Quantum computing
A machine that computes with quantum states rather than bits — faster on a handful of problems, slower on everything else.
Richard Feynman proposed in 1981 that the only sensible way to simulate quantum systems is with a computer that is itself quantum mechanical. David Deutsch formalised the idea in 1985. The point is not to try every answer at once, which is the commonest misconception, but to arrange the computation so that wrong answers cancel through interference while the right one is amplified.
The advantage applies to a narrow set: factoring, certain search problems, and simulation of molecules and materials. For databases, web servers and machine learning generally, there is no reason to expect anything. A quantum computer will sit beside ordinary computers as an accelerator, not replace them.