## 3 Results and Discussion
### Manipulation of Many-Electron States by In-Plane Electric Fields  
Next, we investigate the possibility of manipulating the localization of the charge inside the neuromorphic system. This can be achieved by slight variations in the confinement potential, which correspond to an in-plane electric field. Depending on its orientation, it drives the electron charge towards a certain terminal or groups of terminals. The confinement potential is modified by linear contributions along the \(x\) and \(y\)-directions, with maximum perturbations \(\Delta W(x,y)|_{x=\pm d}\) and \(\Delta W(x,y)|_{y=\pm d}\), respectively, with the values \(\pm 50\) meV at the edges of the active layer. The total potential energy becomes \(W_{\text{cf}}(x,y)=W_{\text{cf},0}(x,y)+\Delta W(x,y)\), where \(W_{\text{cf},0}(x,y)\) is the confinement potential in the absence of the in-plane field. The reference and predicted charge densities for 10 perturbing potentials uniformly spanning the interval \([-50,50]\) meV for both directions \(\vec{e}_{x}\) and \(\vec{e}_{y}\) for non-interacting (\(N=1\)) and interacting (\(N=2\)) systems are depicted in Figure 5.  
Starting with the \(\vec{e}_{x}\)-oriented field, we observe that the initially confined charge at the location of the output terminal is gradually shifted towards the input terminals as evidenced in Figure 5a. Although, overall, the non-interacting and interacting cases seem quite similar, particularly in the case of large values \(\Delta W\), which localizes the charge densities at the left and right edges of the active layer, there are still some noticeable differences. For small \(\Delta W\), the Coulomb interaction induces a larger spread in the charge distribution for \(N=2\), in contrast to the non-interacting case. Furthermore, as the in-plane field is completely reversed, we notice the accumulations at the input leads. Again, the Coulomb interaction has an important role in separating the charge patches, which does not occur for the non-interacting case. As the field is maximized, higher modes become visible in the input terminals. When the in-plane field is oriented along the \(\vec{e}_{y}\) direction, the charge switching occurs between the outer terminals. At maximum values of the electric field, the outer input terminals are the most populated, whereas the output terminal is typically depleted if it is placed in the middle of the active region. However, in the example shown in Figure 5b, the positioning of the output terminal is in the upper half, which makes it retain a considerable amount of charge along with the uppermost input terminal. As before, for small perturbing potentials, the Coulomb interaction induces a larger dispersion. Figure 4: Prediction accuracy for the charge density maps, measured by the \(R^{2}\) coefficient of determination, \(\langle\text{SSIM}\rangle\) and \(\langle\text{Lo}_{\infty}\rangle\): (**a**) narrow leads, \(R_{0}=10\) nm and (**b**) wide leads, \(R_{0}=20\) nm. For training and testing the model, a total of 1000 samples were generated from the previously selected 100 test samples, each subject to 10 values of the perturbing potential. From this new set, a group of 10 potential \(\times\) 10 \(\Delta W\) values were extracted as a test set, while the remaining 900 samples were used for training. Overall, quite good predictions were achieved for the density maps at small fields, while for larger ones, more significant deviations occurred. This is due to the more complex superposition of electronic states, as the quantum wells are significantly modified in the strong electric fields. Furthermore, we investigated the effect of a rotating in-plane field and analyzed the switching of electronic charge between the input and output terminals. The charge maps shown in Figure 6 indicate that, for some orientations of the in-plane field, it is possible to completely focus the charge at the outer input terminals, as well as at the output terminal.