Two-level Defects Research Articles

Mitigation of interfacial dielectric loss in aluminum-on-silicon superconducting qubits

We demonstrate aluminum-on-silicon planar transmon qubits with time-averaged T1 energy relaxation times of up to 270 μs, corresponding to Q = 5 million, and a highest observed value of 501 μs. Through materials analysis techniques and numerical simulations we investigate the dominant source of energy loss, and devise and demonstrate a strategy toward its mitigation. Growing aluminum films thicker than 300 nm reduces the presence of oxide, a known host of defects, near the substrate-metal interface, as confirmed by time-of-flight secondary ion mass spectrometry. A loss analysis of coplanar waveguide resonators shows that this results in a reduction of dielectric loss due to two-level system defects. The correlation between the enhanced performance of our devices and the film thickness is due to the aluminum growth in columnar structures of parallel grain boundaries: transmission electron microscopy shows larger grains in the thicker film, and consequently fewer grain boundaries containing oxide near the substrate-metal interface.

Alternating-bias assisted annealing of amorphous oxide tunnel junctions

Superconducting quantum bits (qubits) rely on ultra-thin, amorphous oxide tunneling barriers that can have significant inhomogeneities and defects as grown. This can result in relatively large uncertainties and deleterious effects in the circuits, limiting the scalability. Finding a robust solution to the junction reproducibility problem has been a long-standing goal in the field. Here, we demonstrate a transformational technique for controllably tuning the electrical properties of aluminum-oxide tunnel junctions. This is accomplished using a low-voltage, alternating-bias applied individually to the tunnel junctions, with which resistance tuning by more than 70% can be achieved. The data indicates an improvement of coherence and reduction of two-level system defects. Transmission electron microscopy shows that the treated junctions are predominantly amorphous, albeit with a more uniform distribution of alumina coordination across the barrier. This technique is expected to be useful for other devices based on ionic amorphous materials.

Reducing two-level systems dissipations in 3D superconducting niobium resonators by atomic layer deposition and high temperature heat treatment

Superconducting qubits have arisen as a leading technology platform for quantum computing, which is on the verge of revolutionizing the world's calculation capacities. Nonetheless, the fabrication of computationally reliable qubit circuits requires increasing the quantum coherence lifetimes, which are predominantly limited by the dissipations of two-level system defects present in the thin superconducting film and the adjacent dielectric regions. In this paper, we demonstrate the reduction of two-level system losses in three-dimensional superconducting radio frequency niobium resonators by atomic layer deposition of a 10 nm aluminum oxide Al2O3 thin films, followed by a high vacuum heat treatment at 650 °C for few hours. By probing the effect of several heat treatments on Al2O3-coated niobium samples by x-ray photoelectron spectroscopy plus scanning and conventional high resolution transmission electron microscopy coupled with electron energy loss spectroscopy and energy dispersive spectroscopy, we witness a dissolution of niobium native oxides and the modification of the Al2O3-Nb interface, which correlates with the enhancement of the quality factor at low fields of two 1.3 GHz niobium cavities coated with 10 nm of Al2O3.

Dynamic phases induced by two-level system defects on driven qubits

Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes–Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker–Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displaced Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Furthermore, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.

Effects of laser-annealing on fixed-frequency superconducting qubits

As superconducting quantum processors increase in complexity, techniques to overcome constraints on frequency crowding are needed. The recently developed method of laser-annealing provides an effective post-fabrication method to adjust the frequency of superconducting qubits. Here, we present an automated laser-annealing apparatus based on conventional microscopy components and demonstrate preservation of highly coherent transmons. In addition, we perform noise spectroscopy to investigate the change in defect features, in particular, two-level system defects, after laser-annealing. Finally, we present a local heating model as well as demonstrate aging stability for laser-annealing on the wafer scale. Our work constitutes an important step toward both understanding the underlying physical mechanism and scaling up laser-annealing of superconducting qubits.

