Measurement of the Noise Spectrum Using a Multiple-Pulse Sequence

A method is proposed for obtaining the spectrum for noise that causes the phase decoherence of a qubit directly from experimentally available data. The method is based on a simple relationship between the spectrum and the coherence time of the qubit in the presence of a pi pulse sequence. The relationship is found to hold for every system of a qubit interacting with the classical-noise, bosonic, and spin baths.