Two-level Fluctuators Research Articles

Decoherence induced by a sparse bath of two-level fluctuators: Peculiar features of 1/f noise in high-quality qubits

Progress in fabrication of semiconductor and superconductor qubits has greatly diminished the number of decohering defects, thus decreasing the devastating low-frequency 1/f noise and extending the qubits' coherence times (dephasing time T2* and the echo decay time T2). However, large qubit-to-qubit variation of the coherence properties remains a problem, making it difficult to produce a large-scale register where all qubits have a uniformly high quality. In this work, we show that large variability is a characteristic feature of a qubit dephased by a sparse bath made of many (n≫1) decohering defects, coupled to the qubit with similar strength. We model the defects as two-level fluctuators (TLFs) whose transition rates γ are sampled from a log-uniform distribution over an interval [γm,γM], which is a standard model for 1/f noise. We investigate decoherence by such a bath in the limit of high-quality qubit, i.e., when the TLF density d is small (the limit of sparse bath, with d=n/w≪1, where n is the number of TLFs and w=ln[γM/γm] is the log-width of the distribution). We show that different realizations of the bath produce very similar noise power spectra S(f)∼1/f, but lead to drastically different coherence times T2* and T2. Thus the spectral density S(f) does not determine coherence of a qubit coupled to a sparse TLF bath, as opposed to a dense bath; instead, decoherence is controlled by only a few exceptional fluctuators, determined by their value of γ. We show that removing only two of these TLFs greatly increases T2 and T2* times. Our findings help theoretical understanding and further improvements in the coherence properties of semiconductor and superconductor qubits, battling the 1/f noise in these platforms. Published by the American Physical Society 2024

Modeling Low- and High-Frequency Noise in Transmon Qubits with Resource-Efficient Measurement

Transmon qubits experience open-system effects that manifest as noise at a broad range of frequencies. We present a model of these effects using the Redfield master equation with a hybrid bath consisting of low- and high-frequency components. We use two-level fluctuators to simulate 1/f-like noise behavior, which is a dominant source of decoherence for superconducting qubits. By measuring quantum state fidelity under free evolution with and without dynamical decoupling (DD), we can fit the low- and high-frequency noise parameters in our model. We train and test our model using experiments on quantum devices available through IBM quantum experience. Our model accurately predicts the fidelity decay of random initial states, including the effect of DD pulse sequences. We compare our model with two simpler models and confirm the importance of including both high frequency and 1/f noise in order to accurately predict transmon behavior. Published by the American Physical Society 2024

Controlling I-V Hysteresis in Al/Pt Bilayer Symmetric SQUIDs at Millikelvin Temperatures

We study operation of a superconducting quantum interference devices (SQUIDs) based on a new bilayer material. They can be used for the ultra-sensitive detection of magnetic momentum at temperatures down to milliKelvin range. Typically, thermal origin hysteresis of the symmetric SQUID current-voltage curves limits operating temperatures to T>0.6Tc. We used a new bilayer material for SQUID fabrication, namely proximity-coupled superconductor/normal-metal (S/N) bilayers (aluminum 25 nm/platinum 5 nm). Because of the 5 nm Pt-layer, Al/Pt devices show nonhysteretic behavior in a broad temperature range from 20 mK to 0.8 K. Furthermore, the Al/Pt bilayer devices demonstrate an order of magnitude lower critical current compared to the Al devices, which decreases the screening parameter (βL) and improves the modulation depth of the critical current by magnetic flux. Operation at lower temperatures reduces thermal noise and increases the SQUID magnetic field resolution. Moreover, we expect strong decrease of two-level fluctuators on the surface of aluminum due to Pt-layer oxidation protection and hence significant reduction of the 1/f noise. Optimized geometry of Al/Pt symmetric SQUIDs is promising for the detection of single-electron spin flip.

Impact of charge noise on electron exchange interactions in semiconductors

The electron exchange interaction is a promising medium for the entanglement of single-spin qubits in semiconductors as it results in high-speed two-qubit gates. The quality of such entangling gates is reduced by the presence of noise caused by nearby defects acting as two-level fluctuators. To date, the effect of charge noise has been calculated assuming a Gaussian distribution of exchange interaction frequencies between the qubits equivalent to a linear coupling of charge noise with the exchange interaction. In reality the coupling can differ significantly from this linear-coupling approximation depending on the inter-qubit tunnel coupling, detuning of the qubit system, and the magnitude of charge noise. We derive analytical expressions for the frequency spectra of exchange oscillations that encompasses both linear and non-linear coupling to charge-noise. The resulting decoherence times and decay profiles of the exchange oscillations vary considerably. When compared with recent experiments our model shows that non-linear charge-noise coupling is significant and requires consideration to characterise and optimise exchange-based entangling gates.

