Session Y48: Decoherence in Superconducting Qubits: Noise

Design and Simulation of Microwave Attenuators for Superconducting Quantum Devices

We have found that dephasing times for quantum superconducting transmons operating nominally at T $=$ 20 mK can be limited by thermal photons in the read-out cavity due to non-equilibrium noise on our input microwave line. In an effort to reduce this noise, we have used finite-element simulations to design attenuators that provide better thermalization of the input microwave signals being delivered to our devices. Our thermal simulations incorporate both electron-phonon decoupling effects due to dissipated power in each element of the attenuator as well as phonon thermal conduction and Kapitza boundary effects. We combine the resulting thermal map with a thermal noise model of each dissipative element of the filter to estimate the effective noise temperature of our filter design.   

Cavity Dephasing in Transmon Qubits from Non-equilibrium Noise

The dephasing times for transmon qubits in a 3D cavity can be limited by coupling of the cavity input and output lines to non-equilibrium noise from higher temperature stages. In our system, the dominant source of thermal photons in the cavity is the last microwave attenuator in the microwave input line which is mounted on the 20 mK stage. Guided by thermal and microwave simulations, we have fabricated microwave attenuators and tested them in a 3D transmon measurement system. The performance of the attenuators was quantified by measuring the Ramsey decay time of a transmon qubit as a function of the temperature of the mixing chamber and power dissipated in the attenuator. Based on the Ramsey decay times and properties of the transmon-cavity system, we estimate the effective output noise temperature of the attenuator and compare our results to simulations.   

Qubit dephasing due to photon shot noise from coherent and thermal sources

We investigate qubit dephasing due to photon shot noise in a superconducting flux qubit transversally coupled to a coplanar microwave resonator. Due to the AC Stark effect, photon fluctuations in the resonator cause frequency shifts of the qubit, which in turn lead to dephasing. While this is universally understood, we have made the first quantitative spectroscopy of this noise for both thermal (i.e., residual photons from higher temperature stages) and coherent photons (residual photons from the readout and control pulses). We find that the bandwidth of the shot noise from thermal and coherent photons differ by approximately a factor of two, which we attribute to differences in the correlation time for the two noise sources. By comparing the results with noise spectra measured without any externally applied photons, we conclude that the qubit coherence times in our setup were limited by photon shot noise from thermal radiation, with an average resonator photon population of 0.006. Equipped with this knowledge, we improved the filtering for thermal noise and thereby improved the qubit coherence times by more than a factor of two, with T2 echo times approaching 100 us. From the measured T2 decay, we determine an upper bound on the residual photon population of 0.0004.   

Suppression of photon shot noise dephasing in a tunable coupling superconducting qubit

We report on the suppression of photon shot noise dephasing in a tunable coupling qubit (TCQ). This is achieved by eliminating the dispersive coupling rate, $\chi$, between the TCQ and the readout cavity. We observe that the coherence time approaches twice the relaxation time and becomes less sensitive to thermal photon noise when $\chi$ is tuned close to zero. Experimental results of tunable $\chi$ and its impact on qubit coherence will be presented.   

Dephasing of superconducting asymmetric transmon qubits

As quantum computing implementations based on superconducting qubits increase in scale and complexity, fabrication tolerances and frequency crowding make it desirable to have layouts with at least some of the qubit frequencies being tunable. Split-junction transmon qubits allow for the tuning of qubit energy levels with a magnetic flux. However, this tunability can lead to excess dephasing due to flux noise. By making the two junctions asymmetric, the modulation range of the qubit energy bands can be reduced along with the sensitivity to flux noise. Such asymmetric transmons have been used previously for demonstrations of flux-modulated first-order sideband transitions between a qubit and cavity. We will report on the sensitivity of qubit dephasing to magnetic flux noise for different junction asymmetry. For large asymmetries, of the order of 10:1, the dephasing due to flux noise is greatly reduced compared to a symmetric junction device, whilst still maintaining a useful level of frequency tunability.   

