For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as
SPhi(f)propto1/falpha, where
alphalesssim1, 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
PhisqproptoR/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
SPhi(f)=A2/(f/1 hboxHz)alpha, where
A is of the order of 1~
muPhi0,hboxHz−1/2 and
0.6leqalphaleq1.2;
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
tauphi of Ramsey and echo pulse sequences on
alpha for fixed
A show that
tauphi decreases rapidly as
alpha is reduced. We find that
tauphi is relatively insensitive to the noise bandwidth,
f1leqfleqf2, for all
alpha provided the ultraviolet cutoff frequency
f2>1/tauphi. We calculate the ratio
tauphi,E/tauphi,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
SPhi(f0) is fixed at the ``pivot frequency''
f0neq1~Hz while
alpha is varied, and find that the choice of
f0 can greatly influence the sensitivity of
tauphi,E and
tauphi,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.
Impurity spins randomly distributed at the surfaces and interfaces of superconducting wires are known to cause flux noise in superconducting quantum interference devices (SQUIDs), providing a dominant mechanism for decoherence in flux-tunable superconducting qubits. While flux noise is well characterized experimentally, the microscopic model underlying spin dynamics remains a great puzzle. The main problem is that first-principles theories based on an integration of the quantum Heisenberg equations of motion for interacting spins are too computationally expensive to capture spin diffusion over large length scales, hindering comparisons between microscopic models and experimental data. In contrast, third-principles approaches lump spin dynamics into a single phenomenological spin-diffusion operator $D{\ensuremath{\nabla}}^{2}$ that is not able to describe the quantum noise regime and connect to microscopic models and different disorder scenarios such as spin clusters. 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 superconducting wire, with paramagnon-paramagnon interactions leading to spin diffusion, and interactions between paramagnons and other degrees of freedom such as phonons, electrons, and two-level systems leading to spin energy relaxation. At high frequency $\ensuremath{\omega}$, we obtain an upper bound for flux noise, showing that the (super)Ohmic noise observed in experiments is not originating from interacting spin impurities. We apply the method to Heisenberg models in two-dimensional square lattices with a random distribution of vacancies, with nearest-neighbor spins coupled by a constant exchange. Explicit numerical calculations of flux noise show that it follows the observed power law $A/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$, with amplitude
A and exponent $\ensuremath{\alpha}$ depending on temperature and inhomogeneities such as spatial confinement and disorder. These results are compared to experiments in niobium and aluminum devices. The method establishes a connection between flux noise experiments and microscopic Hamiltonians with the goal of identifying relevant microscopic mechanisms and guiding strategies for reducing flux noise.
Superconducting quantum devices, from qubits and magnetometers to dark matter detectors, are influenced by magnetic flux noise originating from paramagnetic surface defects and impurities. These spin systems can feature complex dynamics, including a Berezinskii-Kosterlitz-Thouless transition, that depend on the lattice, interactions, external fields, and disorder. However, the disorder included in typical models is not materials-specific, diminishing the ability to accurately capture measured flux noise phenomena. We present a first principles-based simulation of a spin lattice consisting of paramagnetic O
2 molecules on an Al
2O
3 surface, a likely flux noise source in superconducting qubits, to elucidate opportunities to mitigate flux noise. We simulate an ensemble of surface adsorbates with disordered orientations and calculate the orientation-dependent exchange couplings using density functional theory. Thus, our spin simulation has no free parameters or assumed functional form of the disorder, and captures correlation in the defect landscape that would appear in real systems. We calculate a range of exchange interactions between electron pairs, with the smallest values, 0.016 meV and -0.023 meV, being in the range required to act as a two-level system and couple to GHz resonators. We calculate the flux noise frequency, temperature, and applied external magnetic field dependence, as well as the susceptibility-flux noise cross-correlation. Calculated trends agree with experiment, demonstrating that a surface harboring paramagnetic adsorbates arranged with materials-specific disorder and interactions captures the various properties of magnetic flux noise observed in superconducting circuits. In addition, we find that an external electric field can tune the spin-spin interaction strength and reduce magnetic flux noise.
The performance of SQUIDs and superconducting qubits based on magnetic flux is degraded by the presence of magnetic flux noise with a spectral density scaling approximately inversely with frequency. It is generally accepted that the noise arises from the random reversal of spins on the surface of the superconductors. We introduce a numerical method of calculating the mean square flux noise from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, is proportional to 〈 B ( r ) 2 〉, 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 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 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 is significant—even dominant—in narrow-linewidth loops.
The spectral density S(Φ)(f) = A(2)/(f/1 Hz)(α) of magnetic flux noise in ten dc superconducting quantum interference devices (SQUIDs) with systematically varied geometries shows that α 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. These results are incompatible with a model based on the random reversal of independent, surface spins.
This paper is the third in a series of long-form summaries, one for each volume of a three-volume monograph on the inter-site field theory of 1/f noise. It summarizes the third and concluding volume, A Field Theory of Superconducting Fluctuations and Circuit Dissipation (Self-published, KDP, ASIN B0HLMS97ZZ), and builds on the classical and quantum papers of the series (10.5281/zenodo.22942255 and 10.5281/zenodo.22981164). It is written to be cited. Energy relaxation, dielectric loss, critical-current noise and flux noise in superconducting circuits are usually treated as separate problems. The standard tunneling model assumes a flat distribution of two-level-system parameters but does not supply a microscopic generator for it. Here the isolated-defect picture is replaced by a continuous, fluctuating electrostatic manifold spanning the tunnel barrier and its interfaces. Morse topology identifies the double wells of the standard tunneling model as rank-1 saddles, and the vector central limit theorem gives a Gaussian density of states whose width is fixed in closed form by the structural correlation length and the barrier thickness. From this single construction the paper derives: critical-current noise with 1/A area scaling, and the dielectric loss tangent, as longitudinal and transverse projections of one field; transmon energy relaxation through capacitive participation ratios; a geometric cross-correlation between Josephson-energy and charging-energy fluctuations that suppresses pure dephasing; a millikelvin quantum floor from soft-phonon bremsstrahlung under non-cancellation phase agitation; SQUID flux noise from a coupled surface-spin manifold; Differential Josephson Spectroscopy (DJS), an operando probe of barrier height and disorder width. Eleven principal results are stated with their assumptions and numbered for citation, together with twelve testable predictions (P1–P12) and their failure conditions. Structural results depend on stated assumptions and not on fitted constants. Quantitative results, such as the roughly 31 μs Ramsey dephasing floor for canonical planar transmons, depend on material inputs and are presented as order-of-magnitude statements.