Random Pulse Sequences for Noise Spectroscopy

Qubit noise spectroscopy is an important tool for experimental investigations of open quantum systems. However, conventional noise spectroscopy techniques are time-consuming, because they require repeated measurements of the noise spectral density S(ω) at different frequencies ω. Here we describe an alternative method for quickly and approximately characterizing S(ω). This method uses random pulse sequences, with carefully-controlled correlations among the pulses, to measure arbitrary linear functions of S(ω). This method has many applications. We can do parametric estimation of noise spectra and learning an effective description of the environment, such as the 1-D chain representation. We also develop several compressed sensing protocals to characterizing noise spectra that consist of a few isolated peaks. We illustrate these applications by simulations on quantum dots and superconducting qubits.