Noisy intermediate-scale quantum algorithms

Noisy quantum computers can in principle perform reliable quantum computations, but truly scalable systems require noise levels lower than are presently achieved. Still, moderate-complexity computations can be performed. This review discusses what is possible in this ``noisy intermediate scale'' quantum (NISQ) era. Topic areas include the simulation of many-body physics and chemistry, combinatorial optimization, and machine learning. It is evident that the NISQ era has produced new paradigms for programming that will be built upon as quantum computers are further perfected.