Researchers have successfully utilized a 20-qubit trapped-ion quantum processing unit to compute ground-state energies and quasi-particle dispersions in the thermodynamic limit. This was achieved through the implementation of a numerical linked-cluster expansion with a quantum algorithm, known as NLCE+QA. The NLCE+QA framework is particularly well-suited for near-term quantum devices, as it can extract thermodynamic-limit properties from small-cluster calculations. By leveraging this approach, scientists can overcome the limitations of current quantum hardware and gain insight into complex quantum systems. The ability to study thermodynamic-limit dispersion relations on trapped-ion quantum hardware has significant implications for the development of quantum technologies1. This breakthrough matters to practitioners because it demonstrates the potential for near-term quantum devices to tackle complex problems in quantum physics, paving the way for future advancements in the field.