Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Sources of noise in niobium-based superconducting quantum circuits

Allison Dove

Published Jan 1, 2014• 2 citations
OpenAlex

Abstract

Quantum computation is a fascinating field that combines novel physics with improvements in computation times and has been rapidly growing in the past few years. Using superconductors to form the qubits has the potential for large-scale computing, if the decoherence inherent in these devices can be understood and reduced. Two-level fluctuators due to defects in the materials are thought to cause changes to the Josephson critical current or the flux through the superconducting loop of a flux qubit, which leads to decoherence in the qubit. Alternatively, defects in the crystal lattice give rise to electron localization which in turn traps spins with random orientations at the substrate/metal interface, again producing decoherence. My work studied the proposed noise mechanisms by using Molecular Beam Epitaxy to fabricate single-crystal niobium-based Josephson junctions. Using RHEED, AFM, and TEM/STEM, I studied the epitaxy of the niobium film at the substrate interface to reduce noise due to crystal defects. I then measured flux noise in these films; the noise in the epitaxial films is lower than the comparative polycrystalline films. Further measurements using ex-situ Josephson junctions and epitaxial niobium loops resulted in the lowest reported flux noise measurements to date. Additionally, EELS measurements made in the course of the STEM analysis of the crystal structure reveal oxygen depletion from the substrate at elevated growth temperatures. This depletion leads to oxygen vacancies in the aluminum oxide substrate, which can in turn lead to charge traps at the substrate/metal interface and hence to decoherence in the qubit. Critical current noise was investigated by changing the oxidation dose of the alumina barrier in more than 50 separate Josephson junctions. Films which were grown with lower oxidation doses have a non-ideal critical current temperature dependence as well as higher critical current noise values, suggesting that insufficient oxygen is being incorporated into these junctions. Finally, I studied the effect of surface cleaning after fabrication for resonators and transmons. Microscopy shows that an oxygen ash and BOE dip together removes all photoresist residue from the chip. Internal-Q measurements do not show a marked improvement due to this cleaning, but the coherence times do improve upon the cleaning step.

Related papers

Material and Interface Engineering Strategies to Mitigate Decoherence in Superconducting Qubits

Dominic P. Goronzy, Anthony McFadden, David A. Garcia Wetten +16 more

While significant strides have been made to increase the coherence time of superconducting qubits, further advancements are essential for realizing scalable quantum computing. Decoherence is often a result of loss and noise stemming from two-level systems and excess quasiparticles, arising due to material defects, fabrication processes, and ambient exposure, particularly at surfaces and interfaces. Our recent efforts to mitigate these decoherence mechanisms have employed a variety of strategies, including low-loss surface encapsulation materials, advanced substrate preparation techniques, modifications to metal film growth, and the development of novel fabrication processes. The structural and chemical properties of materials, surfaces, and interfaces are studied using scanning probe microscopy, electron microscopy, photoelectron spectroscopy, mass spectrometry, and X-ray diffraction, which is correlated to device performance metrics, including superconducting resonator internal quality factor and qubit T1 time. This information is used to identify and understand material sources of loss and their origins in the device fabrication process. Through multi-institution efforts within SQMS we have identified the loss mechanism of interstitial hydrogen in niobium-based devices and shown how standard fabrication processes introduce these hydrides, developing strategies to mitigate their formation.1 Furthermore, we have characterized the metal-substrate interface, including the loss of niobium-silicides formed at that interface, and developed silicon surface treatments that reduce atomic scale roughness and oxygen content at the metal-substrate and Josephson junction interfaces.2-4 By developing the connection between materials properties and the overall performance of superconducting quantum circuitry, we can develop fabrication strategies to mitigate material losses, thus supporting the ongoing efforts to enhance coherence time in superconducting quantum devices. 1. Torres-Castanedo, C. G.*, Goronzy, D. P.*, et al., Adv. Funct. Mater., 2401365 (2024) 2. Lu, X., et al., Phys. Rev. Materials 6, 064402 (2022) 3. Berti, G., Appl. Phys. Lett. 122, 192605 (2023) 4. Kopas, C. J., Goronzy, D. P., et al., arXiv:2408.02863 (2024)

