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

TL;DR

This work demonstrates that the Variational Quantum Eigensolver (VQE) can compute the hydrogen molecule's ground-state energy along a 100-point potential energy surface with substantial HPC acceleration. The authors implement a four-phase parallelization—optimizer + JIT compilation, GPU acceleration, MPI-based distributed computation, and multi-GPU scaling—achieving up to ~117× overall speedup and 99.4% parallel efficiency across 4 NVIDIA H100 GPUs, while identifying memory limits that cap qubit simulability on a single GPU. A three-factor decomposition shows that algorithmic optimization (JIT/Optax) and MPI-driven parallelism dominate the performance gains, with GPU acceleration providing scale-dependent improvements. The results enable interactive quantum chemistry exploration on near-term hardware and lay a scalable blueprint for extending VQE and related variational algorithms to larger molecular systems and more complex ansätze.

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.

Figures (4)

• Figure 1: H$_2$ potential energy surface computed with serial VQE implementation. The curve shows the characteristic bonding minimum near 0.74 Å and dissociation behavior at large bond lengths.
• Figure 2: CPU vs GPU scaling study from 4--26 qubits. Left: Runtime comparison (log scale). Right: GPU speedup factor, showing increasing advantage with qubit count.
• Figure 3: Performance analysis: (a) Runtime comparison across implementations, (b) Speedup vs serial baseline, (c) MPI strong scaling with ideal linear scaling reference, (d) Parallel efficiency showing plateau beyond 16 processes.
• Figure 4: Multi-GPU benchmark on 4$\times$ NVIDIA H100: (a) GPU memory scaling with qubit count, showing the 80GB limit and maximum achieved simulation size of 29 qubits, (b) Multi-GPU speedup demonstrating 4.0$\times$ improvement with 99.4% parallel efficiency.