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Towards Improved Uniform Random Sampling using Grover's Algorithm

A Software Product Line (SPL) represents a paradigm for modeling systems with extensive configurability, encapsulating the variation within such systems. The com- prehensive examination of all viable configurations, collectively termed the config- uration space, becomes impractical due to exponential growth correlating to the quantity of features, particularly in the most complex scenarios. Typically, a lim- ited set of representative configurations are selected for practical use, often deployed in the context of software testing or hardware verification processes. However, the intrinsic pseudo-random nature of contemporary computational systems can intro- duce a degree of statistical bias in these samples. The advent of quantum computing presents an opportunity to achieve truly random and uniform sampling of configura- tions. This enhanced randomness is derived from the fundamentally stochastic na- ture of quantum physical phenomena. Ammermann et al. introduced a methodology for encoding the entirety of a configuration space within a quantum superposition, followed by the extraction of a single random sample, as detailed in their publica- tion [ABE+23]. Their research demonstrated the uniformity of this method across numerous samples and explored its scalability across various feature models. The present thesis aims to avoid limitations in quantum circuit creation induced by the Qiskit framework and to delve into potential enhancements of the implementation by Ammermann et al., focusing on the exploration of novel quantum gate designs that could augment scalability. Additionally, this thesis will provide a comprehen- sive analysis of the capabilities and constraints of quantum computing in the context of uniform random sampling, taking into consideration both the current state and prospective advancements of quantum hardware. Finally coming to the conclusion that the new implementation, while working as intended, does still in the current noisy intermediate-scale quantum (NISQ) era of quantum computing not provide an advantage over uniform random sampling in classical computing.

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