SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians

2026-03-25

AI Summary

This work addresses key challenges in ground-state search for spin Hamiltonians using conventional variational quantum eigensolvers (VQE)—namely barren plateaus, limited ansatz expressivity, and strong dependence on problem-specific structures—by reframing quantum circuit design as a generative modeling task. The proposed approach employs a Transformer decoder architecture to autoregressively generate quantum gate sequences that prepare low-energy states, trained via a weighted mean squared error loss. This is the first application of generative modeling to ground-state preparation in spin systems, offering a scalable and general-purpose paradigm that requires no prior knowledge of symmetries or structural assumptions. Validated on a four-qubit Heisenberg model, the framework achieves high-fidelity ground-state approximation using only a compact 12-layer, 8-head Transformer and 12-gate sequences, demonstrating both efficacy and efficiency.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The ground state search problem is central to quantum computing, with applications spanning quantum chemistry, condensed matter physics, and optimization. The Variational Quantum Eigensolver (VQE) has shown promise for small systems but faces significant limitations. These include barren plateaus, restricted ansatz expressivity, and reliance on domain-specific structure. We present SpinGQE, an extension of the Generative Quantum Eigensolver (GQE) framework to spin Hamiltonians. Our approach reframes circuit design as a generative modeling task. We employ a transformer-based decoder to learn distributions over quantum circuits that produce low-energy states. Training is guided by a weighted mean-squared error loss between model logits and circuit energies evaluated at each gate subsequence. We validate our method on the four-qubit Heisenberg model, demonstrating successfulconvergencetonear-groundstates. Throughsystematichyperparameterexploration, we identify optimal configurations: smaller model architectures (12 layers, 8 attention heads), longer sequence lengths (12 gates), and carefully chosen operator pools yield the most reliable convergence. Our results show that generative approaches can effectively navigate complex energy landscapes without relying on problem-specific symmetries or structure. This provides a scalable alternative to traditional variational methods for general quantum systems. An open-source implementation is available at https://github.com/Mindbeam-AI/SpinGQE.

Problem

• ground state search
• spin Hamiltonians
• Variational Quantum Eigensolver
• barren plateaus
• quantum computing

Innovation

• Generative Quantum Eigensolver
• Transformer-based circuit generation
• Spin Hamiltonians
• Barren plateau mitigation
• Symmetry-agnostic optimization