Phase-space simulations of ultra-cold atoms and photonic quantum networks

Modern computers are powerful enough to solve a large swathe of problems in a reasonable time-frame. However, even the most powerful computers cannot solve certain problems in less than exponential time. Quantum computers aim to utilize the unique properties of quantum mechanics to drastically speed-up the computation time of such problems, but this introduces a problem: How does one validate their outputs? This thesis investigates this question for two types of specialized quantum computers: Gaussian boson samplers and false vacuum decay. Methods are developed to simulate such devices in the computationally hard regime, providing a means to validate their outputs.