instructions) that leads to the desired blind computation. This idea was formalised in the *universal blind quantum computation* (UBQC) protocol in [@bfk].

We denote $ran_i$ collectively all the parameters that $\delta_i$ depends on other than $\phi_i$. We use bold and suppress the subscript that refers to a particular qubit in the graph to denote a full string, e.g. $\boldsymbol{\phi}:=\{\phi_1,\cdots,\phi_N\},\mathbf{ran}=\{ran_1,\cdots,ran_N\}$. We then define the past of qubits, which allows us to calculate upper bounds on the number of dependencies for various computation graphs.

We define $P_i = Z_i \cup X_i$ to be the set of qubits $j$ that have $X$ or $Z$ dependency on $i$. We define influence-past $c_i$ of qubit $i$ to be an assignment of an outcome $b_j \in \{0, 1\}$ for all qubits $j \in P_i$.

For example the brickwork state [@bfk], which can be used for universal quantum computation, has for each qubit a single X-dependent qubit and at most two Z-dependent qubits, and so the cardinality $\abs{P_i}$ is at most $3$ for all $i$. To each influence-past $c_i$ corresponds a unique value of $\delta_i$ (the corrected measurement angle for this influence-past). Note that we will denote $\boldsymbol{\delta}$ the set of instructions that include the measurement angles 