•Sep 23, 2024•0 citations

Optimizing Superconducting Qubits: Insights into Oxides Microstructures

Jin‐Su Oh, Haotian Wu, Lin Zhou

Improving qubit lifetime is essential for fault-tolerant quantum computing. It is widely acknowledged that intricate processing techniques introduce defects at the interfaces and surfaces of superconducting quantum circuits, which can create sources of decoherence. Therefore, a precise understanding of how a material's structure contributes to decoherence is critical for enhancing the performance of superconducting qubits. This talk highlights our recent advancements in understanding surface oxides in resonators and ultrathin aluminum oxide barriers in Josephson junctions (JJs) using transmission electron microscopy and spectroscopy techniques [1-4]. The Superconducting Quantum Materials & Systems Center (SQMS) demonstrated that encapsulating niobium surfaces with a ∼10nm tantalum layer results in 2-5x longer T1​ than bare niobium [2]. Our collaborative investigation shows that this improvement is attributed to tantalum's less lossy surface oxide, which contains fewer sub-oxides than niobium oxide. Moreover, the amorphous Ta2O5 shows a bonding nature closer to crystalline form than amorphous Nb2O5, potentially reducing hydrogen diffusion toward the oxide/metal interface [1, 2]. Moreover, we will briefly discuss our preliminary study of the thin film structure under cryogenic conditions down to 20K, conducted using a liquid helium TEM holder in a Thermo Cs-corrected Titan. We also explored the effect of aluminum deposition rates on aluminum oxide microstructure and qubit lifetime. Although increasing the deposition rate from 0.5 Å/s to 5 Å/s significantly improved oxide layer roughness and thickness variation, the qubits’ coherence remained unchanged. This is likely due to Cooper pairs only tunneling through the thinnest parts of the barrier, making them less affected by the grain boundaries in the thin aluminum films. Additionally, we uncovered a stress-induced grain boundary sliding mechanism, which contributes to short-circuit failures in JJs [4]. Our discovery provides vital insight into oxide microstructure and superconducting qubits’ functionality [5].

Microscopy and Microanalysis•Jul 1, 2025•0 citations

Study of the effects of surface cladding on 3D transmon

Zachary Yoscovits

Quantum computing is a very interesting field, due to the ability of quantum computers to solve many problems much faster than a classical computer. Superconducting qubits are electronic circuits composed of superconducting capacitors, inductors and Josephson junctions, which can implement a physical qubit. However they need improvements in their coherence time to create a viable quantum computing. In this work I study the effect on decoherence caused by two level systems in the native oxide that forms on the surface of qubit. To this end I fabricate 3D transmon qubits using materials grown my molecular beam epitaxy, to which a variety of different surface treatments had been applied. I began by fabricating qubits from niobium/aluminum oxide/niobium trilayers. To this end I developed a self-aligned process for fabricating sub-micron Josephson junctions. This process presented many challenges. During the development of this process, it became clear that niobium was an inferior material for fabricating qubits compared to aluminum. I then switched to making qubits from Aluminum. I began by studying the growth of aluminum on sapphire, and was able to achieve aluminum films with an RMS roughness of 0.2 nm by growing on c-plane sapphire that had been annealed in oxygen at 1100 °C and dipped in BOE. Next I fabricated 3D transmon qubits by adapting the standard shadowmask process for use with MBE. I fabricated qubits with a long in situ oxidation to fully passivate the surface before exposure to air. I also passivated the surface by means of growing co deposited aluminum oxide, and by grown aluminum nitride using a nitrogen plasma source. The coherence times of these qubits were compared to those a control sample that had been exposed to air immediately after growth. Overall it doesn’t appear that cladding the surface changes the coherence time much, however it is difficult to form conclusions with this small sample size. The coated samples appeared to have slightly longer coherence times than the untreated samples, with diffusive oxidation and coating with aluminum oxide providing the largest increase in T1 and diffusive oxidation providing the largest increase in T2.

