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

我们介绍了一种量子振幅估计（QAE）的变体，称为迭代QAE（IQAE），它不依赖于量子相位估计（QPE），而是仅基于Grover算法，从而减少了所需的量子位和门数。我们对IQAE进行了严格的分析，并证明与传统的蒙特卡洛模拟相比，IQAE的二次加速速度提高了两倍，并且可证明的常数开销很小。此外，我们通过一项实证研究表明，我们的算法在没有QPE的情况下优于其他已知的QAE变量，甚至有几个数量级，即，我们的算法需要更少的样本才能达到相同的估计精度和置信度。