TOF-SIMS analysis of decoherence sources in superconducting qubits

Superconducting qubits have emerged as a potentially foundational platform technology for addressing complex computational problems deemed intractable with classical computing. Despite recent advances enabling multiqubit designs that exhibit coherence lifetimes on the order of hundreds of μs, material quality and interfacial structures continue to curb device performance. Two-level system defects in the thin superconducting film and adjacent dielectric regions introduce stochastic noise and dissipate electromagnetic energy at the cryogenic operating temperatures. In this study, we utilize time-of-flight secondary ion mass spectrometry to understand the role specific fabrication procedures play in introducing such dissipation mechanisms in these complex systems. We interrogated Nb thin films and transmon qubit structures fabricated through slight modifications in the processing and vacuum conditions. We find that when the Nb film is sputtered onto the Si substrate, oxide and silicide regions are generated at various interfaces. We also observe that impurity species, such as niobium hydrides and carbides, are incorporated within the niobium layer during the subsequent lithographic patterning steps. The formation of these resistive compounds likely impacts the superconducting properties of the Nb thin film. Additionally, we observe the presence of halogen species distributed throughout the patterned thin films. We conclude by hypothesizing the source of such impurities in these structures in an effort to intelligently fabricate superconducting qubits and extend coherence times moving forward.

Resonant Coupling Parameter Estimation with Superconducting Qubits

Today's quantum computers are comprised of tens of qubits interacting with each other and the environment in increasingly complex networks. In order to achieve the best possible performance when operating such systems, it is necessary to have accurate knowledge of all parameters in the quantum computer Hamiltonian. In this article, we demonstrate theoretically and experimentally a method to efficiently learn the parameters of resonant interactions for quantum computers consisting of frequency-tunable superconducting qubits. Such interactions include, for example, those to other qubits, resonators, two-level state defects, or other unwanted modes. Our method is based on a significantly improved swap spectroscopy calibration and consists of an offline data collection algorithm, followed by an online Bayesian learning algorithm. The purpose of the offline algorithm is to detect and roughly estimate resonant interactions from a state of zero knowledge. It produces a square-root reduction in the number of measurements. The online algorithm subsequently refines the estimate of the parameters to comparable accuracy as traditional swap spectroscopy calibration, but in constant time. We perform an experiment implementing our technique with a superconducting qubit. By combining both algorithms, we observe a reduction of the calibration time by one order of magnitude. We believe the method investigated will improve present medium-scale superconducting quantum computers and will also scale up to larger systems. Finally, the two algorithms presented here can be readily adopted by communities working on different physical implementations of quantum computing architectures.

Stabilization of Qubit Relaxation Rates by Frequency Modulation

Temporal, spectral, and sample-to-sample fluctuations in coherence properties of qubits form an outstanding challenge for the development of upscaled fault-tolerant quantum computers. A ubiquitous source for these fluctuations in superconducting qubits is a set of atomic-scale defects with a two-level structure. Here we propose a way to mitigate these fluctuations and stabilize the qubit performance. We show that frequency modulation of a qubit or, alternatively, of the two-level defects, leads to averaging of the qubit relaxation rate over a wide interval of frequencies.

Stability of superconducting resonators: Motional narrowing and the role of Landau-Zener driving of two-level defects.

Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy loss and hinders quantum processor tune-up. Its main source is dielectric noise originating in surface oxides. Thorough noise studies are needed to develop a comprehensive understanding and mitigation strategy of these fluctuations. We use a frequency-locked loop to track the resonant frequency jitter of three different resonator types—one niobium nitride superinductor, one aluminum coplanar waveguide, and one aluminum cavity—and we observe notably similar random telegraph signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which, for increasing power, coalesce into one frequency due to motional narrowing caused by sympathetic driving of two-level system defects by the resonator. In all three devices, we identify a dominant fluctuator whose switching amplitude (separation between states) saturates with increasing drive power, but whose characteristic switching rate follows the power law dependence of quasi-classical Landau-Zener transitions.

