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 $R_y$ 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.

G.1.6; I.2.8; F.1.1; J.2

arXiv:2609.00235 [quant-ph]

(or arXiv:2609.00235v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.00235 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.