We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as $\ensuremath{\sim}10%$ of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic
1/f noise spectra with a roll-off to
1/f2, providing independent validation of our theoretical insights.
Abstract A scheme is proposed for achieving robust population inversion in five‐level systems by means of composite pulses. An example of such a system consists of the magnetic sublevels with angular momenta and . Through elaborately constructing the relative phases of pulse pairs, the composite sequences perform well in suppressing the uncorrelated pulse area errors. In particular, the five pulse‐pair sequence possesses good robustness and a short evolution time. The composite sequences are further designed to compensate for a single type of pulse area errors to any desired order. This work provides a high‐efficiency way for robust quantum state manipulation in five‐level systems.