Random Pulse Sequences for Qubit Noise Spectroscopy

Qubit noise spectroscopy is an important tool in experimental investigations of quantum information processors and open quantum systems. However, conventional noise spectroscopy techniques are time-consuming, because they require repeated measurements of the noise spectral density S(w) at different frequencies w. Here we describe an alternative method for quickly and approximately characterizing S(w). This method uses random pulse sequences, with carefully-controlled correlations among the pulses, in order to measure arbitrary linear functionals of S(w). This method has several applications, such as efficient characterization of noise spectra that consist of a few isolated peaks (via compressed sensing), parametric estimation of Lorentzian noise spectra, and learning effective descriptions of the environment (such as 1-D chain representations).