Financial crimes fast proliferation and sophistication require novel approaches that provide robust and effective solutions. This paper explores the potential of quantum algorithms in combating financial crimes. It highlights the advantages of quantum computing by examining traditional and Machine Learning (ML) techniques alongside quantum approaches. The study showcases advanced methodologies such as Quantum Machine Learning (QML) and Quantum Artificial Intelligence (QAI) as powerful solutions for detecting and preventing financial crimes, including money laundering, financial crime detection, cryptocurrency attacks, and market manipulation. These quantum approaches leverage the inherent computational capabilities of quantum computers to overcome limitations faced by classical methods. Furthermore, the paper illustrates how quantum computing can support enhanced financial risk management analysis. Financial institutions can improve their ability to identify and mitigate risks, leading to more robust risk management strategies by exploiting the quantum advantage. This research underscores the transformative impact of quantum algorithms on financial risk management. By embracing quantum technologies, organisations can enhance their capabilities to combat evolving threats and ensure the integrity and stability of financial systems.