## 4 Experiments
### Results  
Based on the experiment configuration, the average statistics of the quantum walk simulation with different \(\Delta k\) values are listed in Table 2, and when \(\Delta k=0.13\), the statistics were the best, so the optimal fitting parameter \(\Delta k\) of quantum walk for the seven exits was set to 0.13. Besides, the coefficients of RQTM are listed in Table 3. The \(\alpha_{i}\) coefficient for seven exits was between 25.23 and 503.42, which is proportional to the total number of vehicles passing through each exit. For the coefficients of the autoregressive moving average model for the regularity part \(F_{ikd}\), it is obvious that the autoregressive coefficient of the quantum walk residual series modeling has same the coefficients of \(p=2\), except N3, which is \(p=3\). This indicates a significant time correlation of 2 h in the fluctuation structure of vehicle flow series, which is consistent with the situation that the travel time from Nanjing to Changzhou is less than 2 h. From the coefficient of the moving average coefficient, the moving average coefficients \(q\) of the quantum walk modeling residuals are larger than the \(q\) of the classical random walk modeling residuals, indicating that the residual of the quantum walk modeling is more stationary than that of the classical random walk modeling. The simulation results based on the RQTM are shown in Figure 4, respectively. We found that the RQTM reproduces real observation data well. The distribution of peaks and troughs obtained in different time periods is consistent with the law of quasi-periodic fluctuation found in the traffic origin-destination matrix in recent studies [38; 39]. The statistics of the model performance of the RQTM and \"RW + ARMA\" are listed in Table 4, and the R\({}^{2}\) of RQTM ranged from 0.5 (N5) to 0.85 (N1). Compared with the \"RW + ARMA\" \begin{table}
\begin{tabular}{c c} \hline \hline
**Statistical Index** & **Definition** \\ \hline Mean Absolute Error (MAE) & \(MAE=\frac{1}{\pi}\sum\limits_{i=1}^{m}|y_{i}-\hat{y_{i}}|\) \\ Root Mean Square Error (RMSE) & \(RMSE=\sqrt{\frac{1}{\pi}\sum\limits_{i=1}^{m}(y_{i}-\hat{y_{i}})^{2}}\) \\ Coefficient of Determination (R\({}^{2}\)) & \(R^{2}=1-\sum\limits_{i=1}^{m}|y_{i}-\hat{y_{i}}|^{2}/\sum\limits_{i=1}^{m}|y_{i }-\overline{y_{i}}|^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model performance evaluation indicators. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\Delta k\) & **MAE** & **RMSE** \\ \hline
0.1 & 25.04 & 32.86 \\
0.13 & 23.62 & 31.28 \\
0.2 & 25.23 & 32.74 \\
0.3 & 25.34 & 32.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average statistics of quantum walk simulation with different \(\Delta k\). model, the increment of R\({}^{2}\) is from 21.28% (N7) to 104.98% (N3), and the decrement of the RMSE is from 11.61% (N2) to 32.92% (N1), and the decrement of MAE is from 13.42% (N2) to 30.34% (N1). In general, the RQTM can model the traffic flow of each exit well. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Exits** & **Methods** & **MAE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{2}{*}{N1} & RQTM & 24.84 & 34.71 & 0.85 \\  & “RW + ARMA” & 35.66 & 89.32 & 0.67 \\ \hline \multirow{2}{*}{N2} & RQTM & 3.33 & 4.76 & 0.57 \\  & “RW + ARMA” & 3.91 & 5.66 & 0.45 \\ \hline \multirow{2}{*}{N3} & RQTM & 5.17 & 7.11 & 0.66 \\  & “RW + ARMA” & 7.39 & 13.44 & 0.32 \\ \hline \multirow{2}{*}{N4} & RQTM & 7.93 & 10.95 & 0.76 \\  & “RW + ARMA” & 11.13 & 17.29 & 0.55 \\ \hline \multirow{2}{*}{N5} & RQTM & 2.80 & 3.77 & 0.50 \\  & “RW + ARMA” & 3.30 & 4.85 & 0.34 \\ \hline \multirow{2}{*}{N6} & RQTM & 7.00 & 9.43 & 0.77 \\  & “RW + ARMA” & 8.95 & 14.50 & 0.61 \\ \hline \multirow{2}{*}{N7} & RQTM & 4.06 & 5.46 & 0.68 \\  & “RW + ARMA” & 4.69 & 9.80 & 0.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of the model performance of RQTM and “RW + ARMA”. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Exits** & **Methods** & \(\alpha_{i}\) & \begin{tabular}{c} **ARMA** \\ **Model (p, q)** \\ \end{tabular}