum codes using measurements on cluster states

The Measurement-based quantum computation provides an alternate model for quantum computation compared to the well-known gate-based model. It uses qubits prepared in a specific entangled state followed by single-qubit measurements. The stabilizers of cluster states are well defined because of their graph structure. We exploit this graph structure extensively to design non-CSS codes using measurement in a specific basis on the cluster state. % We aim to construct $[[n,1]]$ non-CSS code from a $(n+1)$ qubit cluster state. The procedure is general and can be used specifically as an encoding technique to design any non-CSS codes with one logical qubit. We show there exists a $(n+1)$ qubit cluster state which upon measurement gives the desired $[[n,1]]$ code.