Fig. 11: Full decomposition of the BPQM circuit in Fig. 8.

The variable node unitaries \({U}_{ \circledast }(\theta ,\theta ^{\prime} )\) are decomposed in Fig. 9. The two-qubit-controlled coherent versions of these unitaries as well as the single-qubit rotation \({K}_{{m}_{1}}\), which is a function of the measurement result m₁, are decomposed in Fig. 10.