the client the result of each measurement, for more details see [@bfk].

Let $I$ and $O$ be respectively the sets of input and output qubits. A flow is defined by a function ($f : O^c \rightarrow I^c$) from measured qubits to non-input qubits and a partial order $(\preceq)$ over the vertices of the graph such that $\forall i, i \preceq f(i)$ and $\forall j \in N_G(i), f(i) \preceq j$, where $N_G(i)$ denotes the neighbours of $i$ in graph $G$. Each qubit $i$ is $X$-dependent on $X_i = f^{-1}(i)$ and $Z$-dependent on all qubits $j$ such that $i \in N_G(j)$ (this set is called $Z_i$). The existence of such a flow in all the graphs used for computations in MBQC patterns guarantees that the number of dependencies does not blow up. Given the sets $X_i$ and $Z_i$ the computation angle for qubit $i$ needs to be adjusted as such : let $s_i^X = \oplus_{j \in D_i^X} s_j$ and $s_i^Z = \oplus_{j \in D_i^Z} s_j$, where $s_j$ corresponds to the outcome of the measurement on qubit $j$ and $D_i^X$ and $D_i^Z$ are subsets of $X_i$ and $Z_i$ respectively (these qubits in $D_i^X$ and $D_i^Z$ have all already been measured as they belong 