Parallelizing the Variational Quantum Eigensolver: From JIT Compilation to Multi-GPU Scaling

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for computing ground state energies of molecular systems. We implement VQE to calculate the potential energy surface of the hydrogen molecule (H$_2$) across 100 bond lengths using the PennyLane quantum computing framework on an HPC cluster featuring 4$\times$ NVIDIA H100 GPUs (80GB each). We present a comprehensive parallelization study with four phases: (1) Optimizer + JIT compilation achieving 4.13$\times$ speedup, (2) GPU device acceleration achieving 3.60$\times$ speedup at 4 qubits scaling to 80.5$\times$ at 26 qubits, (3) MPI parallelization achieving 28.5$\times$ speedup, and (4) Multi-GPU scaling achieving 3.98$\times$ speedup with 99.4% parallel efficiency across 4 H100 GPUs. The combined effect yields 117$\times$ total speedup for the H$_2$ potential energy surface (593.95s $\rightarrow$ 5.04s). We conduct a CPU vs GPU scaling study from 4--26 qubits, finding GPU advantage at all scales with speedups ranging from 10.5$\times$ to 80.5$\times$. Multi-GPU benchmarks demonstrate near-perfect scaling with 99.4% efficiency and establish that a single H100 can simulate up to 29 qubits before hitting memory limits. The optimized implementation reduces runtime from nearly 10 minutes to 5 seconds, enabling interactive quantum chemistry exploration.