Paramagnetic Spins on -Al$_{2}$O$_{3}$ with Varied Surface Termination

Superconducting qubits (SQs) are promising building blocks for a quantum computer, however, coherence in SQs is reduced by unintended coupling to magnetic noise sources. The microscopic origins of the magnetic noise have not been satisfactorily characterized. Building on previous computational studies [PRL 112, 017001 (2014)] of magnetic spins induced by molecules adsorbed on bare Al terminated Al2O3, we present a density functional theory investigation of magnetic noise associated with other Al2O3 surfaces likely to be encountered in experiment. We calculate the exchange interaction between native defects and adsorbed molecules, as well as the magnetic states energy splitting and anisotropy, on fully hydroxylated Al2O3, with and without a water over-layer. We also present simulated x-ray adsorption and x-ray magnetic circular dichroism spectra of these systems with the aim of aiding experimental surface characterization.   

Suppression of 1/f Flux Noise in Superconducting Quantum Circuits

Low frequency 1/f magnetic flux noise is a dominant contributor to dephasing in superconducting quantum circuits. It is believed that the noise is due to a high density of unpaired magnetic defect states at the surface of the superconducting thin films. We have performed X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) experiments that point to adsorbed molecular oxygen as the dominant source of magnetism in these films. By improving the vacuum environment of our superconducting devices, we have achieved a significant reduction in surface magnetic susceptibility and 1/f flux noise power spectral density. These results open the door to realization of superconducting qubits with improved dephasing times.   

Measurement of the Magnetic Flux Noise Spectrum in Superconducting Xmon Transmon Quantum Bits

Dephasing induced by magnetic flux noise limits the performance of modern superconducting quantum processors. We measure the flux noise power spectrum in planar, frequency-tunable, Xmon transmon quantum bits (qubits), with several SQUID loop geometries. We extend the Ramsey Tomography Oscilloscope (RTO) technique by rapid sampling up to 1 MHz, without state reset, to measure the flux noise power spectrum between $10^{-2}$ and $10^{5}$ Hz. The RTO measurements are combined with idle gate randomized benchmarking and Ramsey decay to give a more complete picture of dephasing in SQUID-based devices.   

1/f noise driven qubit dynamics in presence of a bosonic thermostat

Motivated by observations of distinct sources of noise in superconducting flux qubits over a wide frequency range, we analyze a qubit, a two level system, coupled to two microscopic sources of noise: 1/f low frequency noise and the Ohmic high frequency noise. The noise sources are treated as independent and characterized by different temperatures. We analyze the steady state regime of the resulting out-of-equilibrium dynamics focusing in particular on the effects of the interplay of the two types of noise on spectroscopic characteristics of the qubit. We calculate both analytically and numerically the steady state population of the qubit energy levels, relaxation and dephasing times and effective renormalization of the qubit's energy level splitting.   

1/f permittivity noise probed uniformly in a film with two level systems: The power law of field saturation and the relationship to loss

Noise from atomic tunneling two-level systems (TSs) limit the performance of various superconducting devices, ranging in application from astronomy to quantum computing. We study superconducting resonators with films containing TS and measure the resulting 1/f frequency noise caused by resonant TS. The resonators are designed such that they apply a uniform ac electric field to the films which allows a direct measurement of permittivity noise in the film as a function the electric field. An intrinsic value of noise is found as well as the power law for ac-field saturation. The temperature dependence of 1/f noise below 200 mK fits to a relationship found previously in high-Q resonators. However, our data lead us to a model different than a previous experimental study; in our work TS phenomena are modeled with frequency diffusion. Our measured noise times the temperature is found to be the same to within error in the different films when normalized to the loss tangent at low temperature, despite dramatically different loss tangents. Following from the general nature of the TS models, we expect the same permittivity noise in many other devices.   

Flux noise due to magnetic impurities in superconducting circuits: Optimal spin texture and role of phase transition

Superconducting quantum interference devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density $1/f^{\alpha}$ with $\alpha < 1$ whose origin is believed to be due to spin impurities. We present a theory of flux noise in the presence of phase transitions and arbitrary spin textures in the impurity spin system [1]. At higher temperatures we find that the spin-spin correlation length scale (describing, e.g., the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. At lower temperatures we find that flux noise is quite sensitive to the particular spin texture realized by the spin system ground state. Remarkably, we show that flux-noise is exactly equal to zero when the spins form a poloidal texture. Flux noise is nonzero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates the idea of engineering spin textures and/or intersurface correlation as a method to reduce flux noise in superconducting circuits.\\ \\ \noindent[1] S. LaForest and R. de Sousa, Phys. Rev. B {\bf 92}, 054502 (2015).   

