Improving Generalization and Trainability of Quantum Eigensolvers via Graph Neural Encoding

• URL: http://arxiv.org/abs/2602.19752v1
• Date: Mon, 23 Feb 2026 12:01:14 GMT
• Title: Improving Generalization and Trainability of Quantum Eigensolvers via Graph Neural Encoding
• Authors: Jungyun Lee, Daniel K. Park,
• Abstract summary: Ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and optimization.<n>We propose an end-to-end representation learning framework that combines a graph autoencoder with a classical neural network.<n>We demonstrate improved generalization and trainability, manifested as reduced test error and a significantly milder decay of gradient variance.
• Score: 0.5013248430919223
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size. Even on fault-tolerant quantum computers, quantum algorithms with convergence guarantees -- such as quantum phase estimation and quantum subspace methods -- require an initial state with sufficiently large overlap with the true ground state to be effective. Variational quantum eigensolvers (VQEs) are natural candidates for preparing such states; however, standard VQEs typically exhibit poor generalization, requiring retraining for each Hamiltonian instance, and often suffer from barren plateaus, where gradients can vanish exponentially with circuit depth and system size. To address these limitations, we propose an end-to-end representation learning framework that combines a graph autoencoder with a classical neural network to generate VQE parameters that generalize across Hamiltonian instances. By encoding interaction topology and coupling structure, the proposed model produces high-overlap initial states without instance-specific optimization. Through extensive numerical experiments on families of one- and two-local Hamiltonians, we demonstrate improved generalization and trainability, manifested as reduced test error and a significantly milder decay of gradient variance. We further show that our method substantially accelerates convergence in quantum subspace-based eigensolvers, highlighting its practical impact for downstream quantum algorithms.

Related papers

• Quantum-accelerated conjugate gradient methods via spectral initialization [0.0]
  A fault-tolerant quantum algorithm is used exclusively to construct a spectrally informed initial guess for a classical conjugate gradient (CG) solver.<n>A central feature of QACG is a controllable decomposition of the condition number between the quantum and the classical solver.<n>Results illustrate a concrete pathway toward the scientific and industrial use of early-stage fault-tolerant quantum computing.
  arXiv  Detail & Related papers  (2026-02-10T11:51:42Z)
• Quantum neural ordinary and partial differential equations [38.77776626953413]
  We present a unified framework that brings the continuous-time formalism of classical neural ODEs/PDEs into quantum machine learning and quantum control.<n>We define QNODEs as the evolution of finite-dimensional quantum systems, and QNPDEs as infinite-dimensional (continuous-variable) counterparts.
  arXiv  Detail & Related papers  (2025-08-24T18:43:44Z)
• Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians [0.0]
  ExcLQA is a classical, physics-inspired algorithm that identifies excited states of classical Ising Hamiltonians.<n>We benchmark ExcLQA on the shortest vector problem (SVP), a fundamental lattice problem underlying the security of many postquantum cryptographic schemes.<n>Our results show that ExcLQA manages to solve SVP instances up to rank 46, and outperforms the Metropolis-Hastings algorithm in solved ratio, number of shots, and approximation factor.
  arXiv  Detail & Related papers  (2025-07-16T16:40:49Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning [48.12231190677108]
  Quantum Annealing Multi-Head Attention (QAMA) is proposed, a novel drop-in operator that reformulates attention as an energy-based Hamiltonian optimization problem.<n>In this framework, token interactions are encoded into binary quadratic terms, and quantum annealing is employed to search for low-energy configurations.<n> Empirically, evaluation on both natural language and vision benchmarks shows that, across tasks, accuracy deviates by at most 2.7 points from standard multi-head attention.
  arXiv  Detail & Related papers  (2025-04-15T11:29:09Z)
• Unleashed from Constrained Optimization: Quantum Computing for Quantum Chemistry Employing Generator Coordinate Inspired Method [9.95432381301196]
  We introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the Unitary Coupled Cluster excitation generators.<n>This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization.
  arXiv  Detail & Related papers  (2023-12-12T19:36:51Z)
• Sparse Quantum State Preparation for Strongly Correlated Systems [0.0]
  In principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register offers a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialisation of the qubits to a high-quality approximation of the sought-after ground state. Quantum State Preparation (QSP) allows the preparation of approximate eigenstates obtained from classical calculations, but it is frequently treated as an oracle in quantum information.
  arXiv  Detail & Related papers  (2023-11-06T18:53:50Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Hamiltonian Quantum Generative Adversarial Networks [4.806505912512235]
  We propose Hamiltonian Quantum Generative Adversarial Networks (HQuGANs) to learn to generate unknown input quantum states. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states.
  arXiv  Detail & Related papers  (2022-11-04T16:53:55Z)
• Provably efficient variational generative modeling of quantum many-body systems via quantum-probabilistic information geometry [3.5097082077065003]
  We introduce a generalization of quantum natural gradient descent to parameterized mixed states. We also provide a robust first-order approximating algorithm, Quantum-Probabilistic Mirror Descent. Our approaches extend previously sample-efficient techniques to allow for flexibility in model choice.
  arXiv  Detail & Related papers  (2022-06-09T17:58:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.