Symmetry analysis for variational quantum eigensolvers on a Rydberg-atom quantum simulator

As quantum computing moves through the noisy intermediate-scale quantum era, the variational quantum eigensolver (VQE) has been proposed for ground state preparation using current or near-term quantum devices. However, a major challenge in VQE implementations is to understand and predict whether a given quantum architecture can even reach the target ground state, particularly in the presence of inherent symmetries. We develop and study reachability conditions for VQE using symmetry and Lie-algebraic methods, while building on smaller-scale examples. Applying our symmetry analysis to a Rydberg-atom quantum simulator, we evaluate its ability to reach certain Ising and Heisenberg ground states. These results are also validated with numerical VQE simulations. While inherent symmetries can limit the success of VQE implementation, they also point to additional quantum resources required to overcome these limitations and thus offer practical guidance to enhance quantum simulation architectures.