Ground-state reachability for variational quantum eigensolvers: a Rydberg-atom case study

TL;DR

This paper investigates the conditions under which variational quantum eigensolvers can reach ground states in Rydberg-atom quantum simulators, using symmetry analysis to predict success and suggest improvements.

Contribution

It introduces a symmetry-based framework to assess ground-state reachability in VQE, specifically applied to Rydberg-atom systems, and offers practical strategies to overcome symmetry restrictions.

Findings

Symmetry analysis predicts VQE success in reaching ground states.

Simulations confirm the reliability of symmetry-based predictions.

Adding resources or changing initial states can overcome symmetry barriers.

Abstract

As quantum computing progresses, variational quantum eigensolvers (VQE) for ground-state preparation have become an attractive option in leveraging current quantum hardware. However, a major challenge in implementing VQE is understanding whether a given quantum system can even reach the target ground state. In this work, we study reachability conditions for VQE by analyzing their inherent symmetries. We consider a Rydberg-atom quantum simulator with global controls and evaluate its ability to reach ground states for Ising and Heisenberg target Hamiltonians. Symmetry-based conclusions for a smaller number of qubits are corroborated by VQE simulations, demonstrating the reliability of our approach in predicting whether a given quantum architecture could successfully reach the ground state. Our framework also suggests approaches to overcome symmetry restrictions by adding additional quantum resources or choosing different initial states, offering practical guidance for implementing VQE in quantum simulation architectures. Finally, we illustrate connections to adiabatic state preparation.