Quantum computing is evolving as a revolutionary technology, capable of solving complex problems that are far beyond the reach of traditional computers.  Google and China as the global leaders in the race taking their distinct paths with their research and development strategies.  Through the Sycamore quantum processor and its Gemini AI, Google focuses on taking the artificial intelligence to the next level, improving optimization, and building practical tools for commercial use.  From the Google’s work, especially with the Sycamore quantum processor and its Gemini AI ecosystem, it focuses on advancing artificial intelligence, improving optimization, and building practical tools for commercial use. In contrast, China’s progress, demonstrated through systems like the Jiuzhang photonic platform and the superconducting Zuchongzhi processor, is closely tied to national objectives such as cybersecurity, secure communication, and long-term strategic advantage.  This literature review studies the recent researches to compare the two approaches to understand their motivations and examine how their innovations are influencing the future of computing. It also points out existing limitations, challenges in scaling hardware and integrating quantum computing with AI systems. Finally, it emphasizes the key areas where further researches are needed to sustain progress and unleash the full potential of quantum technologies.