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arXiv:2509.17322 · IEEE International Conference on Acoustics Speech and Signal Processing

VQEzy: An Open-Source Dataset for Parameter Initialization in Variational Quantum Eigensolvers

Chi Zhang, Mengxin Zheng, Qian Lou, Hui Min Leung, Fan Chen

Published Apr 21, 2026• 0 citations
arXivHTMLPDF

Abstract

Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms, whose performance is highly sensitive to parameter initialization. Although recent machine learning–based initialization methods have achieved state-of-the-art performance, their progress has been limited by the lack of comprehensive datasets. Existing resources are typically restricted to a single domain, contain only a few hundred instances, and lack complete coverage of Hamiltonians, ansatz circuits, and optimization trajectories. To overcome these limitations, we introduce VQEzy, the first large-scale dataset for VQE parameter initialization. VQEzy spans three major domains and seven representative tasks, comprising 12,110 instances with full VQE specifications and complete optimization trajectories. The dataset is available at https://github.com/chizhang24/VQEzy, and will be continuously refined and expanded to support future research in VQE optimization.

DOI
10.1109/icassp55912.2026.11464259

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arXiv:2505.01236•May 2, 2025•1 citation
Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms, whose performance is highly sensitive to parameter initialization. Although recent machine learning–based initialization methods have achieved state-of-the-art performance, their progress has been limited by the lack of comprehensive datasets. Existing resources are typically restricted to a single domain, contain only a few hundred instances, and lack complete coverage of Hamiltonians, ansatz circuits, and optimization trajectories. To overcome these limitations, we introduce VQEzy, the first large-scale dataset for VQE parameter initialization. VQEzy spans three major domains and seven representative tasks, comprising 12,110 instances with full VQE specifications and complete optimization trajectories. The dataset is available at https://github.com/chizhang24/VQEzy, and will be continuously refined and expanded to support future research in VQE optimization.
Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms with broad applications in quantum physics and quantum chemistry. However, as system size increases, VQE optimization is increasingly hindered by the barren plateau phenomenon, where gradients vanish and the loss function becomes trapped in local minima. While machine learning-based parameter initialization methods have been proposed to address this challenge, they often show limited effectiveness in complex VQE problems. This is primarily due to their inadequate ability to model the intricate correlations embedded in the Hamiltonian structure and the associated ansatz circuits. In this paper, we propose Qracle, a graph neural network (GNN)-based parameter initializer for VQEs. Qracle systematically encodes both the Hamiltonian and the associated ansatz circuit into a unified graph representation and leverages a GNN to learn a mapping from VQE problem graphs to optimized ansatz parameters. Compared to state-of-the-art initialization techniques, Qracle achieves a reduction in initial loss of up to 10.86, accelerates convergence by decreasing optimization steps by up to 64.42%, and improves final performance with up to a 26.43% reduction in Symmetric Mean Absolute Percentage Error (SMAPE), with all results averaged over the validation set of each respective application. The source code is publicly available at https://github.com/chizhang24/Qracle.
Variational Quantum Algorithms (VQAs) are widely used in the noisy intermediate-scale quantum (NISQ) era, but their trainability and performance depend critically on initialization parameters that shape the optimization landscape. Existing machine learning–based initializers achieve state-of-the-art results yet remain constrained to single-task domains and datasets of only hundreds of samples. We address these limitations by reformulating VQA parameter initialization as a generative modeling problem and introducing DiffQ, a parameter initializer based on the Denoising Diffusion Probabilistic Model (DDPM). To support robust training and evaluation, we construct a dataset of 15,085 instances spanning three domains and five representative tasks. Experiments demonstrate that DiffQ surpasses baselines, reducing initial loss by up to 8.95 and convergence steps by up to 23.4%. The code and data used in this paper are available at https://github.com/chizhang24/DiffQ.
The Variational Quantum Eigensolver (VQE) is a promising candidate for quantum applications on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Despite a lot of empirical studies and recent progress in theoretical understanding of VQE's optimization landscape, the convergence for optimizing VQE is far less understood. We provide the first rigorous analysis of the convergence of VQEs in the over-parameterization regime. By connecting the training dynamics with the Riemannian Gradient Flow on the unit-sphere, we establish a threshold on the sufficient number of parameters for efficient convergence, which depends polynomially on the system dimension and the spectral ratio, a property of the problem Hamiltonian, and could be resilient to gradient noise to some extent. We further illustrate that this overparameterization threshold could be vastly reduced for specific VQE instances by establishing an ansatz-dependent threshold paralleling our main result. We showcase that our ansatz-dependent threshold could serve as a proxy of the trainability of different VQE ansatzes without performing empirical experiments, which hence leads to a principled way of evaluating ansatz design. Finally, we conclude with a comprehensive empirical study that supports our theoretical findings.
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.
Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications, including lattice field theory. However, the inherent noise of Noisy Intermediate-Scale Quantum (NISQ) devices poses a significant challenge for running VQEs as these algorithms are particularly susceptible to noise, e.g., measurement shot noise and hardware noise. In a recent work, it was proposed to enhance the classical optimization of VQEs with Gaussian Processes (GPs) and Bayesian Optimization, as these machine-learning techniques are well-suited for handling noisy data. In these proceedings, we provide additional insights into this new algorithm and present further numerical experiments. In particular, we examine the impact of hardware noise and error mitigation on the algorithm's performance. We validate the algorithm using classical simulations of quantum hardware, including hardware noise benchmarks, which have not been considered in previous works. Our numerical experiments demonstrate that GP-enhanced algorithms can outperform state-of-the-art baselines, laying the foundation for future research on deploying these techniques to real quantum hardware and lattice field theory setups.
Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms with broad applications in quantum physics and quantum chemistry. However, as system size increases, VQE optimization is increasingly hindered by the barren plateau phenomenon, where gradients vanish and the loss function becomes trapped in local minima. While machine learning-based parameter initialization methods have been proposed to address this challenge, they often show limited effectiveness in complex VQE problems. This is primarily due to their inadequate ability to model the intricate correlations embedded in the Hamiltonian structure and the associated ansatz circuits. In this paper, we propose \textit{Qracle}, a graph neural network (GNN)-based parameter initializer for VQEs. \textit{Qracle} systematically encodes both the Hamiltonian and the associated ansatz circuit into a unified graph representation and leverages a GNN to learn a mapping from VQE problem graphs to optimized ansatz parameters. Compared to state-of-the-art initialization techniques, \textit{Qracle} achieves a reduction in initial loss of up to 10.8610.8610.86, accelerates convergence by decreasing optimization steps by up to 64.42%64.42\%64.42%, and improves final performance with up to a 26.43%26.43\%26.43% reduction in Symmetric Mean Absolute Percentage Error (SMAPE).