Grover's algorithm

Grover's algorithm is a quantum search algorithm designed to find a specific item in an unsorted database much faster than a classical computer. It provides a quadratic speedup over classical exhaustive search algorithms.

While Shor's algorithm is famous for breaking RSA by factoring integers exponentially faster, Grover's algorithm only provides a quadratic speedup for brute-forcing symmetric keys. This effectively halves the bit security of algorithms like AES, meaning a 256-bit key would only offer 128-bit quantum security.

When searching through an unsorted database of N items, Grover's algorithm takes approximately the square root of N (√N) steps to find the target. A classical computer would require an average of N/2 steps to do the same task.

No, Grover's algorithm requires a quantum computer to utilize quantum superposition and interference. You can simulate a basic version of it on a classical computer using libraries like Qiskit, but the quantum speedup is lost in the simulation.