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arXiv · 2604.11688

Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms

Sandip Maiti
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Abstract

Geometric frustration, arising from competing interactions that prevent simultaneous energy minimization, presents a fundamental challenge for variational quantum algorithms applied to quantum many-body systems. We investigate the transverse-field Ising model on a square lattice with frustrated diagonal coupling and show that geometric frustration leads to strongly inhomogeneous correlations that are difficult to capture using standard Hamiltonian-inspired ans\"atze with global parameters. As a result, the required circuit depth increases significantly in the intermediate-field regime. We demonstrate that this limitation is not caused by optimization difficulties such as barren plateaus, but instead arises from insufficient expressibility of the ansatz. By introducing bond-resolved variational parameters, we recover accurate results at reduced circuit depth. We also study low-energy excitations and find that near-degenerate spectra in the frustrated regime further challenge variational methods. Our results provide a clear physical explanation for the limitations of variational quantum algorithms in frustrated systems and suggest improved ansatz design strategies for quantum simulation.

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Sandip Maiti. 2026-04-13. Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms. https://arxiv.org/abs/2604.11688

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