1Grover's Algorithm: Searching with Phase
Unlike classical search which must check items one by one, Grover's uses quantum interference to amplify the correct answer. It doesn't find the item instantly, but it provides a quadratic speedup that is provably optimal for unstructured data.
2Shor's Algorithm: The RSA Killer
Shor's algorithm is the reason governments are investing billions in quantum computing. It converts the hard problem of factoring into a period-finding problem, which a quantum computer can solve efficiently using the Quantum Fourier Transform.
