Qubits and Grover's Algorithm

Over the weekend, I introduced myself to the first quantum computing algorithm: the quintessential search algorithm. It truly blew my mind. Before this, I had a theoretical understanding of a quantum bit, a qubit, but its power became apparent only when I saw it in action within this algorithm.

To start, unlike a classical bit that can only be in one of two stable states (0 or 1) at any given time, the state of a qubit is not determined until it is measured. This uncertainty opens up a new world of possibilities, as a qubit can represent 0 or 1 with different probabilities. When multiple qubits, say n, are present, any 2^n states can exist, each with 2^n different probabilities, subject to normalization.

What particularly amazed me about the quantum search algorithm was a technique called Grover's Iteration, attributed to Professor Lov Kumar Grover, who devised it in 1996. This technique allows searching for the correct answer in approximately pi*sqrt{N}/4 iterations if the search space consists of N unordered items. So, if we had to locate one thing out of one trillion possibilities, the classical computer would have to examine a trillion states (worst-case scenario). Still, a quantum computer has the potential to find it in approximately 800 thousand iterations, which is a considerable speedup.

I intend to write about Grover's Algorithm in more detail soon. Please stay tuned!