What Is a Quantum Algorithm?

A handful of quantum algorithms have known, mathematically proven speedups over the best classical alternative. The most famous is Shor's algorithm, which factors large numbers exponentially faster than any known classical method. This is the reason quantum computing is taken seriously as a future threat to RSA encryption, which relies on factoring being hard. Grover's algorithm gives a quadratic speedup for searching an unsorted list, meaningful, but far more modest than Shor's, and it doesn't threaten most encryption. Quantum simulation algorithms (the original motivation Richard Feynman proposed for quantum computing in 1981) let you model how molecules and materials actually behave at the quantum level, something classical computers scale very badly at.

It's worth being precise here because this is one of the most overstated areas in quantum coverage: there is no known general-purpose quantum algorithm that speeds up arbitrary computation. The problems with real quantum speedups are specific and mathematically identified. They don't generalize to "computing gets faster now." A large amount of current research is exactly about finding new problems where a genuine quantum advantage exists, which is still an open and active area, not a solved one.