The strong force in nature, which is at the core of nuclear-physics phenomena, is described by the theory of quantum chromodynamics (QCD). It has long generated an active and growing field of research and discovery. In fact, despite the development of QCD more than half a century ago, plenty of questions remain open into the 21st century: What does the phase diagram of matter governed by strong interactions, such as the interior of neutron stars, look like? How does matter evolve and thermalize after energetic processes such as after the Big Bang or in particle colliders? How do elementary particles in QCD and their interactions give rise to the complex structure of a proton or a nucleus, and their response to various probes? A successful program called lattice QCD has enabled a first-principles look into some properties of matter with the aid of classical computing. At the same time, we have yet to come up with a more powerful computational tool to predict the complex dynamics of matter from the underlying interactions. Can a large reliable (digital or analog) quantum simulator eventually enable studies of the strong force? What does a quantum simulator have to offer to simulate QCD, and how far away are we from such a dream? In this talk, I will describe a vision for how we may go on a journey toward quantum simulating QCD, by taking insights from early to late developments of lattice QCD and its achievements, by motivating the need for novel theoretical, algorithmic, and hardware approaches to quantum-simulating this unique problem, and by providing examples of the early steps taken to date in establishing a quantum-computational lattice-QCD program.