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.
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.
We present measurements of 1/f frequency noise in both linear and Josephson-junction-embedded superconducting aluminum resonators in the low power, low temperature regime—typical operating conditions for superconducting qubits. The addition of the Josephson junction does not result in additional frequency noise, thereby placing an upper limit for fractional critical current fluctuations of 1×10−8 (1/Hz) at 1 Hz for sub-micron, shadow evaporated junctions. These values imply a minimum dephasing time for a superconducting qubit due to critical current noise of 40–1400 μs depending on qubit architecture. Occasionally, at temperatures above 50 mK, we observe the activation of individual fluctuators which increase the level of noise significantly and exhibit Lorentzian spectra.
Superconducting qubit circuits require high quality low critical current density Josephson tunnel junctions. We have developed high quality epitaxial NbN/AlN/NbN tunnel junctions with critical current density, Jc, ranging from as low as a few A/cm2to a few tens of kA/cm2. In this work, we measured current-voltage characteristics for junctions with a Jc~ 32 A/cm2in the temperature range from 17 mK to above 6.7 K. All the junctions are in good quality and have a high gap voltage (>; 5.5 mV). We found that the junctions' sub-gap resistances were temperature dependent above 2.5 K and saturated at temperatures below 2.5 K. A junction sub-gap leakage current Irof about 23 pA was measured. The voltage noise power spectral density for 3 junctions with different sizes has been measured at the base temperature of 17 mK with the junctions biased above the gap voltage. The spectral densities clearly show 1/fbehavior at low frequency and are proportional to the junction's linear dimension.
We have measured the low-frequency noise in the critical current Ic of six dc superconducting quantum interference devices (SQUIDs) with resistively shunted Nb–NbOx–PbIn Josephson junctions in the temperature range T=0.09–4.2K. Each device is voltage biased, the applied flux is an integer number of flux quanta, and the current fluctuations are measured with a second dc SQUID. At low frequencies f, there is a component of the power spectrum of the critical current fluctuations given approximately by SIc(f)=CIc2T2∕Af, where A is the area of both junctions, and C≈(3.9±0.4)×10−23m2∕K2. For quantum bits based on Josephson junctions, the scaling of SIc(f) with T2 implies that the dephasing time limited by critical current l∕f noise should scale as 1∕T for temperatures down to at least 0.09K.
We measured the low-frequency-voltage noise properties of a small-sized stack of intrinsic Josephson junctions formed on the surface of a cleaved Bi2Sr2CaCu2Oy (Bi-2212) single crystal, containing a few intrinsic Josephson junctions. A stack with an area of 2×2μm was fabricated by electron-beam lithography and argon-ion-milling. The current–voltage (I–V) characteristics along the c-axis direction of the stack were measured by a three-terminal method. The stack showed (I–V) and dV∕dI-V curves without backbending due to heating effects. Five discrete resistive branches with hysteresis were observed in the low-voltage region of these curves. The measured noise-voltage spectral density SV(f) had a 1∕f dependence on frequency. We estimated the magnitude of the 1∕f noise parameter η from SV(f) in a Bi-2212 stack and found that above the sum-gap voltage in a small-sized stack η was almost the same as that for low-Tc Nb∕Al+AlOx∕Nb high-quality tunnel junctions.