As quantum computers gain attention and accessibility, new possibilities are emerging, making cellular automata an interesting topic of exploration. Large cellular automata are computationally demanding, therefore, the use of quantum computers could enable better management of large cellular automata. However, quantum programming differs significantly from classical programming, creating hurdles for traditional computer scientists to start quantum coding. This thesis analysed a quantum implemented cellular automaton to explore potential improvements and challenges.

The thesis starts with a detailed introduction to the concept of cellular automata, including cellular automata implementations for classical computers using Python. Next, a comprehensive explanation of the concept of quantum computing including the quantum mechanical phenomena is provided. Lastly, an implementation of a quantum elementary cellular automaton using Qiskit is analysed and interpreted to identify potential improvements.

The analysis and interpretation revealed that the quantum implementation of the elementary cellular automaton does not make much use of the advantages of quantum computation, but potential for improvement exists. Superposition could be used to parallel evolve different cellular automata over generations, improving efficiency. Entanglement could enable faster communication between neighbouring cells, while interference could amplify or suppress specific patterns respectively computational paths. Although these potential improvements, current quantum computers face challenges, such as their noisiness, which makes them prone to errors. Moreover, implementing more complex or larger cellular automata, such as two-dimensional ones, would significantly increase the required number of qubits and necessitate research into large-scale initialisation techniques. Additionally, new quantum gates suited for these complex implementations are needed. Despite these limitations, the thesis emphasised the potential of quantum cellular automata. Future research is required to overcome hardware constraints and to fully use quantum mechanics in implementations of quantum cellular automata.