Quantum mechanics revolutionized our understanding of the natural world in the early 20th century. Today, more than 100 years later, experimental control of certain physical systems described by quantum theory has led to a tantalizing pursuit. Can we build a computer that stores and acts on information encoded in the quantum mechanical wave function of a physical system? Can such a machine be made computationally useful? Could it be made general purpose? In this talk, I will discuss the physics advances that have created platforms for the pursuit of a quantum computer, along with key areas of research that can unlock new capabilities for future machines. In particular, I will describe the need for multi-platform integration; the intrinsic role of quantum communication; and the need for advances in quantum computer architecture.