Quantum efficiency, purity and stability of a tunable, narrowband microwave single-photon source

We demonstrate an on-demand source of microwave single photons with 71–99% intrinsic quantum efficiency. The source is narrowband (300 kHz) and tuneable over a 600 MHz range around 5.2 GHz. Such a device is an important element in numerous quantum technologies and applications. The device consists of a superconducting transmon qubit coupled to the open end of a transmission line. A π-pulse excites the qubit, which subsequently rapidly emits a single photon into the transmission line. A cancellation pulse then suppresses the reflected π-pulse by 33.5 dB, resulting in 0.005 photons leaking into the photon emission channel. We verify strong antibunching of the emitted photon field and determine its Wigner function. Non-radiative decay and 1/f flux noise both affect the quantum efficiency. We also study the device stability over time and identify uncorrelated discrete jumps of the pure dephasing rate at different qubit frequencies on a time scale of hours, which we attribute to independent two-level system defects in the device dielectrics, dispersively coupled to the qubit. Our single-photon source with only one input port is more compact and scalable compared to standard implementations.

Microscopic relaxation channels in materials for superconducting qubits

Despite mounting evidence that materials imperfections are a major obstacle to practical applications of superconducting qubits, connections between microscopic material properties and qubit coherence are poorly understood. Here, we combine measurements of transmon qubit relaxation times (T1) with spectroscopy and microscopy of the polycrystalline niobium films used in qubit fabrication. By comparing films deposited using three different techniques, we reveal correlations between T1 and intrinsic film properties such as grain size, enhanced oxygen diffusion along grain boundaries, and the concentration of suboxides near the surface. Qubit and resonator measurements show signatures of two-level system defects, which we propose to be hosted in the grain boundaries and surface oxides. We also show that the residual resistance ratio of the polycrystalline niobium films can be used as a figure of merit for qubit lifetime. This comprehensive approach to understanding qubit decoherence charts a pathway for materials-driven improvements of superconducting qubit performance.

Intrinsic Photon Loss at the Interface of Superconducting Devices.

We present a quantum theory of dielectric energy loss arising from the piezoelectric coupling between photons and phonons in superconducting devices. Photon loss is shown to occur predominantly at the interface, where the piezoelectric effect is nonzero even when the materials are perfectly crystalline (epitaxial) and free of two-level system defects. We present explicit numerical calculations for the value of the intrinsic loss tangent at several interfaces to conclude that the T_{1} of superconducting qubits may reach over 10^{4} μs if the device is made with defect-free interfaces.

Investigation of two-level defects in injection dependent lifetime spectroscopy

In the majority of studies involving injection dependent lifetime spectroscopy, it is assumed that the investigated defect is a single-level defect following Shockley-Read-Hall recombination statistics. Nevertheless, in real life, two-level defects or multi-level defects are more common than single-level defects. In this study, we first investigated the possible consequences of misinterpreting a two-level defect as two single-level defects. A procedure to properly fit two-level defects in lifetime spectroscopy is subsequently proposed. At the end, we use boron-oxygen related defects as an experimental demonstration. Our experimental results reveal that the recombination statistics of boron-oxygen related defects cannot be explained by the coexistence of two independent single-level defects. A two-level defect parameterization appears to be more suitable.

Improving the Time Stability of Superconducting Planar Resonators

ABSTRACTQuantum computers are close to become a practical technology. Solid-state implementations based, for example, on superconducting devices strongly rely on the quality of the constituent materials. In this work, we fabricate and characterize superconducting planar resonators in the microwave range, made from aluminum films on silicon substrates. We study two samples, one of which is unprocessed and the other cleaned with a hydrofluoric acid bath and by heating at 880 °C in high vacuum. We verify the efficacy of the cleaning treatment by means of scanning transmission electron microscope imaging of samples’ cross sections. From 3 h-long resonator measurements at ≈ 10 mK and with ≈ 10 photonic excitations, we estimate the frequency flicker noise level using the Allan deviation and find an approximately tenfold noise reduction between the two samples; the cleaned sample shows a flicker noise power coefficient for the fractional frequency of ≈ 0.23 × 10−15. Our preliminary results follow the generalized tunneling model for two-level state defects in amorphous dielectric materials and show that suitable cleaning treatments can help the operation of superconducting quantum computers.

