  The great promise of quantum computers comes with the dual challenges of
building them and finding their useful applications. We argue that these two
challenges should be considered together, by co-designing full-stack quantum
computer systems along with their applications in order to hasten their
development and potential for scientific discovery. In this context, we
identify scientific and community needs, opportunities, a sampling of a few use
case studies, and significant challenges for the development of quantum
computers for science over the next 2--10 years. This document is written by a
community of university, national laboratory, and industrial researchers in the
field of Quantum Information Science and Technology, and is based on a summary
from a U.S. National Science Foundation workshop on Quantum Computing held on
October 21--22, 2019 in Alexandria, VA.
