## 2 Model Systems and Computational Methods  
### Neuromorphic Electron Waveguides  
The transfer of quantum information between QD registers relies on electron waveguides. In neuromorphic systems, these take the form of dendritic-like structures, where several QDs are linked into a single output. A prototypical device is illustrated in Figure 1. The neuromorphic QI is defined on a two-dimensional active layer by using a charged top-gate array. This controls the confinement potential, where few electrons can reside, injected from the input into the output QD register. The top-gate array can be designed as a floating gate array of quantum dots, where the floating gates can be charged by tunneling using an STM-like tip. This structure ensures a high resolution for the confinement potential in the active layer. Similar structures have been used for light-erasable field-effect transistor memories [15]. The charge localization inside the QI is directly connected to the shapes of the electron waveguides, which are set by their curvatures and branching points. The many-electron states can be further influenced by in-plane electric fields, induced by modifications in the floating gate charging. In an experimental setup, the charge density can be extracted by measuring the tunneling current, using a sharp tip as in a usual scanning electron microscopy (STM) experiment. In this way, we obtain the read-out of the charge density, which can be found by deconvoluting the tunneling current map. The reconfigurable character of the device would enable real-time adjustments and, together with the supportive description of ML, allows an efficient optimization of the QI. More specifically, the QIs are assembled on a square shaped area \(2d\times 2d\), where \(d\) is half the size of the square side, using \(N_{\text{vg}}=4\) input waveguides with shapes defined by the generalized logistic function, also known as the Richards curve:  
\[f(x)=A+\frac{K-A+L}{(C+Qe^{-B(x-M)})^{1/v}}. \tag{1}\]  
Figure 1: Schematic representation of the reconfigurable neuromorphic system. (**a**) A layer containing a floating gate array of QDs controls the confinement in the active layer; STM tips perform the charging of the floating gate QDs and the read-out of the charge densities. (**b**) An in-plane view of the active layer, where the QI is defined. QD registers are connected to the input and output terminals, supplying and collecting electrons. The parameters \(B=6.0/d\) (growth rate), \(C=1\), \(K=d/2\), \(Q=1/2\), \(v=1/2\) are fixed, setting the curvature of the waveguides, while \(A=-3d/4\), \(-d/4\), \(d/4\), and \(3d/4\) represent the asymptotic \(y\) positions for each of the four waveguides. A large class of QI systems is generated by choosing \(L\) and \(M\) parameters. For a given QI, \(L=r_{1}\cdot d/2\), with \(r_{1}\in(-2.5,0.5)\) is a random number. For each waveguide, we choose \(M=(\delta+r_{2}/2)\cdot d\), where \(r_{2}\in(0,1)\) and \(\delta=0\) for outer leads (\(in_{1}\), \(in_{4}\)) and \(\delta=-1/2\) for the inner ones (\(in_{2}\), \(in_{3}\)). The outcome is the waveguide structure with four incoming leads merging into one outgoing lead. The \(L\) parameter sets the \(y\)-position of the outgoing lead, while the \(M\) parameters influence the x-positions of the branching points. The width of the waveguides \(\Delta_{\rm wg}\) is set at the same value for all leads. In order to keep the constant width of the waveguide, they were carved out of a potential block of height \(V_{b}\), using a circular shape with radius \(R_{0}\) while moving along the path given by Equation (1) so that we obtain a uniform \(\Delta_{\rm wg}=2R_{0}\). The theoretical design proposed here makes use of existing technologies like floating gate arrays and STM. We chose here a symmetric active region, but other geometries can be accommodated. Keeping the linear scales of the active area below the coherence length, the number of input terminals can be increased up to the resolution limit given by the floating gate dimensions.