  Achieving high-performance computation on quantum systems presents a
formidable challenge that necessitates bridging the capabilities between
quantum hardware and classical computing resources. This study introduces an
innovative distribution-aware Quantum-Classical-Quantum (QCQ) architecture,
which integrates cutting-edge quantum software framework works with
high-performance classical computing resources to address challenges in quantum
simulation for materials and condensed matter physics. At the heart of this
architecture is the seamless integration of VQE algorithms running on QPUs for
efficient quantum state preparation, Tensor Network states, and QCNNs for
classifying quantum states on classical hardware.
  For benchmarking quantum simulators, the QCQ architecture utilizes the
cuQuantum SDK to leverage multi-GPU acceleration, integrated with PennyLane's
Lightning plugin, demonstrating up to tenfold increases in computational speed
for complex phase transition classification tasks compared to traditional
CPU-based methods. This significant acceleration enables models such as the
transverse field Ising and XXZ systems to accurately predict phase transitions
with a 99.5% accuracy. The architecture's ability to distribute computation
between QPUs and classical resources addresses critical bottlenecks in
Quantum-HPC, paving the way for scalable quantum simulation.
  The QCQ framework embodies a synergistic combination of quantum algorithms,
machine learning, and Quantum-HPC capabilities, enhancing its potential to
provide transformative insights into the behavior of quantum systems across
different scales. As quantum hardware continues to improve, this hybrid
distribution-aware framework will play a crucial role in realizing the full
potential of quantum computing by seamlessly integrating distributed quantum
resources with the state-of-the-art classical computing infrastructure.
