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The origin of magnetic flux noise in Superconducting Quantum InterferenceDevices with a power spectrum scaling as $1/f$ ($f$ is frequency) has been apuzzle for over 20 years. This noise limits the decoherence time ofsuperconducting qubits. A consensus has emerged that the noise arises fromfluctuating spins of localized electrons with an areal density of$5\times10^{17}$m$^{-2}$. We show that, in the presence of potential disorderat the metal-insulator interface, some of the metal-induced gap states becomelocalized and produce local moments. A modest level of disorder yields theobserved areal density.

Localization of Metal-Induced Gap States at the Metal-Insulator Interface:Origin of Flux Noise in SQUIDs and Superconducting Qubits