Influence of two-level defects on the transmission of a microwave signal in an open coplanar waveguide

Microwave superconducting quantum circuits are strongly affected by various defects that are unavoidable during the production process. This paper presents a new method for measuring losses in an open transmission line. This line interacts through a capacitive coupling with a coplanar quarter-wavelength resonator, which is used to study losses therein. The authors have investigated the dependencies of losses on power and temperature (in the millikelvin range). It has been shown that major losses in a transmission line are due to the interaction of a microwave field with defects which are effectively described by two-level systems.

Testing quantum fault tolerance on small systems

We extensively test a recent protocol to demonstrate quantum fault tolerance on three systems: (1) a real-time simulation of five spin qubits coupled to an environment with two-level defects, (2) a real-time simulation of transmon quantum computers, and (3) the 16-qubit processor of the IBM Q Experience. In the simulations, the dynamics of the full system is obtained by numerically solving the time-dependent Schr\"odinger equation. We find that the fault-tolerant scheme provides a systematic way to improve the results when the errors are dominated by the inherent control and measurement errors present in transmon systems. However, the scheme fails to satisfy the criterion for fault tolerance when decoherence effects are dominant.

1/f frequency noise of superconducting resonators in large magnetic fields

Recent experiments have indicated surface spins in superconducting devices to be associated with both flux- and charge noise. In particular, for superconducting resonators, where the frequency noise is dominated by the electric field from the resonator coupling to spurious two-level material defects, information on noise in applied magnetic fields is lacking. Here, we present measurements of frequency noise in a superconducting resonator with a centre frequency f0=6.1 GHz in fields exceeding the Zeeman splitting of surface spins (up to 310 mT), showing that the charge-induced noise is unaffected by the applied magnetic field.

Rabi noise spectroscopy of individual two-level tunneling defects

Understanding the nature of two-level tunneling defects is important for minimizing their disruptive effects in various nano-devices. By exploiting the resonant coupling of these defects to a superconducting qubit, one can probe and coherently manipulate them individually. In this work we utilize a phase qubit to induce Rabi oscillations of single tunneling defects and measure their dephasing rates as a function of the defect's asymmetry energy, which is tuned by an applied strain. The dephasing rates scale quadratically with the external strain and are inversely proportional to the Rabi frequency. These results are analyzed and explained within a model of interacting standard defects, in which pure dephasing of coherent high-frequency (GHz) defects is caused by interaction with incoherent low-frequency thermally excited defects.

Symmetry reduction for tunneling defects due to strong couplings to phonons

Tunneling two-level systems (TLSs) are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect–phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a tunneling defect in a crystal strongly coupled to phonons incorporating the full 3D geometry in our description. We find that inversion symmetric tunneling is not dressed by phonons whereas other tunneling pathways are dressed by phonons and, thus, are suppressed by strong defect–phonon coupling. We provide the linear acoustic and dielectric response functions for a tunneling defect in a crystal for strong defect–phonon coupling. This allows direct experimental determination of the defect–phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric TLSs play a unique role in the low energy properties of disordered solids.

Projected Dipole Moments of Individual Two-Level Defects Extracted Using Circuit Quantum Electrodynamics.

Material-based two-level systems (TLSs), appearing as defects in low-temperature devices including superconducting qubits and photon detectors, are difficult to characterize. In this study we apply a uniform dc electric field across a film to tune the energies of TLSs within. The film is embedded in a superconducting resonator such that it forms a circuit quantum electrodynamical system. The energy of individual TLSs is observed as a function of the known tuning field. By studying TLSs for which we can determine the tunneling energy, the actual p_{z}, dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 p_{z}. We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values p=p_{1}=2.8±0.2 D and p=p_{2}=8.3±0.4 D. For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with p_{z} and tunneling energy. This allows a measurement of the circuit's zero-point electric-field fluctuations, in a method that does not need the electric-field volume.