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

Abstract

Given $N_{\text{tot}}$ 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 $\mathcal{O}\left[1/\sqrt{N_{\text{tot}}}\right]$ to $\mathcal{O}\left[1/N_{\text{tot}}\right]$. Owing to the limited resources available to near-term quantum devices, entanglement-free protocols have been developed, which achieve a $\mathcal{O}\left[\log (N_{\text{tot}})/N_{\text{tot}}\right]$ {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 $\mathcal{O}\left[\sqrt{\log (\log N_{\text{tot}})}/N_{\text{tot}}\right]$. 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 $N_{\text{tot}}$.