Optimization Landscape Geometry in VQE for Frustrated Quantum Spin Models
Abstract
We benchmark eight classical optimizers for exact-statevector VQE calculations on a controlled hierarchy of frustrated spin models, ranging from a diagonal Ising glass to transverse-field Ising and anisotropic Heisenberg models. The benchmark includes local, stochastic-gradient, evolutionary, covariance-adaptation, and swarm-based optimization methods under matched function-evaluation budgets. To understand their performance beyond final energies, we characterize the underlying Hamiltonian--ansatz landscapes in terms of local minima, gradients, curvature, and ground-state reachability. We use simple variational circuits, from an Ry product-state ansatz for the diagonal model to shallow Ry--CNOT hardware-efficient circuits for the noncommuting models, and study how increasing circuit depth changes their expressivity, reachability, and optimization geometry. We find that optimizer performance changes substantially across the model hierarchy and is closely connected to landscape structure, while the variational gap represents a separate source of error. These results show how classical optimization, variational expressivity, and landscape geometry jointly determine VQE performance for frustrated spin models.
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BibTeX
@misc{novak2026optimization,
title = {{Optimization Landscape Geometry in VQE for Frustrated Quantum Spin Models}},
author = {Vojtěch Novák and Ivan Zelinka and Swagatam Das and Martin Beseda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00235},
eprint = {2609.00235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00235},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimization Landscape Geometry in VQE for Frustrated Quantum Spin Models
AU - Vojtěch Novák
AU - Ivan Zelinka
AU - Swagatam Das
AU - Martin Beseda
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.00235
UR - https://arxiv.org/abs/2609.00235
AB - We benchmark eight classical optimizers for exact-statevector VQE calculations on a controlled hierarchy of frustrated spin models, ranging from a diagonal Ising glass to transverse-field Ising and anisotropic Heisenberg models. The benchmark includes local, stochastic-gradient, evolutionary, covariance-adaptation, and swarm-based optimization methods under matched function-evaluation budgets. To understand their performance beyond final energies, we characterize the underlying Hamiltonian--ansatz landscapes in terms of local minima, gradients, curvature, and ground-state reachability. We use simple variational circuits, from an R_y product-state ansatz for the diagonal model to shallow R_y--CNOT hardware-efficient circuits for the noncommuting models, and study how increasing circuit depth changes their expressivity, reachability, and optimization geometry. We find that optimizer performance changes substantially across the model hierarchy and is closely connected to landscape structure, while the variational gap represents a separate source of error. These results show how classical optimization, variational expressivity, and landscape geometry jointly determine VQE performance for frustrated spin models.
ER -