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

• URL: http://arxiv.org/abs/2206.06392v1
• Date: Mon, 13 Jun 2022 18:00:09 GMT
• Title: An iterative quantum-phase-estimation protocol for near-term quantum hardware
• Authors: Joseph G. Smith, Crispin H. W. Barnes and David R. M. Arvidsson-Shukur
• Abstract summary: entanglement-free protocols have been developed, which achieve a $mathcalO left[ sqrtlog (log N_textrmtot) / N_textrmtot right]$ mean-absolute-error scaling. Here, we propose a new two-step protocol for near-term phase estimation, with an improved error scaling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $N_{\textrm{tot}}$.

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