Session Z29: Focus Session: Superconducting Qubits: Noise and Anomalous Temperature

Measurement-induced qubit state mixing from upconverted low frequency noise

We observe readout-induced qubit state mixing in a flux-tunable transmon qubit coupled to a planar resonator. Our results indicate that dephasing noise at the qubit-cavity detuning frequency $\Delta$ is upconverted by photons in the readout cavity, causing spurious qubit state transitions in agreement with theory [1]. Using a superconducting parametric amplifier to perform continuous high-fidelity qubit measurement, we characterize the transition rate dependence on cavity photon population and the intensity of added low frequency noise injected from a broadband fast flux excitation line. From the remnant excitation rate in the absence of added noise, we extract a noise spectral density at frequencies $\sim$ 1 GHz. We also measure the noise spectral density from 0.02-0.5 Hz and 1-20 MHz using Ramsey fringes and Rabi oscillations, respectively. Postulating that flux noise is the dominant source of dephasing in our qubit, we fit the measured noise to a $1/f^\alpha$ power law, finding a slope $\alpha=0.6$ and amplitude $(1.4\mu\Phi_0)^2$/Hz at 1 Hz. These values are in agreement with other measurements of low-frequency flux noise. Our results suggest that 1/f flux noise persists to GHz frequencies. \\[4pt] [1] Boissonneault et al., PRA 79, 013819 (2009).   

1/f Noise of Josephson Tunnel Junction Embedded Microwave Resonators at Single Photon Energies and Millikelvin Temperatures

We present measurements of the 1/f frequency noise of superconducting aluminum lumped and distributed element resonators in the low power, low temperature operating regime characteristic of superconducting qubits. A comparison was made between these devices and similar co-fabricated linear resonators to infer the level of critical current noise associated with the tunnel junctions. At 25 mK and in the single photon regime, the observed frequency fluctuations of junction embedded and linear resonators were comparable. Attributing all the observed noise to critical current fluctuations, we report an upper bound for 1/f critical current fluctuations in 0.5-2 $\mu$A junctions of 3 x $10^{-8}(1/\sqrt{Hz})$ at 1 Hz. We note that for some samples we observed the activation of a single fluctuator above 50 mK which increased the level of noise significantly.   

Flux Noise in SQUIDs Due to Hyperfine Interactions

Although there have been significant advances in superconducting qubits, they continue to be plagued by noise and decoherence. Low frequency $1/f$ flux noise in superconducting quantum interference devices (SQUIDs) is one of the dominant sources of noise in superconducting flux and phase qubits. Recent experiments implicate spins on the surface of metals as the source of flux noise in SQUIDs, and indicate that these spins are able to relax without conserving total magnetization. We present a model of $1/f$ flux noise in which electron spins on the surface of metals can relax via hyperfine interactions. Our results indicate that flux noise would be significantly reduced in superconducting materials where the most abundant isotopes do not have nuclear moments such as zinc and lead.   

Pure dephasing in flux qubits due to flux noise with spectral density scaling as $1/ f^\alpha$

Magnetic flux noise is a major source of pure dephasing in superconducting flux qubits. This noise, common to SQUIDs, is believed to arise from localized electrons whose spins reverse randomly. We present representative measurements on dc SQUIDs over a range of temperatures showing, in general, $S_\Phi(f)= A^2/(f/(1~$Hz$))^\alpha$. In our measurements, $A$ is of the order of 1~$\mu\Phi_0$Hz$^{-1/2}$ and $0.6<\alpha<1$. Motivated by these results, for arbitrary values of $\alpha$ we calculate pure dephasing times for both Ramsey and echo pulse sequences assuming linear coupling between the energy level splitting and the flux through the qubit. We find that the dephasing time $\tau_\phi$ decreases dramatically as $\alpha$ is reduced. In addition, the frequency bandwidth to which the qubit is sensitive---defined by the infrared and ultra-violet cutoff frequencies---can significantly affect $\tau_\phi$ in a manner depending on the type of sequence and value of $\alpha$. For each sequence, $\tau_\phi$ becomes independent of the ultra-violet cutoff frequency when its value exceeds $1/\tau_\phi$. Finally, we present calculated dephasing times corresponding to our measured spectra.   

Very-low-frequency spectroscopy of both flux and tunnel-coupling noise in a flux qubit

We inferred the very-low-frequency noise (0.01 to 100 Hz) of a superconducting flux qubit by repeatedly subjecting it to free induction during a fixed length of time and sampling the binary read-out signal. The excited-state probability varies as the qubit-transition frequency fluctuates due to noise, and we control the sensitivities to noise in the energy and tunnel coupling terms of the Hamiltonian by tuning the static flux (energy) bias. At low temperature, interestingly, both types of low-frequency noise follow the same 1/f-type power laws observed at much higher frequencies. We will further present the temperature dependence of both noises from 10 to 200 mK.   

