  Quantum computing is one of the most enticing computational paradigms with
the potential to revolutionize diverse areas of future-generation computational
systems. While quantum computing hardware has advanced rapidly, from tiny
laboratory experiments to quantum chips that can outperform even the largest
supercomputers on specialized computational tasks, these noisy-intermediate
scale quantum (NISQ) processors are still too small and non-robust to be
directly useful for any real-world applications. In this paper, we describe
NASA's work in assessing and advancing the potential of quantum computing. We
discuss advances in algorithms, both near- and longer-term, and the results of
our explorations on current hardware as well as with simulations, including
illustrating the benefits of algorithm-hardware co-design in the NISQ era. This
work also includes physics-inspired classical algorithms that can be used at
application scale today. We discuss innovative tools supporting the assessment
and advancement of quantum computing and describe improved methods for
simulating quantum systems of various types on high-performance computing
systems that incorporate realistic error models. We provide an overview of
recent methods for benchmarking, evaluating, and characterizing quantum
hardware for error mitigation, as well as insights into fundamental quantum
physics that can be harnessed for computational purposes.
