An iterative quantum-phase-estimation protocol for near-term quantum hardware

TL;DR

This paper introduces a two-step iterative quantum phase estimation protocol tailored for near-term quantum hardware, achieving improved error scaling and reduced circuit depth compared to existing entanglement-free methods.

Contribution

The authors develop a novel two-step iterative protocol that enhances phase estimation accuracy and efficiency on near-term quantum devices, outperforming previous entanglement-free approaches.

Findings

Achieves mean absolute error scaling as √(log(log N))/N

Reduces circuit depth and constant factors compared to prior methods

Can outperform asymptotically optimal algorithms for realistic N_{tot}

Abstract

Given $N_{\textrm{tot}}$ applications of a unitary operation with an unknown phase $\theta$, a large-scale fault-tolerant quantum system can {reduce} an estimate's {error} scaling from $\mathcal{O} \left[ 1 / \sqrt{N_{\textrm{tot}}} \right]$ to $\mathcal{O} \left[ 1 / {N_{\textrm{tot}}} \right]$. Owing to the limited resources available to near-term quantum devices, entanglement-free protocols have been developed, which achieve a $\mathcal{O} \left[ \log(N_{\textrm{tot}}) / N_{\textrm{tot}} \right]$ {mean-absolute-error} scaling. Here, we propose a new two-step protocol for near-term phase estimation, with an improved {error} scaling. Our protocol's first step produces several low-{standard-deviation} estimates of $\theta $, within $\theta$'s parameter range. The second step iteratively hones in on one of these estimates. Our protocol's {mean absolute error} scales as $\mathcal{O} \left[ \sqrt{\log (\log N_{\textrm{tot}})} / N_{\textrm{tot}} \right]$. Furthermore, we demonstrate a reduction in the constant scaling factor and the required circuit depths: our protocol can outperform the asymptotically optimal quantum-phase estimation algorithm for realistic values of $N_{\textrm{tot}}$.