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

TL;DR

This paper demonstrates a highly optimized, multi-GPU parallelization of the Variational Quantum Eigensolver (VQE) algorithm, achieving over 100x speedup and enabling rapid quantum chemistry simulations on classical HPC hardware.

Contribution

It introduces a comprehensive parallelization approach for VQE on multi-GPU systems, significantly improving runtime and scalability for quantum chemistry calculations.

Findings

Achieved 117x total speedup for hydrogen molecule energy calculations.

GPU implementation outperforms CPU across all qubit scales, with up to 80.5x speedup.

Near-perfect multi-GPU scaling with 99.4% efficiency, enabling large qubit simulations.

Abstract

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.