•Sep 16, 2014•0 citations

Impact of Oxygen Vacancies in Josephson Junction on Decoherence of Superconducting Qubits

Hanqin Bai, Shi-Yao Hou, Mu Lan

Superconducting quantum circuits are promising platforms for scalable quantum computing, where qubit coherence is critically determined by microscopic defects in the oxide tunneling barrier of Josephson junctions. Amorphous Al$_2$O$_3$ is widely used as a barrier material, but under irradiation, oxygen vacancy (V$_O$) defects are readily generated, introducing noise sources that accelerate qubit decoherence. We systematically investigate the structural characteristics and electronic impact of V$_O$ defects in amorphous Al$_2$O$_3$ using first-principles calculations and \textit{ab initio} molecular dynamics. Our results show that both the coordination environment and concentration of V$_O$s strongly influence electrical conductivity. In particular, two- and three-coordinated V$_O$s, unique to the amorphous structure, enhance conductivity more than conventional four-coordinated vacancies. Increasing V$_O$ concentration amplifies conductivity fluctuations, which we link to critical current noise in Josephson junctions. Using a noise model, we estimate that higher V$_O$ densities lead to shorter qubit coherence times. These findings provide insights for radiation-hard design of superconducting quantum devices.

quant-pharXiv:2603.11469•Mar 13, 2026•0 citations

A Josephson junction with h -BN tunnel barrier: observation of low critical current noise

Jifa Tian, Luis A. Jauregui, Christopher D. Wilen +4 more

Abstract Decoherence in quantum bits (qubits) is a major challenge for realizing scalable quantum computing. One of the primary causes of decoherence in qubits and quantum circuits based on superconducting Josephson junctions is the critical current fluctuation. Many efforts have been devoted to suppressing the critical current fluctuation in Josephson junctions. Nonetheless, the efforts have been hindered by the defect-induced trapping states in oxide-based tunnel barriers and the interfaces with superconductors in the traditional Josephson junctions. Motivated by this, along with the recent demonstration of 2D insulator h -BN with exceptional crystallinity and low defect density, we fabricated a vertical NbSe 2 / h -BN/Nb Josephson junction consisting of a bottom NbSe 2 superconductor thin layer and a top Nb superconductor spaced by an atomically thin h -BN layer. We further characterized the superconducting current and voltage ( I – V ) relationships and Fraunhofer pattern of the NbSe 2 / h -BN/Nb junction. Notably, we demonstrated the critical current noise (1/ f noise power) in the h -BN-based Josephson device is at least a factor of four lower than that of the previously studied aluminum oxide-based Josephson junctions. Our work offers a strong promise of h -BN as a novel tunnel barrier for high-quality Josephson junctions and qubit applications.

Journal of Physics Condensed Matter•Sep 14, 2021•8 citations

Magnetic flux noise in SQUIDs and qubits

Steven M. Anton

For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as $S_Phi(f) propto 1/f^alpha$, where $alpha lesssim 1$, 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 noise.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, because $1/f$ 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 $Phisq$ from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, $Phisq$ is proportional to $langleBbf(rbf)^2rangle$, where $Bbf(rbf)$ is the magnetic field generated by a circulating current around the loop and $rbf$ 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 $Phisq$ 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 $Phisq propto R/W$ 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 $Phisq$ is significant---even dominant---in narrow-linewidth loops.To calculate theoretical dephasing rates in qubits, we consider flux noise with a spectral density $S_Phi(f) = A^2/(f/1~hbox{Hz})^alpha$, where $A$ is of the order of 1~$muPhi_0 , hbox{Hz}^{-1/2}$ and $0.6 leq alpha leq 1.2$; $Phi_{0}$ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, our calculations of the dependence of the pure dephasing time $tau_phi$ of Ramsey and echo pulse sequences on $alpha$ for fixed $A$ show that $tau_phi$ decreases rapidly as $alpha$ is reduced. We find that $tau_phi$ is relatively insensitive to the noise bandwidth, $f_1 leq f leq f_2$, for all $alpha$ provided the ultraviolet cutoff frequency $f_2 > 1/tau_phi$. We calculate the ratio $tau_{phi,E} / tau_{phi,R}$ of the echo ($E$) and Ramsey ($R$) sequences, and the dependence of the decay function on $alpha$ and $f_2$. We investigate the case in which $S_Phi(f_0)$ is fixed at the ``pivot frequency'' $f_0 neq 1$~Hz while $alpha$ is varied, and find that the choice of $f_0$ can greatly influence the sensitivity of $tau_{phi,E}$ and $tau_{phi,R}$ 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.

