A PCM Framework for Quantum Computing: Insights in Key Models and Algorithms

Quantum computing has the potential to revolutionize science and technology. This paper provides a comprehensive overview of key quantum computing models, such as the Hubbard model and Shore's algorithm, from physics, chemistry, and mathematics (PCM) perspectives. We explore how these models shape the future of quantum algorithms and applications. Our analysis emphasizes the importance of many-body quantum systems in designing effective quantum error correction methods. In addition, we examine Shor's algorithm and its implications for cryptography, particularly its ability to solve complex problems more efficiently. This study concludes that a holistic PCM-based approach is key to developing quantum computing and unlocking its full potential.