## 4 Conclusions  
In this article, we continued our studies in accelerating spin initialization for a QD in the Voigt configuration using nearby two-dimensional materials [22] by studying the problem of a QD near a MoS\({}_{2}\) monolayer and studied in detail the fidelity for initialization under different excitation processes and different MoS\({}_{2}\) material qualities and host dielectric material permittivities. By calculating the modified spontaneous emission rates for a QD near the MoS\({}_{2}\) monolayer and using the results in the corresponding density matrix equations, we showed that highly efficient electron spin initialization was obtained for short time intervals. The fidelities obtained were much higher than for the QD in free-space. We examined two different cases of the interaction of the QD with the applied optical field. First, we used a continuous wave laser field and determined for various QD \(-\) MoS\({}_{2}\) layer distances the field strength, which led to acceptable fidelity levels. The effect of the quality of the MoS\({}_{2}\) material, as well as the effect of the host dielectric environment permittivity on the fidelity of spin initialization were also examined. We also studied the interaction of the QD with a laser pulse and applied numerical optimal control, using a state-of-the-art optimal control solver, to obtain the time-dependent field strength, which led to maximum final fidelity for short time intervals. The latter approach gave beneficial results in comparison to the continuous wave field excitation. We also found that the resulting optimal pulse was robust to the positioning error of the QD \(-\) MoS\({}_{2}\) monolayer structure  
Figure 6: Three examples with optimized time-dependent control for duration \(T=2/\gamma=1.097\) ns: good quality MoS\({}_{2}\) layer at \(R=3.5\) nm (first row), medium quality MoS\({}_{2}\) layer at \(R=6\) nm (second row), and bad quality MoS\({}_{2}\) layer at \(R=7.5\) nm (third row). (**a,d,g**) Optimal control \(\Omega(t)\). (**b,e,h**) Corresponding \(\rho_{22}(t)\). The final value \(\rho_{22}(T)=0.9963\) exceeds the value \(0.9945\) achieved with constant Rabi frequency in the second column of Figure 3. (**c,f,i**) Sensitivity diagram of \(\rho_{22}(T)\) achieved with the optimal profile \(\Omega(t)\), for a positioning error around the nominal value \(R=3.5,6,7.5\) nm and a constant error \(\delta\Omega\) in the control.  
and to additive constant control error. The overall conclusion of this work was that high-fidelity rapid initialization of a QD in the Voigt geometry may occur near a MoS\({}_{2}\) monolayer using both excitation methods, for different material qualities and different host dielectric material permittivities. The fidelity and robustness was similar to that obtained for a QD near a graphene monolayer [22], so the MoS\({}_{2}\) monolayer was a valid alternative to graphene for achieving rapid initialization of a QD in the Voigt geometry.  
Conceptualization, E.P. and D.S.; methodology, D.S. and V.K.; software, D.S. and V.K.; validation, N.I.; investigation, V.K.; writing, original draft preparation, D.S., V.K., and E.P.; writing, review and editing, E.P., D.S., and N.I.; visualization, N.I.; supervision, E.P.; funding acquisition, E.P. All authors have read and agreed to the published version of the manuscript.  
The research is implemented through the Operational Program \"Human Resources Development, Education and Lifelong Learning\" and is co-financed by the European Union (European Social Fund) and Greek national funds (Project EABM34, Code MIS 5005825).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
Qd Quantum dot