### Proposed Algorithm for Optimizing the QZD Evolution  
In the raw QZD evolution, the same threshold operators are considered for all the qubits in all the iterations, potentially screening the achievable performance of our contri  
Figure 4: Logarithmic negativity of \(\rho_{DE}\) after the implementation of quantum Zeno dynamics with \(n\) iterations. The numerical simulation yields \(LN(\rho_{DE}^{n})\approx 0.8\) for \(n=3345\), showing the superactivation of bound entanglement of the initial \(\rho_{A_{1}A_{2}B_{2}C_{1}C_{2}DE}\) state following the scenario in Figure 1 but without requiring quantum state teleportations or Bell measurements. Figure 5: Superactivation of BE in (**a**) by entangling all the qubits via QZD results in a genuine eight-qubit FE state in (**b**). bution. To overcome this problem, we propose an algorithm with a variable greediness level for optimizing the evolution throughout QZD. Unlike the raw evolution with a single threshold operator corresponding to a fixed inhibited subspace, our algorithm starts with applying all the available threshold operators in parallel for \(t\) iterations. In other words, the QZD evolution takes place in all the possible 64 uninhibited subspaces in parallel universes for \(t\) iterations. Next, the best result based on the chosen KPI is evaluated, and the corresponding \(\rho^{rm}\) system is set as the new starting point for the next evolution block of \(t\) iterations. Repeating this step \(k\) times, the overall \(n=kt\) iterations are completed. Without loss of generalization, the algorithm is illustrated in Figure 6 for the present problem as an example where QZD is performed on six qubits, implying 64 available threshold operators in each iteration running from \(I_{1}^{1}=(\ket{0}\bra{0})^{\otimes 6}\) and \(I_{1}^{2}=(\ket{0}\bra{0})^{\odot 5}\otimes\ket{1}\bra{1}\), to \(J_{1}^{64}=(\ket{1}\bra{1})^{\otimes 6}\). Here, note that the \(J_{0}^{i}=I^{\otimes 6}-I_{1}^{i}\) operator is applied in each rotate-measure step, and in the presentation, we omit the identity operators for the untouched two qubits, \(D\) and \(E\), for simplicity. Parameter \(t\) determines the level of greediness where \(t=1\) corresponds to the greediest case such that the KPI evaluation is performed and the best system is set as the new starting point in every single iteration. Similar to [PERSON]'s algorithm, considering that acting upon a small gain in each iteration might miss a greater gain in the longer run, we will consider \(t>1\) scenarios as well. The raw QZD algorithm can be considered the special case of the optimized algorithm where only the rightmost branch in Figure 6 is performed in every iteration with \(k=1\) and \(t=n\). Recording throughout the simulation which threshold operator yields the best throughput in each block of \(t\) iterations provides the guideline for experimentalists to choose the optimal subspace to inhibit the evolution. The current optimization's drawback is the increased computational complexity. In addition to finding the best throughput system after each block of \(t\) iterations by maximization over the KPI, not a single but \(b\) times rotate-measure operations are performed in each iteration, \(b\) being the branching factor, which is \(b=64\) in the present problem. Note that if all the possible threshold measurement operators are applied after each measurement, i.e., all the possible \(b\) branches follow each branch in Figure 6, better results  
Figure 6: Algorithm for optimizing the QZD evolution. For \(t\) iterations, the evolution takes place in all the possible uninhibited subspaces with the threshold operators \(J_{0}^{i}=I^{\otimes 6}-J_{1}^{i}\) as the basic evolution block. Then the best \(\rho^{rm}\) is chosen and set as the new starting point for the next block of \(t\) operations. Repeating the block of \(t\) operations for \(k\) times, the overall \(n=kt\) operations are completed. Parameter \(t\) determines the level of the greediness of the algorithm. Please see the text for details.