Abstract : Qubit dephasing is governed by low-frequency noise in the bias parameters that control the energy separation between the qubit states. It has been shown that dephasing in phase and flux qubits is dominated by an excess low frequency magnetic flux noise with a 1/f power spectrum and magnitude at 1 Hz of order 1 microPhi0/sqrt(Hz). Recent experiments by McDermott et al. provide clear evidence for the existence of unpaired magnetic states on the surfaces of superconducting thin film devices; it is now believed that fluctuations of these surface spin states are the source of the ubiquitous 1/f flux noise. However, the microscopic mechanism that drives fluctuations of these spins is not understood; moreover, there is no clear path to reducing the flux noise magnitude. This program is devoted to a systematic investigation of magnetic surface defects in SQUIDs and phase qubits. Measurements of surface spin susceptibility and susceptibility noise will yield valuable clues about the microscopic nature of the magnetic fluctuators, and shed light on interactions between defects. The role of qubit loop geometry on flux noise magnitude and dephasing will be explored in detail. The experiments will guide theoretical efforts to develop improved models for flux noise.
Low-frequency noise caused by critical-current fluctuations in Josephson junctions can lead to substantial, measurement-induced dephasing in superconducting qubits. The purpose of this work is to measure this noise as a function of temperature and to simulate its effect on the measurement dynamics associated with superconducting qubits. In Nb trilayer junctions we measure the noise power at 1 Hz down to 10 mK and verify a T2 dependence for T > 1 K, below which we observe a flattening of the noise magnitude versus temperature. In Al trilayer junctions we measure the critical-current noise power at 1 Hz from 10 mK to 1.4 K and find no dependence on temperature over this range. Possible reasons for the deviation from a T2 dependence are explored, including heating and sample quality. Simulations of the effect of 1/f noise are performed to examine the consequence of using different qubit sampling methods on expected dephasing times. Using the two sampling methods, we can probe the spectral nature and possible source of the dominant noise in a qubit.
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.
Critical current fluctuations with a 1∕f spectral density (f is frequency) are potentially a limiting source of intrinsic decoherence in superconducting quantum bits (qubits) based on Josephson tunnel junctions. Prior measurements of this noise were made at nonzero voltages whereas qubits are operated in the zero voltage state. We report measurements of 1∕f noise in a dc superconducting quantum interference device first, coupled to a resonant tank circuit and operated in a dispersive mode at zero voltage, and, second, operated conventionally with a current bias in the voltage regime. Both measurements yield essentially the same magnitude of critical current 1∕f noise.
A general method for directly measuring the low-frequency flux noise (below 10 Hz) in compound Josephson-junction superconducting flux qubits has been used to study a series of 85 devices of varying design. The variation in flux noise across sets of qubits with identical designs was observed to be small. However, the levels of flux noise systematically varied between qubit designs with strong dependence upon qubit wiring length and wiring width. Furthermore, qubits fabricated above a superconducting ground plane yielded lower noise than qubits without such a layer. These results support the hypothesis that local impurities in the vicinity of the qubit wiring are a key source of low-frequency flux noise in superconducting devices.
We compute the decoherence caused by
1∕f fluctuations at low frequency
f in the critical current
I0 of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ scales as ${I}_{0}∕\ensuremath{\Omega}\ensuremath{\Lambda}{S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$, where $\ensuremath{\Omega}∕2\ensuremath{\pi}$ is the energy-level splitting frequency,
SI0(1Hz) is the spectral density of the critical-current noise at
1Hz, and $\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{\mid}{I}_{0}d\ensuremath{\Omega}∕\ensuremath{\Omega}d{I}_{0}\ensuremath{\mid}$ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time
t scales as $\mathrm{exp}(\ensuremath{-}{t}^{2}∕2{\ensuremath{\tau}}_{\ensuremath{\phi}}^{2})$ when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in
I0 and area
A, and show that their values of
SI0(1Hz) scale to within a factor of 3 of $[144{({I}_{0}∕\ensuremath{\mu}\mathrm{A})}^{2}∕(\mathcal{A}∕\ensuremath{\mu}{\mathrm{m}}^{2})]{(\mathrm{pA})}^{2}∕\mathrm{Hz}$ at
4.2K. We empirically extrapolate
SI01∕2(1Hz) to lower temperatures using a scaling
T(K)∕4.2. Using this result, we find that the predicted values of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ at
100mK range from $0.8\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, and are usually substantially longer than values measured experimentally at lower temperatures.