Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908960233095168 |
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| author | Maiti, Sandip |
| author_facet | Maiti, Sandip |
| contents | 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 ansätze 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms Maiti, Sandip Quantum Physics 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 ansätze 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. |
| title | Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.11688 |