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Fixed-Point Oblivious Amplitude Amplification

Merging fixed-point damping with oblivious amplification to solve the "soufflé" problem. Hit the target state precisely without overshooting, maintaining the absolute optimal quantum speedup.

1. The Core Problem: The "Soufflé" Effect

Standard quantum amplitude amplification (like Grover's algorithm) works by repeatedly applying a unitary operator to increase the probability of finding a target state. However, it suffers from the soufflé problem: if you don't know exactly how many iterations to run, the probability amplitude overshoots the target and begins to decrease.
You have to stop at the exact right moment, or the "soufflé" collapses. This is even worse in oblivious amplitude amplification, where the exact initial state or overlap is unknown.
Ptarget=sin⁡2((2k+1)θ)P_{target} = \sin^2((2k + 1)\theta)
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Target State (Probability = 1)Overshoot!Target State (Probability = 1)Friction gradually appliedUnitary Circuit UDampedOperationAncilla GarbageAncillaDataRyURyTuning friction angle100% Guaranteed Hit0% OVERSHOOTO(√N)OPTIMAL SPEEDUP MAINTAINEDStandard sinusoidal P_L(p)Monotone LCU Schedule (q_n)
Blindly amplifying causes the probability to peak and then violently collapse.