Random-depth Quantum Amplitude Estimation

The quantum amplitude estimation is a critical task in quantum computing and the foundation of quantum numerical integration. The maximum likelihood amplitude estimation (MLAE) algorithm is a practical solution to the quantum amplitude estimation problem, which has a theoretically quadratic speedup over classical Monte Carlo method. Since MLAE requires no use of the quantum Fourier transformation (QFT), it will be more likely to be widely used in the near future than QFT based algorithms. However, we find that MLAE is not unbiased due to the so-called critical points, which is one of the major causes of its inaccuracy. We propose a random-depth quantum amplitude estimation (RQAE) to avoid critical points. We also do numerical experiments to show that our algorithm is approximately unbiased and outperforms MLAE and other quantum amplitude estimation algorithms.