## 5 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **AWS-Braket [75]** & **ibmq_qasm\_simulator [69]** & **Pennylane [74]** \\ \# of Items** & **qRobot’s Capacity** & **\# Qubits** & **Average Time (s)** & **Average Time (s)** & **Average Time (s)** \\ \hline
2 & 15 & 10 & 11.23 & 0.053 & 0.041 \\
3 & 15 & 16 & 22.96 & 0.40 & 0.27 \\
4 & 15 & 24 & 33.07 & 537.46 & 480 \\
5 & 15 & 34 & 57.93 & \(-\) & \(-\) \\
6 & 15 & 46 & 118.41 & \(-\) & \(-\) \\
7 & 15 & 60 & 145.83 & \(-\) & \(-\) \\
8 & 15 & 76 & 296.81 & \(-\) & \(-\) \\
9 & 15 & 94 & 335.64 & \(-\) & \(-\) \\
10 & 25 & 115 & 427.36 & \(-\) & \(-\) \\
11 & 25 & 137 & 650.25 & \(-\) & \(-\) \\
12 & 25 & 161 & 908.71 & \(-\) & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: In this experimentation, both the number of qRobots and their capacities (maximum load) are fixed and are worth 1 and 45, respectively. We compare the execution time of our algorithm in the different public access simulators in the market, solving the picking and batching problem. We see that, for issues of this nature, and especially for the number of qubits required in each scenario, the behavior of the D-Wave is the desired one at the temporal level, comparing it with technologies based on quantum gates. However, it should be noted that, for the experiments on numbers of qubits less than 20, the behavior of these simulators is equated with the D-Wave. This experimentation helps to have a clear vision about the feasibility of this proof of concept. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **The Benchmark of the qRobot’s Algorithm in Different Quantum Simulators.** \\ \hline
**\# of Items** & **\# Qubits** & **DWave—Time (s)** & **Ibmq\_qasm\_simulator—Time (s)** & **Pennylane—Time (s)** \\ \hline
2 & 18 & 1.92 & 1.89 & 1.94 \\
3 & 26 & 3.2 & 737.46 & 656.93 \\
4 & 36 & 4.88 & - & - \\
5 & 48 & 7.60 & - & - \\
6 & 62 & 11.16 & - & - \\
7 & 78 & 15.89 & - & - \\
8 & 96 & 21.72 & - & - \\
9 & 116 & 30.18 & - & - \\
10 & 138 & 43.29 & - & - \\
11 & 162 & 53.28 & - & - \\
12 & 188 & 63.45 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The computational results of our picking and batching algorithm on only 1 qRobot. The value of time is an average and includes the waiting time, queue, execution, and return of the solution. In the case of K is equal to 2 for 9 items with the qRobot capacity equal to 15, the number of qubits is 188. The execution time is on AWS Braket and on the D-Wave Advantage_system1 quantum computer. We can realize that there is a latency time in executing the algorithm from the qRobot to the real quantum computer. In the tests we have done, the quantum computer is in the U.S. West (Oregon). Of all the tests that we have done, we have had an average latency time of about 2 plus all the work management processes that rises more or less to about 8 s. For the number of qubits exceeding 30, it is very convenient to use AWS-Braket (Advantage_system1.1) [81] instead of Qiskit or Pennylane. By the number of qubits and the execution time, that is differentially better. This scenario makes the use of quantum in robotics very viable. For the tests with a value of \(M\) lower than those in the table, the number of qubits is relaxed, and the execution time is improved. This leads us to normalize the weights of the batches since the number of qubits follows the formula \(K(n+1)(n+2)+K[log_{2}M]\).