Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations and hype surrounding quantum computing we ask the question which are the promising applications to realize quantum advantage. We argue that small data problems and quantum algorithms with super-quadratic speedups are essential to make quantum computers useful in practice. With these guidelines one can separate promising applications for quantum computing from those where classical solutions should be pursued. While most of the proposed quantum algorithms and applications do not achieve the necessary speedups to be considered practical, we already see a huge potential in material science and chemistry. We expect further applications to be developed based on our guidelines.

翻译：量子计算机提供了一种新型计算范式，理论上能以显著优势超越任何可想象的经典计算机。这一前景引发了量子算法与硬件研发的淘金热潮。鉴于量子计算领域日益高涨的期望与热潮，我们提出疑问：哪些应用有望真正实现量子优势？我们论证，小规模数据问题与具有超二次加速能力的量子算法是实现量子计算实用化的关键。依据这些准则，可将具有前景的量子计算应用与传统经典方案中更优的解决方案加以区分。尽管大多数已提出的量子算法和应用尚未达到实际应用所需的加速比，但我们在材料科学与化学领域已看到巨大潜力。预计基于我们的准则将涌现更多应用方向。