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 ∊. 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/∊) and the classical one is O(1/∊). The quantum cost gives a quadratic advantage over that of the classical Monte Carlo simulation.