The rapid proliferation of cloud services and virtualization technologies has escalated the demand for ultra-fast, low-latency, and energy-efficient interconnect frameworks. Conventional electronic interconnects, despite incremental improvements, struggle to meet the exponential growth of bandwidth requirements, while recent efforts leveraging purely photonic or terahertz (THz) channels face limitations in scalability, interference handling, and seamless virtualization support. Hybrid models combining optical and THz domains have been investigated, yet they often lack rigorous mathematical integration for dynamic resource allocation and fail to adequately mitigate congestion under heterogeneous workloads. To address these shortcomings, we propose HyperConnect, a novel hybrid high-speed photonic–THz inter-connect framework tailored for virtualized cloud infrastructures. Our design integrates a multi-objective optimization model based on stochastic queuing theory and convex optimization to dynamically orchestrate interconnect bandwidth, minimize migration delays, and ensure resilience against interference. Simulation-driven evaluations reveal that HyperConnect achieves up to 28.6% lower latency and 31.4% higher throughput compared to two state-of-the-art hybrid models, while reducing energy overhead by nearly 22%. These results demonstrate the potential of HyperConnect to redefine the backbone of next-generation cloud infrastructures, offering a scalable and mathematically robust solution for ultra-dense, virtualized environments.