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

Abstract

Given N tot applications of a unitary operation with an unknown phase θ , a large-scale fault-tolerant quantum system can reduce an estimate’s error scaling from O (cid:2) 1 / √ N tot (cid:3) to O [1 /N tot ]. Owing to the limited resources available to near-term quantum devices, entanglement-free protocols have been developed, which achieve a O [log( N tot ) /N tot ] 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 θ , within θ ’s parameter range. The second step iteratively hones in on one of these estimates. Our protocol’s mean absolute error scales as O (cid:104)(cid:112) log(log N tot ) /N tot (cid:105) . 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 tot .