Enhanced coherence of all-nitride superconducting qubits epitaxially grown on silicon substrate

Improving the coherence of superconducting qubits is a fundamental step towards the realization of fault-tolerant quantum computation. However, coherence times of quantum circuits made from conventional aluminum-based Josephson junctions are limited by the presence of microscopic two-level systems in the amorphous aluminum oxide tunnel barriers. Here, we have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on silicon substrates which promise to overcome the drawbacks of qubits based on Al/AlOx/Al junctions. The all-nitride qubits have great advantages such as chemical stability against oxidation, resulting in fewer two-level fluctuators, feasibility for epitaxial tunnel barriers that reduce energy relaxation and dephasing, and a larger superconducting gap of ~5.2 meV for NbN, compared to ~0.3 meV for aluminum, which suppresses the excitation of quasiparticles. By replacing conventional MgO by a silicon substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time {T}_{1}=16.3;{{upmu }}{{{{{rm{s}}}}}} and a spin-echo dephasing time {T}_{2}=21.5;{{upmu }}{{{{{rm{s}}}}}}. These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to the previously reported {T}_{1}approx {T}_{2}approx 0.5;{{upmu }}{{{{{rm{s}}}}}} of NbN-based qubits on MgO substrates. These results are an important step towards constructing a new platform for superconducting quantum hardware.

Microscopic bath effects on noise spectra in semiconductor quantum dot qubits

When a system is thermally coupled to only a small part of a larger bath, statistical fluctuations of the temperature (more precisely, the internal energy) of this "sub-bath" around the mean temperature defined by the larger bath can become significant. We show that these temperature fluctuations generally give rise to 1/f-like noise power spectral density from even a single two-level system. We extend these results to a distribution of fluctuators, finding the corresponding modification to the Dutta-Horn relation. Then we consider the specific situation of charge noise in silicon quantum dot qubits and show that recent experimental data [E. J. Connors, et al., Phys. Rev. B 100, 165305 (2019)] can be modeled as arising from as few as two two-level fluctuators, and accounting for sub-bath size improves the quality of the fit.

Positive- and negative-frequency noise from an ensemble of two-level fluctuators

The analysis of charge noise based on the Bloch-Redfield treatment of an ensemble of dissipative two-level fluctuators generally results in a violation of the fluctuation-dissipation theorem. The standard Markov approximation (when applied to the two-level fluctuators coupled to a bath) can be identified as the main origin of this failure. The resulting decoherence rates only involve the bath response at the fluctuator frequency, and thus completely neglect the effects of frequency broadening. A systematic and computationally convenient way to overcome this issue is to employ the spectator-qubit method: by coupling an auxiliary qubit to the two-level fluctuator ensemble, an analytical approximation for $S({\omega})$ fully consistent with the fluctuation-dissipation theorem can be obtained. We discuss the resulting characteristics of the noise which exhibits distinct behavior over several frequency ranges, including a $1/f$ to $1/f^2$ crossover with a $T^3$ temperature dependence of the crossover frequency.

Current-Resistance Effects Inducing Nonlinear Fluctuation Mechanisms in Granular Aluminum Oxide Nanowires.

The unusual superconducting properties of granular aluminum oxide have been recently investigated for application in quantum circuits. However, the intrinsic irregular structure of this material requires a good understanding of the transport mechanisms and, in particular, the effect of disorder, especially when patterned at the nanoscale level. In view of these aspects, electric transport and voltage fluctuations have been investigated on thin-film based granular aluminum oxide nanowires, in the normal state and at temperatures between 8 and 300 K. The nonlinear resistivity and two-level tunneling fluctuators have been observed. Regarding the nature of the noise processes, the experimental findings give a clear indication in favor of a dynamic random resistor network model, rather than the possible existence of a local ordering of magnetic origin. The identification of the charge carrier fluctuations in the normal state of granular aluminum oxide nanowires is very useful for improving the fabrication process and, therefore, reducing the possible sources of decoherence in the superconducting state, where quantum technologies that are based on these nanostructures should work.

