Five-vertex graph-state circuit simulation

A graph state with edges $13,24,34,45$ simulates $J_2(\gamma )E_{12}(J_1(\alpha )\otimes J_2(\beta ))$ on $|++⟩$. Measure vertices 1 and 2 at angles $\alpha ,\beta$, with results $s_1,s_2$, and vertex 4 at $(-1{)}^{s_2}\gamma$, with result $s_4$. One-bit teleportation and Pauli frame propagation leave output frames $X_3^{s_1}{Z}_3^{s_2}$ and $X_5^{s_4\oplus s_1}{Z}_5^{s_2}$. Computational outputs are therefore corrected by $s_1$ and $s_4\oplus s_1$ respectively.