Amplitude Estimation without Phase Estimation

This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm which consists of many controlled amplification operations followed by the quantum Fourier transform. The whole procedure is however hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to employ the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup yet with reasonable circuit length.