| For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as S phi ( f) ∝ 1/falpha where a≲1, has been known to limit the low-frequency performance of dc superconducting quantum interference devices (SQUIDs). In recent years, experiments indicate that this same noise persists to frequencies up to 1 GHz and is a dominant source of dephasing in flux-sensitive superconducting quantum bits (qubits). Thus, the reduction of flux noise presents a major hurdle towards the successful realization of scalable quantum computers that are based on flux-based qubits. In this thesis, we present experimental measurements, theoretical analyses, and numerical simulations that support a more detailed understanding of both the microscopic and macroscopic properties of flux n.;Our experimental work begins with flux noise measurements of a large number of SQUIDs in the temperature range from 0.1 K to 4 K. We report on measurements of ten SQUIDs with systematically varied geometries and show that alpha increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID washer. We show that these results are incompatible with a model based on the random reversal of independent, spins that are located at the surface of the SQUID washer.;In the course of our flux noise measurements, we became aware of a spurious contribution to low-frequency critical current noise in Josephson junctions normally attributed to charge trapping in the barrier arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. By computing cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions, we show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, becuase 1/ f critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.;Next, we introduce a numerical method of calculating the mean square flux noise F2 from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, F2 is proportional to Br2 , where B(r) is the magnetic field generated by a circulating current around the loop and r varies over the loop surface. By discretizing the loop nonuniformly, we efficiently and accurately compute the current distribution and resulting magnetic field, which may vary rapidly across the loop. We use this method to compute F2 in a number of scenarios in which we systematically vary physical parameters of the loop. We compare our simulations to an earlier analytic result predicting that F2 ∝ R/W in the limit where the loop radius R is much greater than the linewidth W. We further show that the previously neglected contribution of edge spins to F2 is significant---even dominant---in narrow-linewidth loops.;To calculate theoretical dephasing rates in qubits, we consider flux noise with a spectral density Sphi( f) = A2/ (f/1 Hz) alpha, where A is of the order of 1 muphi 0 Hz--1/2 and 0.6 ≤ alpha ≤ 1.2; applied flux, our calculations of the dependence of the pure dephasing time tau &phis; Ramsey and echo pulse sequences on alpha for fixed A show that tau&phis; decreases rapidly as alpha is reduced. We find that tau&phis; is relatively insensitive to the noise bandwidth, f1 ≤ f ≤ f2 for all alpha provided the ultraviolet cutoff frequency f2 > 1/tau&phis;. We calculate the ratio tau&phis;,E/tau &phis;, R of the echo (E) and Ramsey (R) sequences, and the dependence of the decay function on alpha and f2. We investigate the case in which S phi(f0) is fixed at the "pivot frequency" f0 ≠ 1 Hz while alpha is varied, and find that the choice of f 0 can greatly influence the sensitivity of tau&phis;, E and tau&phis;, R to the value of alpha.;Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research. |
