The rapid advancements in artificial intelligence (AI), quantum computing, and high-performance computing (HPC) present immense opportunities, yet their siloed development limits their collective impact. AI faces challenges with accessibility and energy demands, quantum computing is in its early stages with limited applications, and HPC requires modernization to integrate with these evolving paradigms. The need for a unified platform is urgent to maximize their potential. The High-Performance Quantum and AI Computing (HQAC) framework provides a transformative open platform that integrates AI, quantum computing, and HPC into a cohesive ecosystem. HQAC emphasizes openness, sustainability, heterogeneity, state-of-the-art performance, and expanding use cases. Early results underscore its effectiveness: a 2x speedup in HPC rendering workloads without quality degradation, a 6x improvement in AI inference latency with a 40% reduction in memory footprint and energy savings, and the successful launch of the Quantum AI Challenge, engaging over 100 participants from 19 countries, including 17 Historically Black Colleges and Universities (HBCUs). HQAC has been implemented as a competitive alternative to generic cloud-based AI and HPC systems and is accessible via the Education Cloud Cluster: https://hbcu1.ecc.fai.institute. It serves as a promising platform to spur research advancements in fields such as drug discovery, material science, and renewable energy.