Anomalous charge noise in superconducting qubits

We have used Ramsey tomography to characterize charge noise in a weakly charge-sensitive superconducting qubit. We find a charge noise that scales with frequency as $1/f^\alpha$ over 5 decades with $\alpha = 1.93$ and a magnitude $S_q(\text{1Hz})= 2.9\times10^{-4}~e^2/\text{Hz}$. The noise exponent and magnitude of the low-frequency noise are much larger than those seen in prior work on single electron transistors, yet are consistent with reports of frequency noise in other superconducting qubits. Moreover, we observe frequent large-amplitude jumps in offset charge exceeding 0.1$e$; these large discrete charge jumps are incompatible with a picture of localized dipole-like two-level fluctuators. The data reveal an unexpected dependence of charge noise on device scale and suggest models involving either charge drift or fluctuating patch potentials.

Microwave magnon damping in YIG films at millikelvin temperatures

Magnon systems used in quantum devices require low damping if coherence is to be maintained. The ferrimagnetic electrical insulator yttrium iron garnet (YIG) has low magnon damping at room temperature and is a strong candidate to host microwave magnon excitations in future quantum devices. Monocrystalline YIG films are typically grown on gadolinium gallium garnet (GGG) substrates. In this work, comparative experiments made on YIG waveguides with and without GGG substrates indicate that the material plays a significant role in increasing the damping at low temperatures. Measurements reveal that damping due to temperature-peak processes is dominant above 1 K. Damping behavior that we show can be attributed to coupling to two-level fluctuators (TLFs) is observed below 1 K. Upon saturating the TLFs in the substrate-free YIG at 20 mK, linewidths of ∼1.4 MHz are achievable: lower than those measured at room temperature.

Electric-field noise from thermally activated fluctuators in a surface ion trap

We probe electric-field noise near the metal surface of an ion trap chip in a previously unexplored high-temperature regime. We observe a non-trivial temperature dependence with the noise amplitude at 1-MHz frequency saturating around 500~K. Measurements of the noise spectrum reveal a $1/f^{\alpha\approx1}$-dependence and a small decrease in $\alpha$ between low and high temperatures. This behavior can be explained by considering noise from a distribution of thermally-activated two-level fluctuators with activation energies between 0.35~eV and 0.65~eV. Processes in this energy range may be relevant to understanding electric-field noise in ion traps; for example defect motion in the solid state and surface adsorbate binding energies. Studying these processes may aid in identifying the origin of excess electric-field noise in ion traps -- a major source of ion motional decoherence limiting the performance of surface traps as quantum devices.

Indications of a soft cutoff frequency in the charge noise of a Si/SiGe quantum dot spin qubit

Characterizing charge noise is of prime importance to the semiconductor spin qubit community. We analyze the echo amplitude data from a recent experiment [Yoneda et al., Nat. Nanotechnol. 13, 102 (2018)] and note that the data shows small but consistent deviations from a $1/f^\alpha$ noise power spectrum at the higher frequencies in the measured range. We report the results of using a physical noise model based on two-level fluctuators to fit the data and find that it can mostly explain the deviations. While our results are suggestive rather than conclusive, they provide what may be an early indication of a high-frequency cutoff in the charge noise. The location of this cutoff, where the power spectral density of the noise gradually rolls off from $1/f$ to $1/f^2$, crucial knowledge for designing precise qubit control pulses, is given by our fit of the data to be around 200 kHz.

Quantum probe of an on-chip broadband interferometer for quantum microwave photonics

Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics. To this end, the strong nonlinearities of superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain. In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task. In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach–Zehnder interferometer composed of two superconducting microwave beam splitters. By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment. For frequencies near the qubit transition frequency, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit. At low frequencies , we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators. Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.

Defects in h-BN tunnel barrier for local electrostatic probing of two dimensional materials

Defects in the hexagonal boron nitride (h-BN) layer can facilitate the tunneling current through thick h-BN tunneling barriers. We have investigated such current-mediating defects as local probes for materials in two dimensional heterostructure stacks. Besides IV characteristics and negative differential conductance, we have characterized the electrical properties of h-BN defects in vertical graphene-h-BN-Cr/Au tunnel junctions in terms of low frequency current noise. Our results indicate a charge sensitivity of 1.5×10−5 e/Hz at 10 Hz, which is equal to good metallic single electron transistors. The noise spectra at low frequency are governed by a few two-level fluctuators. For variations in the electrochemical potential, we achieve a sensitivity of 0.8 μeV/Hz.

