Magnetic fluctuation from oxygen deficiency centers on the SiO$_2$ surface

The magnetic stability of oxygen deficiency centers on the surface of {\alpha}-quartz is investigated with first- principles calculations to understand their role in contributing to magnetic flux noise in superconducting qubits (SQs) and superconducting quantum interference devices (SQUIDs) fabricated on amorphous silica substrates. Magnetic defects on the substrate are likely responsible for some of the 1/f noise that plagues these systems. Dangling-bonds associated with three-coordinated Si atoms allow electron density transfer between spin up and down channels, resulting in low energy magnetic states. Such under-coordinated Si defects are common in both stoichiometric and oxygen deficient silica and quartz and are a probable source of magnetic flux fluctuations in SQs and SQUIDs.