Quantum-Classical-Quantum Workflow in Quantum-HPC Middleware with GPU Acceleration

Achieving high-performance computation on quantum systems is challenging, requiring integration between quantum and classical computing resources. This study presents a distribution-aware Quantum-Classical-Quantum (QCQ) architecture that combines advanced quantum software frameworks with high-performance classical computing to improve quantum simulations for materials and condensed matter physics, including the prediction of quantum phase transitions. The architecture employs Variational Quantum Eigensolver (VQE) algorithms on Quantum Processing Units (QPUs) for efficient quantum state preparation, and Tensor Network states and Quantum Convolutional Neural Networks (QCNNs) on classical hardware for state classification. Utilizing the cuQuantum SDK and PennyLane's Lightning plugin, the QCQ architecture achieves up to tenfold increases in computational speed for complex phase transition classification tasks compared to traditional CPU-based methods, demonstrating 99.5% accuracy in predicting phase transitions in models like the transverse field Ising and XXZ systems. This framework integrates quantum algorithms, machine learning, and Quantum-HPC capabilities, offering transformative insights into the behavior of quantum systems across different scales. As quantum hardware continues to improve, the QCQ framework will play a crucial role in realizing the full potential of quantum computing by seamlessly integrating distributed quantum resources with state-of-the-art classical computing infrastructure.