Spin noise and magnetic screening of impurities in a BCS superconductor

The coupling of a localized impurity to a BCS superconductor (SC) leads to the formation of impurity Cooper-pairs via the proximity effect, generating two bound states within the SC energy gap, the so-called Yu-Rusinov-Shiba (YSR) states. They are similar to the Andreev Bound States that originate from Andreev reflection, e.g. when the impurity is hosted in a Josephson junction, and are known to produce sharp sub-gap resonances in charge noise [de Sousa et al., PRB 2009], providing a natural explanation for the observation of microresonators in superconducting devices [Simmonds et al., PRL 2004]. Here we present a theory for the spin noise generated by magnetic impurities in a SC, and discuss the impact of the Shiba states on models of flux noise in superconducting qubits. We use a combination of analytical methods and the numerical renormalization group technique to calculate the spin noise of an Anderson impurity in a SC, unveiling the competition between the proximity effect and Kondo correlations. Both mechanisms produce magnetic screening and a corresponding reduction in spin noise, giving rise to new insights on the kinds of impurities that are responsible for the observed $1/f^{\alpha}$ flux noise in superconducting circuits.   

Geometrical Effects in Noise Spectra of Superconducting Flux Qubits

We present theoretical study of geometrical effects related to spin diffusion in superconducting flux qubits. We adopt a model of a long superconducting wire surrounded by a thin oxide layer with spins distributed uniformly over cross-sectional area of the oxide layer. Using a continuous transformation from a round cylinder to a flat wire strip, we demonstrate that the noise spectral density tends to a power law $S(\omega)\propto (\omega/\Gamma)^{-s}$ with $s\agt 3/4$, approaching $s=3/4$ for very thin wires. The $\omega^{-s}$ dependence is valid in a broad frequency range above $\omega\agt\Gamma$ stretching up to four orders of magnitude in units of characteristic diffusion decay rate $\Gamma \sim 1- 10^2$ Hz. The effect is highly sensitive to a cross-sectional aspect ratio of a thin wire thus revealing its geometrical origin. We substantiate our findings by detailed comparison with available experimental data and conclude that $3/4$ power law distinguishes spin diffusion flux noise from generic ``$1/f$" family.   

Suppression of dephasing by qubit motion in superconducting circuits

We suggest and demonstrate a protocol which suppresses dephasing due to the low-frequency noise by qubit motion, i.e., transfer of the logical qubit of information in a system of $n \geq 2$ physical qubits. The protocol requires only the nearest-neighbor coupling and is applicable to different qubit structures. Motion of a logical qubit limits the correlation time of the effective noise seen by this qubit and suppresses its decoherence rate. This effect is qualitatively similar to the dynamic decoupling, but relies on the different resource: additional physical qubits, not extra control pulses. In this respect, suggested protocol can serve as the basis for an alternative approach to scalable quantum circuits. We further analyze its effectiveness against noises with arbitrary correlations. Our analysis, together with experiments using up to three superconducting qubits, shows that for the realistic uncorrelated noises, qubit motion increases the dephasing time of the logical qubit as $\sqrt{n}$. In general, the protocol provides a diagnostic tool for measurements of the noise correlations.   

Long range correlations by local dissipation in lattice waveguide QED

In waveguide QED, superconducting qubits acting as artificial atoms are coupled to 1D superconducting transmission lines playing the role of common bath for the qubits. By controlling their effective separation and coupling to the transmission line, it is possible to engineer various types of dissipation-induced interactions between the qubits. In this talk, we consider the situation where multiple superconducting qubits are coupled to a lattice of superconducting transmission lines. We show that this can lead to the creation of highly entangled dark states using local dissipation only. Using tensor networks techniques, we study such large-scale highly-correlated systems.