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

The Quantum Tortoise and the Classical Hare: A simple framework for  understanding which problems quantum computing will accelerate (and which it  will not)