(Invited) Sensitizing Carbon Nanotube Transistors for Single Molecule Sensor Applications

Recent work has demonstrated single-electron sensitivity in carbon nanotube transistors under a variety of conditions, including room temperature. In noncovalent cases like charged adsorbates or SiO2 imperfections, two-level fluctuators near the nanotube perturb the current electrostatically. In other cases, a sidewall defect or other covalent modification directly on the nanotube sidewall sensitizes a particular site. Comparative research has helped reveal differences in the transduction mechanisms of the two cases and provides design rules for maximizing reliable signals for electronic sensing. For example, noncovalent sensitization generally produces a smaller signal amplitude in a background of low-energy fluctuators at varying distances from the nanotube. Covalent modifications are far more sensitive than noncovalent perturbations, but the new degrees of freedom that accompany covalent disorder often have energy scales similar to the signal of interest, leading to multiple independent fluctuations that degrade the overall signal-to-noise for sensing. An outstanding compromise involves short, noncovalent linkers, which can produce highly predictable signal amplitudes without degradation of the device characteristics. Furthermore, noncovalent fabrication methods are scalable, so that wafer-scale arrays of molecular sensors are most likely to follow this path.

Coherent interaction with two-level fluctuators using near field scanning microwave microscopy.

Near field Scanning Microwave Microscopy (NSMM) is a scanning probe technique that non-invasively can obtain material properties on the nano-scale at microwave frequencies. While focus has been on developing room-temperature systems it was recently shown that this technique can potentially reach the quantum regime, opening up for applications in materials science and device characterization in solid state quantum information processing. In this paper we theoretically investigate this new regime of NSMM. Specifically we show that interaction between a resonant NSMM probe and certain types of two-level systems become possible when the NSMM probe operates in the (sub-) single photon regime, and we expect a high signal-to-noise ratio if operated under the right conditions. This would allow to detect single atomic material defects with energy splittings in the GHz range with nano-scale resolution, provided that individual defects in the material under study are well enough separated. We estimate that this condition is fulfilled for materials with loss tangents below tan δ ∼ 10−3 which holds for materials used in today’s quantum circuits and devices where typically tan δ < 10−5. We also propose several extensions to a resonant NSMM that could improve sensitivity and functionality also for microscopes operating in a high power regime.

Non-Gaussian signatures and collective effects in charge noise affecting a dynamically decoupled qubit

The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamically-decoupled qubit are studied. Distinct dynamics are found at different qubit working positions. Exact analytical formulae are derived at pure dephasing and approximate solutions are found at the general working position, for weakly- and strongly-coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on other parameters of the qubit-fluctuators system. These results can be used to determine potential microscopic models for the charge environment by performing noise spectroscopy.

Microwave Losses in YBCO Coplanar Waveguide Resonators at Low Power and Millikelvin Range

We have investigated the temperature dependence of microwave losses in the low-power limit and millikelvin temperature range of a thin-film YBa2Cu3O7-x (YBCO) λ/2 coplanar waveguide resonator patterned on a (La0.3Sr0.7) (Al0.65Ta0.35)O3 (LSAT) substrate covered by a CeO2 seed layer. The unloaded quality factor is mainly governed by the surface resistance of the YBCO film and the dielectric losses caused by resonant absorption due to a bath of two-level fluctuators in the dielectrics. The value of the unloaded quality factor at 20 mK and low power, i.e., Q0∼2000, allows for the realization of YBCO microwave quantum circuits implementing biepitaxial grain-boundary Josephson junctions.

Microscopic models for charge-noise-induced dephasing of solid-state qubits

Several experiments have shown qubit coherence decay of the form $exp[\ensuremath{-}{(t/{T}_{2})}^{\ensuremath{\alpha}}]$ due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependencies of the parameters ${T}_{2}$ and $\ensuremath{\alpha}$. Our description is appropriate to qubits in semiconductors interacting with spurious two-level charge fluctuators coupled to a thermal bath. We find distinct power-law dependencies of ${T}_{2}$ and $\ensuremath{\alpha}$ on temperature depending on the nature of the interaction of the fluctuators with the associated bath. We consider fluctuator dynamics induced by first- and second-order tunneling with a continuum of delocalized electron states. We also study one- and two-phonon processes for fluctuators in either GaAs or Si. These results can be used to identify dominant charge-dephasing mechanisms and suppress them.

Nonequilibrium probing of two-level charge fluctuators using the step response of a single-electron transistor.

We report a new method to study two-level fluctuators (TLFs) by measuring the offset charge induced after applying a sudden step voltage to the gate electrode of a single-electron transistor. The offset charge is measured for more than 20h for samples made on three different substrates. We find that the offset charge drift follows a logarithmic increase over 4 orders of magnitude in time and that the logarithmic slope increases linearly with the step voltage. The charge drift is independent of temperature, ruling out thermally activated TLFs and demonstrating that the charge fluctuations involve tunneling. These observations are in agreement with expectations for an ensemble of TLFs driven out of equilibrium. From our model, we extract the density of TLFs assuming either a volume density or a surface density.