•Jan 1, 2013•0 citations
Quantum computation is a fascinating field that combines novel physics with improvements in computation times and has been rapidly growing in the past few years. Using superconductors to form the qubits has the potential for large-scale computing, if the decoherence inherent in these devices can be understood and reduced. Two-level fluctuators due to defects in the materials are thought to cause changes to the Josephson critical current or the flux through the superconducting loop of a flux qubit, which leads to decoherence in the qubit. Alternatively, defects in the crystal lattice give rise to electron localization which in turn traps spins with random orientations at the substrate/metal interface, again producing decoherence. My work studied the proposed noise mechanisms by using Molecular Beam Epitaxy to fabricate single-crystal niobium-based Josephson junctions. Using RHEED, AFM, and TEM/STEM, I studied the epitaxy of the niobium film at the substrate interface to reduce noise due to crystal defects. I then measured flux noise in these films; the noise in the epitaxial films is lower than the comparative polycrystalline films. Further measurements using ex-situ Josephson junctions and epitaxial niobium loops resulted in the lowest reported flux noise measurements to date. Additionally, EELS measurements made in the course of the STEM analysis of the crystal structure reveal oxygen depletion from the substrate at elevated growth temperatures. This depletion leads to oxygen vacancies in the aluminum oxide substrate, which can in turn lead to charge traps at the substrate/metal interface and hence to decoherence in the qubit. Critical current noise was investigated by changing the oxidation dose of the alumina barrier in more than 50 separate Josephson junctions. Films which were grown with lower oxidation doses have a non-ideal critical current temperature dependence as well as higher critical current noise values, suggesting that insufficient oxygen is being incorporated into these junctions. Finally, I studied the effect of surface cleaning after fabrication for resonators and transmons. Microscopy shows that an oxygen ash and BOE dip together removes all photoresist residue from the chip. Internal-Q measurements do not show a marked improvement due to this cleaning, but the coherence times do improve upon the cleaning step.
While significant strides have been made to increase the coherence time of superconducting qubits, further advancements are essential for realizing scalable quantum computing. Decoherence is often a result of loss and noise stemming from two-level systems and excess quasiparticles, arising due to material defects, fabrication processes, and ambient exposure, particularly at surfaces and interfaces. Our recent efforts to mitigate these decoherence mechanisms have employed a variety of strategies, including low-loss surface encapsulation materials, advanced substrate preparation techniques, modifications to metal film growth, and the development of novel fabrication processes. The structural and chemical properties of materials, surfaces, and interfaces are studied using scanning probe microscopy, electron microscopy, photoelectron spectroscopy, mass spectrometry, and X-ray diffraction, which is correlated to device performance metrics, including superconducting resonator internal quality factor and qubit T1 time. This information is used to identify and understand material sources of loss and their origins in the device fabrication process. Through multi-institution efforts within SQMS we have identified the loss mechanism of interstitial hydrogen in niobium-based devices and shown how standard fabrication processes introduce these hydrides, developing strategies to mitigate their formation.1 Furthermore, we have characterized the metal-substrate interface, including the loss of niobium-silicides formed at that interface, and developed silicon surface treatments that reduce atomic scale roughness and oxygen content at the metal-substrate and Josephson junction interfaces.2-4 By developing the connection between materials properties and the overall performance of superconducting quantum circuitry, we can develop fabrication strategies to mitigate material losses, thus supporting the ongoing efforts to enhance coherence time in superconducting quantum devices. 1. Torres-Castanedo, C. G.*, Goronzy, D. P.*, et al., Adv. Funct. Mater., 2401365 (2024) 2. Lu, X., et al., Phys. Rev. Materials 6, 064402 (2022) 3. Berti, G., Appl. Phys. Lett. 122, 192605 (2023) 4. Kopas, C. J., Goronzy, D. P., et al., arXiv:2408.02863 (2024)
