Superconducting quantum interference devices (SQUIDs) show great promise as quantum bits (qubits) but continue to be hindered by flux noise. The flux noise power spectra of SQUIDs go as 1/f^α, where α is the temperature-dependent noise exponent. Experiments find 0.5 ≲ α ≲ 1. Furthermore, experiments find that the noise power spectra versus frequency at different temperatures pivot about or cross at a common point which is different for each SQUID. To try to better understand the results and motivated by experimental evidence that magnetic moments on the surface of SQUIDs produce flux noise, we have carried out and here present the results of Monte Carlo simulations of various spin systems on 2D lattices. We find that only spin glasses produce α ∼ 1 at low temperature. We find that aliasing of the noise power spectra at high frequencies can lead to spectral pivoting if the knee is in proximity to a knee at a slightly lower frequency. We show that the pivot frequency depends on how often the magnetization is recorded and the method of how lattice sites are selected for orientation: choosing every site once or choosing sites at random. The spectral pivoting that occurs in our simulations is due to aliasing and does not explain the spectral pivoting of experiments.

Silicon quantum dot qubits show great promise but suffer from charge noise with a 1/f^α spectrum, where f is frequency and α ∼ 1. It has recently been proposed that 1/f^α noise spectra can emerge from a few thermally activated two-level fluctuators in the presence of sub-bath temperature fluctuations associated with a two-dimensional electron gas (2DEG). We investigate this proposal by doing Monte Carlo simulations. In one set of simulations, we model a two-level fluctuator as an anisotropic Heisenberg spin with a barrier to spin re-orientations in a bath with a fluctuating temperature. In another set of simulations, the two-level fluctuator is a single Ising spin in a bath with a fluctuating temperature. We find that to obtain noise with a 1/f^α spectrum with α ∼ 1 down to low frequencies, the duration of temperature fluctuations must be comparable to the inverse of the lowest frequency at which the noise is measured. This result is consistent with an analytic calculation in which the fluctuator is a two-state system with dynamics governed by time-dependent switching rates. In this case we find that the noise spectrum follows a Lorentzian at frequencies lower than the inverse of the average duration of the lowest switching rate. We then estimate relaxation times of thermal fluctuations by considering thermal diffusion in an electron gas in a confined geometry. We conclude that temperature fluctuations in a 2DEG sub-bath would require an unphysically long duration to be consistent with experimental measurements of 1/f-like charge noise in quantum dots at frequencies extending well below 1 Hz.

Charge noise in quantum dots has been observed to have a 1/f spectrum. We propose a model in which a pair of quantum dots are coupled to a 2D bath of fluctuators that have electric dipole moments and that interact with each other, i.e., with the other fluctuators. These interactions are primarily via the elastic strain field. We use 2D nearest-neighbor Ising spin glass to represent these elastic interactions and to simulate the dynamics the bath of electric dipole fluctuators in the presence of a ground plane representing metal gates above the oxide layer containing the fluctuators. We calculate the resulting fluctuations in the electric potential at the two quantum dots that lie below the oxide layer. We find that 1/f electric potential noise spectra at the quantum dots and cross correlation in the noise between the two quantum dots are in qualitative agreement with experiment.