The research detailed in this context represents a pioneering effort in the early exploration of quantum computing applications. It is situated within a dynamic landscape marked by the emergence of quantum computing technologies. Notably, a significant technological readiness gap persists between the resource demands of practical quantum algorithms and the current capabilities of physical quantum processors. This disparity prompts researchers to operate with a hardware-agnostic mindset, emphasizing the theoretical aspects of quantum computing algorithms. Consequently, the primary focus lies in establishing theoretical proofs that highlight the computational advantages offered by quantum algorithms, irrespective of the ongoing developments in quantum hardware. This approach underscores the fundamental drive to demonstrate the transformative potential of quantum computing, paving the way for advancements that transcend current hardware limitations.