model [@zareimon], in the sense that here the two quenched and annealed noise parameters determine the coherence phase of the model. On the other hand, we show that the above transition is also related to the error threshold of the Toric code model. Since this result is derived by using the dual correspondence and it can be applied to arbitrary random bond Ising systems, we conclude that the same dual correspondence connects the error threshold of topological CSS codes and the transition point of the dual random bond Ising systems. We give examples to show that this is very useful for studying the error threshold of different topological states. The reason is that by using hypergraphs we can easily find the classical spin model corresponding to any quantum CSS state.

The paper is organized as follows. In Sec.(\[sec1\]) we briefly review the quantum formalism of the partition function for Ising model. In Sec.(\[sec2\]), we introduce a quantum formalism for the order parameter of the random bond Ising model. In Sec.(\[sec3\]), we give the main result of the paper where we introduce a mapping to Toric code model under a sequence of bit-flip noises. Specifically, we map the order parameter of 