Simulations of Magnetic Noise in Classical XY and Heisenberg Spin Models*

Superconducting qubits show great promise but continue to be plagued by flux noise. Experiments show that surface spins are the source of this flux noise, and the noise has a power spectral density of the form 1/f^α with the noise exponent α~1. Experiments also provide evidence for ferromagnetic exchange. We investigate to what extent ferromagnetic exchange is consistent the observed flux noise exponents. With input from density functional theory calculations of magnetic impurities, we present the results of Monte Carlo simulations of the magnetic noise produced by coupled classical XY and Heisenberg spins in 2D lattices. We find the parameters of the models that result in a noise exponent near 1.