Large-scale quantum computers, if and when they can be developed, will be capable of solving otherwise intractable problems with far-reaching applications to cryptology, materials science, and medicine. The quest for scalable quantum computers is a grand challenge for 21st century science and a highly interdisciplinary enterprise, drawing heavily from physical science, computer science, mathematics, and engineering. In this symposium, leading theorists and experimentalists will report on rapidly moving recent developments and assess the prospects for future progress. The speakers are major contributors to the subject who are also highly effective at conveying the excitement of the field to broad audiences. The symposium will address some of the central questions pursued in current research. What is the essential difference between quantum and classical information processing, and what is the source of a quantum computer's power? What can quantum computing teach us about fundamental physical law? Can a quantum computer operate reliably even though its elementary components are imperfect? What is the best way to construct a quantum processor, and how can we build the large systems needed to solve hard computational problems?