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

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 state followed by single-qubit measurements. The stabilizers of cluster states are well defined because of their graph structure. We exploit this graph structure to design non-CSS codes using measurements on cluster states. The procedure is general and can be used as an encoding technique to design arbitrary non-CSS codes with one logical qubit.