Low-depth amplitude estimation on a trapped-ion quantum computer

Amplitude estimation (AE) is a fundamental quantum algorithmic primitive that enables computers to achieve quadratic speedups for large class of statistical problems, including Monte Carlo methods. Recent works have succeeded in somewhat reducing the necessary resources AE by trading off some speedup lower depth circuits, but high quality qubits are still needed demonstrating such algorithms. Here, we report results an experimental demonstration on state-of-the-art trapped ion computer. was used estimate inner product randomly chosen four-dimensional unit vectors, and low-depth algorithms were based maximum likelihood (MLE) Chinese remainder theorem (CRT) techniques. Significant improvements accuracy observed MLE approach when deeper circuits taken into account, with more than 90 two-qubit gates 60, achieving mean additive error order ${10}^{\ensuremath{-}2}$. The CRT found provided accurate estimates many data points less robust against noise average. Last, analyze two take account specifics hardware further improve results.