Session W08: Superconducting Qubits: Materials, Fabrication and Coherence III

Superconducting qubit devices: fabrication suite

Scalable quantum computing architecture and fabrication processes have been a hot research topic in the past decade. We focus on the realization of a quantum computer based on superconducting qubits with a fast qubit reset and initialization techniques, utilizing a quantum-circuit refrigerator [1]. We present the fabricated devices and results achieved to date, which includes resonators with high quality factors, > 1e6, long qubit lifetime > 0.02 ms and 3D integration techniques such as airbridges.   

NbN-based superconducting qubit on Si substrate

In the superconducting qubit composed of aluminum-based Josephson junctions (JJs), the decoherence from microscopic two-level systems in amorphous aluminum oxide is concerned. As alternative materials for qubits, fully epitaxial NbN/AlN/NbN JJs are an attractive candidate with the potential to solve the above problems because of its high crystal quality, its chemical stability against oxidization, and relatively high transition temperature (~ 16 K) of NbN . Here we note that AlN is grown in cubic phase to avoid piezoelectricity. Early studies of superconducting qubits using epitaxially grown nitride JJs showed significant potential, but the qubit energy relaxation time was limited due to dielectric loss from the MgO substrate. [Y. Nakamura et al., APL, 99, 212502 (2011)]. In order to solve this problem, we have employed a Si substrate with TiN buffer layer for the epitaxial growth of this nitride JJs [K. Makise et al., IEEE Trans. Appl. Sup., 26, 1100403, (2016)] and fabricated a transmon qubit with a λ/2 coplanar waveguide resonator. We observed clear Rabi oscillations and Ramsey interference patterns. We will discuss the detailed coherence characteristics.   

Flux qubits fabricated using a high-coherence transmon process

Over the past years, superconducting circuit qubit lifetimes have been continuing to increase, largely due to design enhancements in addition to processing and fabrication evolution. While the earliest designs of Cooper pair boxes exhibited T₁ coherence times on the order of 1 ns, there are recent reports of transmon lifetimes exceeding 100 μs. We now apply these advances in processing to look back upon flux qubits, and we present an 8-qubit ring of alternating flux qubits and tunable transmons, with coupling between nearest neighbors. Preliminary work focuses on optimizing flux qubit design and increasing experimentally observed coherence times, with motivation from theoretical studies and numerical simulations targeting energy structure and noise coupling. Meanwhile, further theoretical investigations into novel two qubit gate designs between flux qubits and transmons, which leverage their opposing anharmonicities, are underway.   

Fabrication and characterization of compact vacuum gap transmon qubits

The large shunt capacitance of the transmon qubit decreases its sensitivity to charge fluctuations but requires sizeable qubit dimensions. Very large capacitor designs furthermore lower the coupling to parasitic losses localized in material interfaces, an approach that improves coherence times consistently, but lowers the achievable integration density and increases parasitic cross coupling and leakage in superconducting processors. Our goal is the development of a compact low-loss transmon qubit by minimizing the electric field participation ratio of metal-dielectric and dielectric-air interfaces. Several attempts to realize vacuum gap capacitors were already implemented [1, 2], usually relying on an out-of-plane geometry that involved a sacrificial layer before releasing the structure. We utilize silicon membranes to fabricate micro-machined resonators and transmon qubits based on suspended in-plane vacuum capacitors [3] with qubits sizes as low as 20 x 20 μm^2.

[1] K. Cicak et al., Appl. Phys. Lett. 96 (2010)
[2] S. J. Bosman et al., Nat. npj Quantum Inf. 3 (2017)
[3] P. Dieterle et al., Phys. Rev. Applied 6, (2016)   

Characterization of Al-based Airbridges for Superconducting Microwave Devices.

The realization of a co-planar waveguide (CPW) for quantum circuits requires only a single wiring layer. However, the usability of the structure is limited by parasitic slotline modes which can modify couplings and act as a loss channel in complex superconducting integrated circuits. Free-standing metallic crossovers known as airbridges [1,2] commonly provide electrical connectivity between ground planes to suppress the parasitic modes. Here, we demonstrate our latest development of Al airbridges in conjunction with Nb CPWs. Our fabrication method relies on three separate optical lithography steps with Al deposition combined with the CPW structures using re-flowed photoresist as a scaffold. We are striving for low-loss airbridges that are robust against sonication and etches during further processing. At present, more than 90% of our airbridges survive the sonication.
[1] Z. Chen et al., Applied Physics Letters 104, 052602 (2014).
[2] Y. Kwon et al., IEEE microwave and wireless components letters 11, 59 (2001).   

