[Verse 1] When Grover's algorithm meets its match And you need more than just database catch There's a framework that extends the reach Amplitude amplification's what we teach Start with any quantum state you choose Mark the targets that you cannot lose Oracle function separates the wheat From the chaff in superposition's beat [Chorus] Rotate and reflect, that's the golden rule Diffusion operator, our primary tool Mark-flip-diffuse, watch probabilities climb Amplitude grows stronger every time Geometric phases spinning round and round Till your desired states can be found [Verse 2] Take your marking oracle, call it A Flips the phase for winners in the fray Then diffusion mirrors around the mean Pushes amplitudes toward the unseen Two reflections make one rotation In the two-dimensional span creation Good and bad states dancing on a sphere As the iterations make success appear [Chorus] Rotate and reflect, that's the golden rule Diffusion operator, our primary tool Mark-flip-diffuse, watch probabilities climb Amplitude grows stronger every time Geometric phases spinning round and round Till your desired states can be found [Bridge] Square root speedup, quadratic gain Classical search feels so mundane When you generalize beyond database search Any amplitude gets its moment to lurch From tiny whisper to thunderous roar Probability mass shifts to your door [Verse 3] Count the good states, calculate the angle Optimal steps prevent the measurement mangle Too many turns and you'll overshoot the peak Trigonometry tells you what to seek Sine and cosine guide your iteration Perfect timing for state elevation [Chorus] Rotate and reflect, that's the golden rule Diffusion operator, our primary tool Mark-flip-diffuse, watch probabilities climb Amplitude grows stronger every time Geometric phases spinning round and round Till your desired states can be found [Outro] From Grover's search to machine learning's call Amplitude amplification conquers all The quantum speedup that breaks classical bounds In polynomial time, the answer's found
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