## 5 Performance Evaluation
### Quantum Approach (IBM's Quantum Simulator Results and Discussions)  
The second phase of the performance evaluation shows the results from the CH selection formulated using [PERSON]'s weighted search algorithm in IBM's quantum simulator (QISKIT). In the initialization of this algorithm, the quantum states \(\ket{0}^{\otimes\text{R}}\) and \(\ket{1}\) are set to an equal superposition state, which can be achieved by implementing a Hadamard gate (H) for each qubit. For this simulation, the algorithm needs five qubits, where one qubit (\(q_{4}\)) represents an ancilla/auxiliary qubit that is initialized to state \(\ket{1}\) by applying a NOT (X) gate, as shown in Figure 6a. After the implementation of the Hadamard gate (H), the amplitude can be represented by \(\frac{1}{\sqrt{N}}\). The next step is to build an Oracle to mark the state. This Oracle can be made by a CZ gate which is a combination of a Hadamard gate and a controlled X (CNOT) gate for a two-qubit system. Our required target states are \(\ket{1001}\) and \(\ket{1100}\), which represent node 10 and node 13. Therefore, to build an Oracle with four qubits, we need to use a quadruple-controlled (cccc-X) gate that can be constructed using a Multi-Controlled Toffoli (MCT) gate, as shown in Figure 6b. Then, we build the circuit by creating a superposition of all of the states, and the final (ancilla) qubit needs to be placed in the \(\ket{-}\) state (negative), as required. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Sensing Region & 200 m \(\times\) 200 m \\ N & 50 \\ \(E_{dec}\) & 50 nJ/bit \\ \(e_{fs}\) & 10 pJ/bit/m2 \\ \(e_{mp}\) & 0.0013 pJ/bit/m4 \\ \(E_{DA}\) & 5 nJ/bit per signal \\ Data packet size (I) & 1 packet = 800 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Computation parameters and values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No. of Clusters**} & \begin{tabular}{c} **No. of Member Nodes** \\ **in One Cluster** \\ \end{tabular} & \begin{tabular}{c} **Average Distance from** \\ **a Member Node to the** \\ **CI (Assumption)** \\ \end{tabular} & \begin{tabular}{c} **Transmission Energy** \\ **(\(E_{x}\), **(\(\mu\))**(Packet) from** \\ **Member Nodes Nodes)** \\ \end{tabular} & \
\begin{tabular}{c} **Transmission Energy** \\ **(\(E_{x}\),**(\(\mu\))**(D) from** \\ **Other Nodes)** \\ \end{tabular} &
\begin{tabular}{c} **Receiving Energy** \\ **(\(E_{x}\),**(\(\mu\))**(D) from** \\ **Cluster (Millipouse)** \\ \end{tabular} & **Energy Savings** \\ \hline
1 & 50 & 90 & 104.8 & 5240 & 20,000 & 25.24 & 1\% \\ \hline
2 & 25 & 85 & 97.84 & 2445 & 10,000 & 12.45 & 51\% \\ \hline
3 & 16 & 60 & 73.8 & 1181 & 6400 & 7.58 & 70\% \\ \hline
4 & 12 & 50 & 60.6 & 720 & 4800 & 5.52 & 78\% \\ \hline
5 & 10 & 30 & 47.2 & 472 & 4000 & 4.47 & 82\% \\ \hline
6 & 8 & 20 & 43.2 & 346 & 3200 & 3.55 & 80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Energy calculation of intra-cluster communications. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No. of Clusters**} & \begin{tabular}{c} **No. of Member Nodes in** \\ **One Cluster** \\ \end{tabular}  & \begin{tabular}{c} **Non-CH Node (m\({}^{-1}\))** \\ **to B5 (m) \\ \end{tabular}  & \ \begin{tabular}{c} **Average Distance from CH** \\ **(\(\mathbf{\text{{CH per Cluster (Millipouse)}}}\))** \\ \end{tabular}  & \begin{tabular}{c} **Transmission Energy of the** \\ **CI per Cluster (Millipouse)** \\ \end{tabular}  & **Energy Savings** \\ \hline
1 & 50 & 49 & 20 & 110.01 & 1\% \\ \hline
2 & 25 & 24 & 25 & 27.51 & 75\% \\ \hline
3 & 16 & 15 & 30 & 11.28 & 89\% \\ \hline
4 & 12 & 11 & 35 & 6.35 & 94\% \\ \hline
5 & 10 & 9 & 40 & 4.43 & 96\% \\ \hline
6 & 8 & 7 & 45 & 2.85 & 97\The next stage in [PERSON]'s algorithm is related to implementing a diffuser, which is also called the amplification stage, which inverts the average of the amplitudes. This can be accomplished using the formula HRH, in which H is the Hadamard transform, and R is a phase shift transform [39].