Improving qubit lifetime is essential for fault-tolerant quantum computing. It is widely acknowledged that intricate processing techniques introduce defects at the interfaces and surfaces of superconducting quantum circuits, which can create sources of decoherence. Therefore, a precise understanding of how a material's structure contributes to decoherence is critical for enhancing the performance of superconducting qubits. This talk highlights our recent advancements in understanding surface oxides in resonators and ultrathin aluminum oxide barriers in Josephson junctions (JJs) using transmission electron microscopy and spectroscopy techniques [1-4]. The Superconducting Quantum Materials & Systems Center (SQMS) demonstrated that encapsulating niobium surfaces with a ∼10nm tantalum layer results in 2-5x longer T1​ than bare niobium [2]. Our collaborative investigation shows that this improvement is attributed to tantalum's less lossy surface oxide, which contains fewer sub-oxides than niobium oxide. Moreover, the amorphous Ta2O5 shows a bonding nature closer to crystalline form than amorphous Nb2O5, potentially reducing hydrogen diffusion toward the oxide/metal interface [1, 2]. Moreover, we will briefly discuss our preliminary study of the thin film structure under cryogenic conditions down to 20K, conducted using a liquid helium TEM holder in a Thermo Cs-corrected Titan. We also explored the effect of aluminum deposition rates on aluminum oxide microstructure and qubit lifetime. Although increasing the deposition rate from 0.5 Å/s to 5 Å/s significantly improved oxide layer roughness and thickness variation, the qubits’ coherence remained unchanged. This is likely due to Cooper pairs only tunneling through the thinnest parts of the barrier, making them less affected by the grain boundaries in the thin aluminum films. Additionally, we uncovered a stress-induced grain boundary sliding mechanism, which contributes to short-circuit failures in JJs [4]. Our discovery provides vital insight into oxide microstructure and superconducting qubits’ functionality [5].
Quantum computing is a very interesting field, due to the ability of quantum computers to solve many problems much faster than a classical computer. Superconducting qubits are electronic circuits composed of superconducting capacitors, inductors and Josephson junctions, which can implement a physical qubit. However they need improvements in their coherence time to create a viable quantum computing. In this work I study the effect on decoherence caused by two level systems in the native oxide that forms on the surface of qubit. To this end I fabricate 3D transmon qubits using materials grown my molecular beam epitaxy, to which a variety of different surface treatments had been applied. I began by fabricating qubits from niobium/aluminum oxide/niobium trilayers. To this end I developed a self-aligned process for fabricating sub-micron Josephson junctions. This process presented many challenges. During the development of this process, it became clear that niobium was an inferior material for fabricating qubits compared to aluminum. I then switched to making qubits from Aluminum. I began by studying the growth of aluminum on sapphire, and was able to achieve aluminum films with an RMS roughness of 0.2 nm by growing on c-plane sapphire that had been annealed in oxygen at 1100 °C and dipped in BOE. Next I fabricated 3D transmon qubits by adapting the standard shadowmask process for use with MBE. I fabricated qubits with a long in situ oxidation to fully passivate the surface before exposure to air. I also passivated the surface by means of growing co deposited aluminum oxide, and by grown aluminum nitride using a nitrogen plasma source. The coherence times of these qubits were compared to those a control sample that had been exposed to air immediately after growth. Overall it doesn’t appear that cladding the surface changes the coherence time much, however it is difficult to form conclusions with this small sample size. The coated samples appeared to have slightly longer coherence times than the untreated samples, with diffusive oxidation and coating with aluminum oxide providing the largest increase in T1 and diffusive oxidation providing the largest increase in T2.
