Producing arbitrary quantum states in mechanical oscillators is an essential part of the research con- cerning combining the theory of quantum mechanics with general relativity. In recent years, a lot of progress was made by the development of optomechanics and circuit quantum electro dynamics using which a quantum mechanical interaction between an LC oscillator and a mechanical oscillator can be created. This only left the need for the ability to create arbitrary desired states in an LC oscillator while keeping its properties as a linear resonator in tact. The interaction needed for this was recently designed in the group and is called the photon-pressure interaction. Using this interaction, effectively a Jaynes-Cummings interaction between a qubit and a LC oscillator was created which can truly be turned on and off, keeping the linear properties of the LC oscillator while the interaction is turned off. In this thesis a protocol that makes use of the Jaynes-Cummings interaction and qubit drives to create arbitrary states in the LC oscillator is developed. To show that the desired oscillator state has been created a protocol is also developed to perform Wigner tomography on the LC oscillator. Both protocols have been tested using simulations with loss effects corresponding to the ones encountered in our lab setting. The simulation results show that using the current lab system settings, states can successfully be produced in the LC oscillator and measured using the tomography protocol. This paves the way for arbitrary state generation and state measurement experimentally in the lab.

Producing arbitrary quantum states in mechanical oscillators is an essential part of the research con- cerning combining the theory of quantum mechanics with general relativity. In recent years, a lot of progress was made by the development of optomechanics and circuit quantum electro dynamics using which a quantum mechanical interaction between an LC oscillator and a mechanical oscillator can be created. This only left the need for the ability to create arbitrary desired states in an LC oscillator while keeping its properties as a linear resonator in tact. The interaction needed for this was recently designed in the group and is called the photon-pressure interaction. Using this interaction, effectively a Jaynes-Cummings interaction between a qubit and a LC oscillator was created which can truly be turned on and off, keeping the linear properties of the LC oscillator while the interaction is turned off. In this thesis a protocol that makes use of the Jaynes-Cummings interaction and qubit drives to create arbitrary states in the LC oscillator is developed. To show that the desired oscillator state has been created a protocol is also developed to perform Wigner tomography on the LC oscillator. Both protocols have been tested using simulations with loss effects corresponding to the ones encountered in our lab setting. The simulation results show that using the current lab system settings, states can successfully be produced in the LC oscillator and measured using the tomography protocol. This paves the way for arbitrary state generation and state measurement experimentally in the lab.

Sixty years after John Bell published his paper in which he showed that local hidden variables with statistical independence are incompatible with quantum mechanics, its implications for the nature of the universe are still hotly debated among physicists and philosophers. In his paper he showed that a universe with local hidden variables and statistical independence should satisfy Bell's inequality, but this is violated by quantum mechanics. Testing Bell's inequality turned out to be difficult, owing to a number of loopholes. These were closed in experiments in 2015 which violated Bell's inequality, putting local hidden variables with statistical independence to rest. In this paper we discuss two conceptually simple versions of Bell's inequality as a game (Maudlin and GHZ) and simulate them using Python. Using local means these games are unlikely to be won, but by utilizing the non-locality of quantum mechanics the game is expected to be won. In our simulations we find that the probability of winning decays exponentially as a function of the length of the game for local strategies in Maudlin's version and we prove that the memory loophole (also known as daily updating) will not help the participants to win. In simulating GHZ as a game we find that the game length follows a geometric distribution.

Geothermal energy can be promising to help the energy transition. Warm water is pumped up from a geothermal well and after it is cooled down, the cold water is reinjected into the hot aquifer underground. The temperature change could cause chemical balances to be disturbed and result in precipitation on the porous medium of the aquifer. This process of clogging of an aquifer is not desirable since it re- duces the efficiency of the production of warm water. This research is a stepping stone for modelling these reactions and clogging of the aquifer. The reactions rates depend on the temperature and the concentration of the reactants in the aquifer. For this reason the temperature distribution of the aquifer was numerically derived with finite difference methods. The velocity field is important for modelling both the temperature and the concentrations. Therefore the pressure and velocity field were modelled with use of mass conservation and the Darcy model. The models were solved numerically with finite difference methods and some results were compared to the analytical solution of the model. It was concluded that the numerical model for the velocity field is accurate when compared to analytical solu- tions of the model equations. In the model used, an increase in porosity resulted in a delay of cooling the aquifer. This is because there was no relation between porosity and permeability implemented in the model. A lower flow rate in the aquifer delays the cooling of the aquifer as well. For further research it is recommended to implement the chemical reactions into the model and use this model to look into how to prevent the clogging in the aquifer.

Random walks have been used in a number of different fields for a long time. With the rise of of quantum random walks a lot of these applications have been made more efficient. Recently there have been a lot of improvements in the realization of these quantum random walks in real world systems.
In this research, the effect of uncertainty in the measurement time and measurement frequency are studied on three problems that make use of a quantum random walk. These problems are the network centrality problem, the graph isomorphism problem and the spatial search problem.
These effects are studied by first looking at the theory behind these problems after which the theoretical results of these three problems are calculated. These theoretical results will then be compared to simulated results that have a certain level of uncertainty in the measurement time or frequency.
For both the network centrality problem and the spatial search problem we concluded that only a small error is made when uncertainties are introduced in the system. This implies that these problems are solvable in realizations of the quantum random walk in real world systems. For the Graph isomorphism problem we saw that the error that is made when uncertainties are introduced was large which implies that this problem would only be solvable for small uncertainties.