Iterative Refinement Quantum Amplitude Estimation

Quantum Amplitude Estimation (QAE) is an important quantum algorithm that has the potential to quadratically speed up Monte Carlo based calculations. In this paper, we present a variant of the QAE without Phase Estimation Algorithm called Iterative Refinement QAE (IRQAE). IRQAE can refine the current estimation to a more accurate estimation iteratively, hence it can provide an estimation with arbitrary required accuracy epsilon. The key idea of IRQAE is to use a rotation gate to create a quantum state for samplings with the current estimation. Using this idea, we show that IRQAE can provide a highly accurate estimation with lower classical computational complexity and with the same quantum computational complexity compared to state-of-the-art QAEs without phase estimation using numerical experiments. We prove that the computational complexity of IRQAE of the quantum part is O(1/epsilon) and the classical one is O(log(1/epsilon)). The quantum cost gives a quadratic advantage over that of the classical Monte Carlo simulation.