Superconducting quantum circuits are promising platforms for scalable quantum computing, where qubit coherence is critically determined by microscopic defects in the oxide tunneling barrier of Josephson junctions. Amorphous Al2_22​O3_33​ is widely used as a barrier material, but under irradiation, oxygen vacancy (VO_OO​) defects are readily generated, introducing noise sources that accelerate qubit decoherence. We systematically investigate the structural characteristics and electronic impact of VO_OO​ defects in amorphous Al2_22​O3_33​ using first-principles calculations and \textit{ab initio} molecular dynamics. Our results show that both the coordination environment and concentration of VO_OO​s strongly influence electrical conductivity. In particular, two- and three-coordinated VO_OO​s, unique to the amorphous structure, enhance conductivity more than conventional four-coordinated vacancies. Increasing VO_OO​ concentration amplifies conductivity fluctuations, which we link to critical current noise in Josephson junctions. Using a noise model, we estimate that higher VO_OO​ densities lead to shorter qubit coherence times. These findings provide insights for radiation-hard design of superconducting quantum devices.
Abstract Decoherence in quantum bits (qubits) is a major challenge for realizing scalable quantum computing. One of the primary causes of decoherence in qubits and quantum circuits based on superconducting Josephson junctions is the critical current fluctuation. Many efforts have been devoted to suppressing the critical current fluctuation in Josephson junctions. Nonetheless, the efforts have been hindered by the defect-induced trapping states in oxide-based tunnel barriers and the interfaces with superconductors in the traditional Josephson junctions. Motivated by this, along with the recent demonstration of 2D insulator h -BN with exceptional crystallinity and low defect density, we fabricated a vertical NbSe 2 / h -BN/Nb Josephson junction consisting of a bottom NbSe 2 superconductor thin layer and a top Nb superconductor spaced by an atomically thin h -BN layer. We further characterized the superconducting current and voltage ( I – V ) relationships and Fraunhofer pattern of the NbSe 2 / h -BN/Nb junction. Notably, we demonstrated the critical current noise (1/ f noise power) in the h -BN-based Josephson device is at least a factor of four lower than that of the previously studied aluminum oxide-based Josephson junctions. Our work offers a strong promise of h -BN as a novel tunnel barrier for high-quality Josephson junctions and qubit applications.
For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as SPhi(f)propto1/falphaS_Phi(f) propto 1/f^alphaSP​hi(f)propto1/falpha, where alphalesssim1alpha lesssim 1alphalesssim1, 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 noise.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 alphaalphaalpha 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, because 1/f1/f1/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 PhisqPhisqPhisq from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, PhisqPhisqPhisq is proportional to langleBbf(rbf)2ranglelangleBbf(rbf)^2ranglelangleBbf(rbf)2rangle, where Bbf(rbf)Bbf(rbf)Bbf(rbf) is the magnetic field generated by a circulating current around the loop and rbfrbfrbf 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 PhisqPhisqPhisq 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 PhisqproptoR/WPhisq propto R/WPhisqproptoR/W in the limit where the loop radius RRR is much greater than the linewidth WWW. We further show that the previously neglected contribution of edge spins to PhisqPhisqPhisq 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 hboxHz)alphaS_Phi(f) = A^2/(f/1~hbox{Hz})^alphaSP​hi(f)=A2/(f/1 hboxHz)alpha, where AAA is of the order of 1~muPhi0,hboxHz−1/2muPhi_0 , hbox{Hz}^{-1/2}muPhi0​,hboxHz−1/2 and 0.6leqalphaleq1.20.6 leq alpha leq 1.20.6leqalphaleq1.2; Phi0Phi_{0}Phi0​ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, our calculations of the dependence of the pure dephasing time tauphitau_phitaup​hi of Ramsey and echo pulse sequences on alphaalphaalpha for fixed AAA show that tauphitau_phitaup​hi decreases rapidly as alphaalphaalpha is reduced. We find that tauphitau_phitaup​hi is relatively insensitive to the noise bandwidth, f1leqfleqf2f_1 leq f leq f_2f1​leqfleqf2​, for all alphaalphaalpha provided the ultraviolet cutoff frequency f2>1/tauphif_2 > 1/tau_phif2​>1/taup​hi. We calculate the ratio tauphi,E/tauphi,Rtau_{phi,E} / tau_{phi,R}tauphi,E​/tauphi,R​ of the echo (EEE) and Ramsey (RRR) sequences, and the dependence of the decay function on alphaalphaalpha and f2f_2f2​. We investigate the case in which SPhi(f0)S_Phi(f_0)SP​hi(f0​) is fixed at the ``pivot frequency'' f0neq1f_0 neq 1f0​neq1~Hz while alphaalphaalpha is varied, and find that the choice of f0f_0f0​ can greatly influence the sensitivity of tauphi,Etau_{phi,E}tauphi,E​ and tauphi,Rtau_{phi,R}tauphi,R​ to the value of alphaalphaalpha.Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research.