Meta-Learning for GPU-Accelerated Quantum Many-Body Problems

TL;DR

The paper tackles slow convergence and initialization sensitivity in variational quantum eigensolvers for large, noisy Hamiltonians. It introduces a size-adaptive LSTM-FC meta-initializer integrated with the CUDAQ GPU backend to produce informed starting parameters for VQE across diverse Hamiltonians. Applied to molecular Hamiltonians from PySCF and SHM physics Hamiltonians, the approach achieves near-FCI energies with favorable scaling and accurately reproduces ground and excited states via VQE and VQD. GPU acceleration delivers substantial speedups, enabling scalable variational workloads and practical workflows for materials and quantum physics; the meta-learned initialization generalizes across problem sizes.

Abstract

We explore the industrial and scientific applicability of the VQE-LSTM framework by integrating meta-learning with GPU accelerated quantum simulation using NVIDIA's CUDA-Q (CUDAQ) platform. This work demonstrates how an LSTM-FC meta-initialization module can extend the practical reach of the Variational Quantum Eigensolver (VQE) in both chemistry and physics domains. In the chemical regime, the framework predicts ground-state energies of molecular Hamiltonians derived from PySCF, achieving near FCI accuracy while maintaining favorable O(N^2) scaling with molecular size. In the physical counterpart, we applied the same model to quantized Simple Harmonic Motion systems (SHM), successfully reproducing its ground and excited states through VQE and Variational Quantum Deflation (VQD) methods. Benchmark results on NVIDIA GPUs reveal significant speedups over CPU-based implementations, validating CUDAQ's capability to handle large-scale variational workloads efficiently. Overall, this study establishes VQE-LSTM as a viable and scalable approach for GPU accelerated quantum simulation, bridging quantum chemistry and condensed-matter physics through a unified, meta-learned initialization strategy.

Figures (10)

• Figure 1: Workflow of the proposed LSTM-VQE framework. During meta-training, the framework module learns a mapping from prior optimization traces with each FC iteration. At inference, this predicted initialization is passed to a standard VQE, where CUDAQ evaluates expectation values on GPU and a classical optimizer refines parameters to convergence.
• Figure 2: Energy deviation and runtime comparison under Adam (top) and SGD (bottom) optimizers. Bars show $\log_{10}(|\Delta E|)$ relative to the classical reference; lines indicate runtime for GPU and CPU backends. LSTM initialization improves convergence reliability and reduces runtime sensitivity across molecules.
• Figure 3: Representative VQE convergence for H$_4$ under HEA. LSTM initialization accelerates entry into a low-energy basin and reduces the number of iterations required to reach a stable solution compared to conventional initialization.
• Figure 4: H$_6$ potential energy curve (PEC) as a function of bond length. LSTM-initialized VQE reproduces the reference curve across the scan range, demonstrating robustness under continuous Hamiltonian variation.
• Figure 5: Impact of diffusion steps on H$_2$O performance. Bars show $|\Delta E|$ and the line shows runtime. Larger diffusion depth increases overhead and does not guarantee improved accuracy.