The body of this dissertation is arranged as follows: Chapter 2 gives an introduction to the Wigner formalism of quantum mechanics and the associated Wigner transport equation. The latter is augmented with the Boltzmann scattering models to yield the Wigner-Boltzmann equation. An overview of the existing deterministic and stochastic solvers for this equation is given. Chapter 3 presents the integral form of the Wigner-Boltzmann equation from which the signed-particle method is derived; the corresponding Monte Carlo approach and the basic building blocks of its algorithm are discussed. Chapter 4 gives a detailed presentation of the various optimizations which have been made to the signed-particle algorithms within the scope of this thesis. The improvements include algorithms with better computational efficiency, statistical enhancements and increased physical accuracy by mitigating discretization artefacts. A validation of the simulation results to illustrate the impact of the enhancements is also shown. Chapter 5 treats the parallelization of the Wigner Monte Carlo (WMC) solver in a distributed-memory environment. The spatial domain decomposition approach is shown and its performance is analysed using a few benchmark tests. Chapter 6 illustrates some applications of the WMC simulator by investigating the various aspects the interaction of wavepackets with electrostatic lenses. Finally, in Chapter 7 the contributions which have been made in the scope of this thesis are reviewed and evaluated.