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A qubit subjected to pure dephasing due to classical Gaussian noise can beturned into a spectrometer of this noise by utilizing its readout underproperly chosen dynamical decoupling (DD) sequences to reconstruct the powerspectral density of the noise. We review the theory behind this DD-based noisespectroscopy technique, paying special attention to issues that arise when theenvironmental noise is non-Gaussian and/or it has truly quantum properties.While we focus on the theoretical basis of the method, we connect the discussedconcepts with specific experiments and provide an overview of environmentalnoise models relevant for solid-state based qubits, including quantum-dot basedspin qubits, superconducting qubits, and NV centers in diamond.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling