Plastic waste transported to oceans through canals and rivers becomes increasingly challenging to retrieve and harmful to ecosystems. Catching systems designed by Noria Sustainable Innovators can be used to capture the plastics as close to their source as possible. Deciding the best locations to place these systems is a difficult task, which is why a model for location optimization of catching systems for plastic waste removal from waterways is designed in this thesis: the Plastic Waste Flow Capturing Location Model (PW-FCLM).

In this model, the plastic waste flow through a network of waterways is represented as a Markov chain, using environmental data as inputs to estimate the initial probabilities and transition probabilities of plastic waste in the network. The PW-FCLM extends an existing Markov Decision Process-based Flow Capturing Location Model by incorporating various types of catching systems, considering sensitive areas, and specifying orientations for the systems. The equivalence of the linearized version of the extended model is demonstrated, a proof of NP-hardness of the problem is given and a greedy heuristic is presented as an alternative solution method.

A sensitivity analysis on the different types of input parameters is performed, and the runtimes for different problem sizes and solution methods are tested for case studies of Delft and Groningen in the Netherlands. The model is most sensitive to changes in the distance between the nodes in the network and to the probability of getting stuck due to water vegetation. For budgets up to B=2 and problem sizes up to n=375 nodes, the exact optimal solution can be found efficiently without a commercial solver license. For larger problem sizes or a higher budget, the heuristic appears to be a more appropriate solution method.

For future research, it is recommended to further study the influence of the distance between the nodes on the optimal solution and to investigate the plastic flow representation in the Markov chain further. Exploring the model's application to larger areas, such as provinces or countries, would be beneficial. The real-life effectiveness of placing catching systems at the optimal locations suggested by the model, depends on the accuracy of the input parameters. In this thesis, the values of the input parameters are primarily based on estimations of experts. It would be beneficial for the user of the model to further validate the values of the input parameters through experiments.

In this research, the implementations of quantum random walks in superconducting circuit-QED are studied. In particular, a walk that moves across the Fock states of a quantum harmonic oscillator by a Jaynes-Cummings model is investigated, which is difficult to implement because of different Rabi frequencies for different Fock states. Theoretically, the lower boundary vacuum state of the harmonic oscillator causes a reflection of the probability amplitudes in the distribution. A walk that moves across a grid of coherent states |nα+imα〉 in phase space is then investigated. A setup for a 1D and 2D quantum random walk is suggested, using controlled displacements of a resonator dispersively coupled to one or two superconducting transmon qubits in circuit-QED, followed by Hadamard gates. From numerical simulations it was observed that the 2D walk commutes for α·β = 0 mod π/2 for which the variance is proportional to the number of steps t squared. For other values of α·β the horizontal and vertical displacements do not commute, resulting in extra phase factors. The numerical simulations showed that for most values of α· β with a larger distance to 0 mod π/2 than 0.01, the probability distribution of the
walk collapses to a distribution centered around origin within t = 100 steps, similar to a classical random walk. Exceptions are the 2D walks for α·β = ±π/6 mod π/2 or ±
π/4 mod π/2, for which the variance is still proportional to the number of steps squared.