  For the last few years, the NASA Quantum Artificial Intelligence Laboratory
(QuAIL) has been performing research to assess the potential impact of quantum
computers on challenging computational problems relevant to future NASA
missions. A key aspect of this research is devising methods to most effectively
utilize emerging quantum computing hardware. Research questions include what
experiments on early quantum hardware would give the most insight into the
potential impact of quantum computing, the design of algorithms to explore on
such hardware, and the development of tools to minimize the quantum resource
requirements. We survey work relevant to these questions, with a particular
emphasis on our recent work in quantum algorithms and applications, in
elucidating mechanisms of quantum mechanics and their uses for quantum
computational purposes, and in simulation, compilation, and physics-inspired
classical algorithms. To our early application thrusts in planning and
scheduling, fault diagnosis, and machine learning, we add thrusts related to
robustness of communication networks and the simulation of many-body systems
for material science and chemistry. We provide a brief update on quantum
annealing work, but concentrate on gate-model quantum computing research
advances within the last couple of years.
