According to Feynman, quantum computers will be the most suitable platforms to simulate nature. Although as of today, quantum computers with capability and reliability comparable or beyond those of classical computers do not exist, rapid progress in quantum technologies, and a vast growth in interest and resources in quantum information sciences, promise a future in which quantum computation may play an important role in addressing computationally-challenging problems in all areas of sciences and technology. Nuclear and high-energy physics is among the areas in which classical high-performance computing has been applied successfully to address a range of problems arising from strong-interactions dynamics. However, our current approach has severe limitations when it comes to investigations of finite-density systems or real-time dynamics. It is believed that a quantum-computational approach to such problems is superior to classical approaches, but it remains an open question how to reformulate problems accordingly to harness the quantum advantage in near-term and future devices. This talk will report on our effort to address this question in simple strongly-interacting models, with a focus on implementation on the existing quantum hardware, in particular, the ion-trap quantum simulators.