Function QAA

Implements the general Amplitude Amplification algorithm.

Amplitude Amplification provides a systematic method for amplifying desired amplitudes in quantum superposition states. It generalizes Grover's algorithm to work with arbitrary state preparations and oracles.

Algorithm Steps:

1. State Preparation: Initialize the quantum register in a superposition
2. Oracle Application: Apply phase flip to marked states
3. Diffusion: Reflect about the initial state
4. Iteration: Repeat oracle + diffusion for optimal number of times

Theoretical Speedup:

• Classical search: O(N) for N items
• Amplitude Amplification: O(√N) with optimal success probability