An adaptive quantum-phase-estimation protocol for NISQ hardware

Given N_tot applications of a unitary operation with an unknown phase, a phase-estimation protocol based on a large-scale fault-tolerant quantum system can reduce the standard deviation of an estimate of the phase from scaling like Ο(1/√N_tot) to scaling like Ο(1/N_tot). Due to the limited resources available to near-term quantum devices, noiseless entanglement-free protocols have been developed, achieving a Ο(log N_tot / N_tot) mean-absolute-error scaling. Here, we propose an adaptive Bayesian protocol for near-term phase estimation, which shows high performance in the presence of noise. Our protocol’s mean absolute error scales as Ο(√(log(log N_tot)) / N_tot) in the noiseless limit and achieves the theoretically optimal scaling when noise is considered. Furthermore, we demonstrate that our protocol can outperform the asymptotically optimal quantum-phase estimation algorithm for realistic values of N_tot.