  Quantum computing promises transformational gains for solving some problems,
but little to none for others. For anyone hoping to use quantum computers now
or in the future, it is important to know which problems will benefit. In this
paper, we introduce a framework for answering this question both intuitively
and quantitatively. The underlying structure of the framework is a race between
quantum and classical computers, where their relative strengths determine when
each wins. While classical computers operate faster, quantum computers can
sometimes run more efficient algorithms. Whether the speed advantage or the
algorithmic advantage dominates determines whether a problem will benefit from
quantum computing or not. Our analysis reveals that many problems, particularly
those of small to moderate size that can be important for typical businesses,
will not benefit from quantum computing. Conversely, larger problems or those
with particularly big algorithmic gains will benefit from near-term quantum
computing. Since very large algorithmic gains are rare in practice and
theorized to be rare even in principle, our analysis suggests that the benefits
from quantum computing will flow either to users of these rare cases, or
practitioners processing very large data.
