Figure 3

The fixed ancilla-register interaction${\mathit{L}}_{\mathit{a}}^{\mathit{j}}$. (a) Decomposition into local and non-local parts. (b) The two-qubit entangling gate $N_k^j$ is implemented on the register qubits j and k via the sequence of Eq. (13) with an ancilla initialised in the state $|0〉$, where the form of $N_k^j$ is given in Eq. (14). This two-qubit gate is not symmetric with respect to the exchange of j and k. (c) The single-qubit gate $v_i=R({\theta }^i+{\theta }_a)uR({\theta }^i+{\theta }_r)$ is applied to a register qubit j by two applications of L with an ancilla initialised in the state $|i〉$, $i=0,1$.