  Impurity spins randomly distributed at the surfaces and interfaces of
superconducting wires are known to cause flux noise in Superconducting Quantum
Interference Devices, providing a mechanism for decoherence in superconducting
qubits. While flux noise is well characterised experimentally, the microscopic
model underlying spin dynamics remains unknown. First-principles theories are
too computationally expensive to capture spin diffusion over large length
scales, third-principles approaches lump spin dynamics into a single
phenomenological spin-diffusion operator that is not able to describe the
quantum noise regime and connect to microscopic models and disorder scenarios.
Here we propose an intermediate "second principles" method to describe general
spin dissipation and flux noise in the quantum regime. It leads to the
interpretation that flux noise arises from the density of paramagnon
excitations at the edge of the wire, with paramagnon-paramagnon interactions
leading to spin diffusion, and interactions between paramagnons and other
degrees of freedom leading to spin energy relaxation. At high frequency we
obtain an upper bound for flux noise, showing that the (super)Ohmic noise
observed in experiments does not originate from interacting spin impurities. We
apply the method to Heisenberg models in two dimensional square lattices with
random distribution of vacancies and nearest-neighbour spins coupled by
constant exchange. Numerical calculations of flux noise show that it follows
the observed power law $A/\omega^{\alpha}$, with amplitude $A$ and exponent
$\alpha$ depending on temperature and inhomogeneities. These results are
compared to experiments in niobium and aluminium devices. The method
establishes a connection between flux noise experiments and microscopic
Hamiltonians identifying relevant microscopic mechanisms and guiding strategies
for reducing flux noise.
