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This study advances quantum simulation by demonstrating that geometrically informed variational circuits can accurately solve the antiferromagnetic Heisenberg model on kagome lattices using shallow hardware-efficient ansätze. The approach achieves robust recovery of spin-spin correlations and static structure factors without relying on explicit error mitigation, while also improving optimizer convergence through the use of the Fubini-Study metric. These results highlight a practical pathway for leveraging near-term quantum devices to tackle complex many-body physics problems that are difficult for classical computers.
Probing the Ground State of the Antiferromagnetic Heisenberg Model on the Kagome Lattice using Geometrically Informed Variational Quantum Eigensolver
arXiv:2509.18029v3 Announce Type: replace Abstract: This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver (VQE) algorithm on real quantum hardware. We demonstrate that the ground state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation (SPSA). We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubit-wise readout error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.
Abstract:This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver (VQE) algorithm on real quantum hardware. We demonstrate that the ground state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation (SPSA). We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubit-wise readout error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.
18 pages, 10 figures, 2 tables. Accepted in Phys. Rev. Research. v3: new results in Fig. 10; sections and figures reorganized
arXiv:2509.18029 [quant-ph]
(or arXiv:2509.18029v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2509.18029 Focus to learn more arXiv-issued DOI via DataCite
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