It has been shown that the Metropolis algorithm can be implemented on quantum computers in a way that avoids the sign problem. However, flat histogram techniques are often preferred as they don’t suffer from the same limitations that afflict Metropolis for problems of real-world interest and provide a host of other benefits. In particular, the Wang-Landau method is known for its efficiency and accuracy. In this dissertation we present research were we designed, implemented, and validated a quantum algorithm for Wang-Landau sampling, greatly expanding the range of quantum many body problems solvable by Monte Carlo simulation. In an unrelated subject we explore the dynamics of a model system of stochastic biological clock oscillators, representing a population of cells of the microbial fungus Neurospora crassa, coupled by a quorum sensing signaling mechanism. At sufficient signaling strength, the population undergoes a dynamic second order phase transition above which cells collectively produce, well-developed, coherent, nearly periodic circadian oscillations. We also incorporate light responsiveness into the model and characterize the observed dynamics as the intensity and period of the ambient light exposure is varied.