Quantum computing in the presence of errors

Quantum computers promise to solve problems that the most advanced supercomputers will never be able to tackle. They range from simple mathematical operations to the simulation of quantum materials or chemical compounds. Spectacular advances in recent years have led to the first prototypes of quantum computers, which can already perform some calculations much more efficiently than any classical device. However, they have imperfections and are not easy to scale up. Still, there is much hope that these prototypes will already be useful in some applications; that is, with them one could gain a (quantum) advantage over existing supercomputers. In this talk I will first discuss how errors may affect quantum computers in optimization problems. Then, I will revisit the problem of solving quantum many-body problems in the presence of errors and the prospects of gaining quantum advantage.