Iterative quantum amplitude estimation

Abstract We introduce a variant of Quantum Amplitude Estimation (QAE) , called Iterative QAE (IQAE), which does not rely on Phase (QPE) but is only based Grover’s Algorithm reduces the required number qubits and gates. provide rigorous analysis IQAE prove that it achieves quadratic speedup up to double-logarithmic factor compared classical Monte Carlo simulation with provably small constant overhead. Furthermore, we show an empirical study our algorithm outperforms other known variants without QPE, some even by orders magnitude, i.e., requires significantly fewer samples achieve same estimation accuracy confidence level.