$T_{1\rho}$ experiment as a noise spectrum analyzer

We performed a $T_{1\rho}$ (spin-locking) experiment on a superconducting flux qubit, enabling us to resolve the environmental noise in the intermediate-frequency range. By driving the qubit along its state polarization, in the rotating frame, it is effectively spin-locked: the decohering effect of low-frequency noise is thereby dramatically reduced compared to Rabi oscillations. We measured the $T_{1\rho}$ relaxation rate in the rotating frame, under different driving amplitudes and flux biases. Relating this driven relaxation rate to the noise at the corresponding Rabi frequency, we extracted the noise power spectral densities of the energy-bias (flux) and tunnel-coupling terms of the qubit's Hamiltonian at frequencies ranging from 0.5 to 100 MHz. In the flux-noise spectrum, we observed features due to non-Gaussian noise, which can be modeled by a strong random-telegraph fluctuator, supporting observations in the decoherence of a spin-echo.   

Characterization of critical-current noise in Josephson junctions and its implications for qubit dephasing

Critical-current noise in Josephson junctions may ultimately limit the coherence of superconducting qubits. Presently qubit coherence times are limited by energy relaxation or other dephasing mechanisms, but recent qubit advances may put the coherence times in the regime where critical-current noise play an important role. We report on the measurement of $I_{c}$-noise in Josephson junctions and compare them to fluctuations in the normal state resistance when superconductivity is suppressed in a magnetic field. We measure the noise scaling with the junction area, normal state resistance, and temperature. We will then discuss the implication of this noise to qubit decoherence.   

Pure dephasing from quasiparticle tunneling in superconducting qubits

Quasiparticles tunneling across Jospehson junctions provide an intrinsic decoherence mechanism in superconducting qubits. The quasiparticle current spectral density $S_{\mathrm{qp}}(\omega)$ determines both the relaxation rate and the pure dephasing rate. The latter is in general proportional to the the spectral density evaluated at zero frequency. In the case of quasiparticle, however, $S_{\mathrm{qp}}(\omega)$ diverges logarithmically as frequency goes to zero, potentially leading to very fast dephasing. Here we show how to regularize this divergence in a self-consistent way. This enable us to estimate the dephasing rate due to quasiparticle tunneling and to study its magnetic flux dependence for various qubit designs.   

Anomalous Temperatures of Superconducting Qubits

We present qubit temperature measurements on several superconducting transmon qubits coupled to compact resonators. By addressing multiple transitions of the artificial atom and cavity system, we measured the temperature as a function of qubit and cavity frequency and cavity Q. For high cavity Q and large detuning, qubit temperatures were found to be greater than 120mK, well in excess of the dilution refrigerator base temperature of 15mK. This unanticipated effect can be explained by the decoupling of the qubit to the cold load damping the cavity. We will present our attempts to produce lower qubit temperatures with additional filtering and dynamical cooling experiments.   

Minimizing environmental decoherence for a superconducting phase qubit - transmon architecture

The coherence of superconducting quantum systems is currently a major obstacle towards high gate fidelity and long-lived memory. We found that quasiparticle generation from stray infrared light is a significant source of energy relaxation. We show that resonator quality factors and phase qubit energy relaxation times are limited by a quasiparticle density of approximately 200 $\mu$m$^{-3}$, induced by 4 K blackbody radiation from the environment. We demonstrate how this influence can be fully removed by isolating the devices from the radiative environment using multistage shielding. In addition, we analyze the decoherence due to circuitry in our new phase qubit-transmon architecture. This architecture - consisting of transmon qubits, resonators, and phase qubits using a frequency domain multiplexed readout - is less affected by Purcell decay. At present, fabrication of samples is ongoing.   

Designs towards improved coherence times in superconducting qubits

Coherence times for superconducting qubits in a planar geometry have increased drastically over the past 10 years with improvements exceeding a factor of 1000. However, recently these appeared to have reached a plateau around 1-2 microseconds, the limits of which were not well understood. Here, we present experimental data showing that one limit is due to infra-red radiation, confirming observations from other groups. We observe increased coherence times after appropriate IR shielding. Further improvements are shown to be possible by increasing the feature size of the interdigitated shunting capacitor, strongly indicating that surface losses at the metal/substrate interface are limiting qubit coherence times. In our experiments we kept the ratio of line width to gap size constant, but increased the overall feature size. We will discuss this and other similar design approaches towards better coherence in superconducting qubits.