In the last three decades, our ability to build and control quantum states has improved dramatically and could become the basis of a new form of numerical calculation. While these machines are still in their infancy (no existing quantum computer can multiply 5 by 3), the hope is that for a very specific class of problem, they could be exponentially faster than their classical counterpart. In this talk, I will give an introduction to quantum computing from the point of view of a physicist (and a skeptic). In particular I will emphasize how the main quantum computing ressource, entanglement, is also its biggest problem, decoherence. If time allows, I will show how a recent class of “quantum inspired” algorithms, that run on perfectly classical computers, might very well deliver some of the promises of quantum computers but on existing hardware.