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, our adaptive optimizer, I-AQNGD, achieves faster convergence -- in 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.