Epitaxial GaAs Loss Measurements and the Merged Element Transmon

Transmon qubits are traditionally composed of two components: a Josephson junction, which is commonly made up of a pair of superconducting aluminum films separated by a thin layer of amorphous aluminum oxide, and a large paddle capacitor. The presence of lossy materials in this design, as well as the significant size of the capacitor paddles, limits the transmon’s performance and scalability. In contrast, the merged element transmon design combines the qubit's nonlinear inductance and capacitance into a single trilayer junction with extremely low dielectric loss. GaAs is a good candidate test material for these trilayer junctions as its epitaxial growth and interface with Al is well-characterized, and single crystal growth and lattice matching is possible. In this work, we use dielectric loss extraction methods to accurately measure the TLS loss for Al/GaAs/Al trilayers.   

Frequency Fluctuations in Tunable Superconducting Microwave Cavities

We present a model for measurements of the scattering matrix elements of tunable microwave cavities in the presence of resonant frequency fluctuations induced by fluctuations in the tuning parameter. We apply this model to the specific case of a two-sided cavity and find an analytic expression for the average scattering matrix elements. A key signature of this `fluctuating model' is a subtle deformation of the trajectories swept out by scattering matrix elements in the complex plane. We apply this model to experimental data and report a direct observation of this deformation in the data. Despite this signature, we show that the fluctuating and non-fluctuating models are qualitatively similar enough to be mistaken for one another, especially in the presence of measurement noise. However, if one applies the non-fluctuating model to data for which frequency fluctuations are significant then one will find damping rates that appear to depend on the tuning parameter, which is a common observation in tunable superconducting microwave cavities. We propose this model as both a potential explanation of and remedy to this apparent phenomenon.   

Investigation of surface induced loss mechanisms in high-quality superconducting Nb resonators

Performance of superconducting qubit devices is limited by two-level system (TLS) defects, predominately found in amorphous interface layers. Reducing microwave loss contributions from these interfaces by proper surface treatments is key to push the device performance forward. We study niobium resonators where the native oxides at the metal-air & substrate-air interface are selectively etched with Hydrofluoric (HF) acid. Although HF treatment right before the low temperature characterization is known to yield an order of magnitude improvement in the resonator’s quality factor, the precise loss contribution from various residual oxides and other defects at the interfaces is still unknown. By combining resonator quality factor measurements with X-ray photoelectron spectroscopy (XPS), electron energy loss spectroscopy (EELS) and other surface characterization techniques, we investigate the reappearance of loss mechanisms introduced by exposure to ambient conditions. This is of particular interest for fabricating air resilient, high-quality superconducting qubit devices as they share the same loss mechanisms with resonators.   

Flux Noise and Spin Dynamics of Multiple Interacting Adsorbates on Superconducting Qubits

Molecular oxygen, OH group, and atomic hydrogen surface adsorbates have been identified as possible sources of magnetic flux noise in superconducting qubits. This noise causes decoherence and frequency jitter that can hinder tunable multi-qubit devices. To better understand the spin dynamics of these fluctuating adsorbates we have extended our model for interacting adsorbed paramagnetic O₂ molecules to include other species adsorbed from the device operation atmosphere, including water at different coverages. We calculate the effects of applied fields on the phases of the spin system, its dynamics, and the charge and flux noise generated. To do this we utilize a thermodynamic ensemble generated with Monte Carlo simulations along with Landau-Lifshitz-Gilbert equation simulations for the dynamics, both parametrized with vdW-corrected density functional theory calculations.   

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

Depolarization of superconducting qubits with intrinsic protection, such as heavy fluxonium or the 0-π qubit, is dominated by excitation rather than relaxation processes. To extract the corresponding excitation rates, it is thus crucial to carefully consider the negative-frequency components of the noise spectral density. We are particularly interested in noise sources with the ubiquitous 1/f spectrum at positive frequencies. Existing models based on an ensemble of two-level fluctuators predict a symmetric noise spectral density valid in the high-temperature limit. We extend the analysis beyond this limit, and derive results explicitly obeying the fluctuation–dissipation theorem. We discuss deviations from pure 1/f behavior and compare with recent experimental observations.   

Random two-level defects in polycrystalline and amorphous alumina

Atomic two-level system (TLSs) are ubiquitous defects in superconducting qubits, however the TLS host material is generally amorphous alumina. We extend a characterization technique to, for the first time, study TLSs in two states of the same material: amorphous and polycrystalline alumina. A large distribution of approximately 400 individual TLS dipole moments are obtained in polycrystalline AlOx along a common axis. The averaged dipole moment in material is approximately 3.1 Debye. On the other hand, the average dipole moment is much larger in amorphous alumina, which is contradicted by expectations. We observe strong TLS frequency drifting phenomenon in the amorphous sample which relates to its TLS-TLS interactions. For the first time, a material characterization technique shows that one can collect a large amount of individual TLS data for material optimization, such as TLS dipole moments and TLS frequency stability.
  

Coplanar silicon/aluminum resonators with internal quality factor above 2M: fabrication*

Extremely low intrinsic loss coplanar resonators are critical elements in superconducting quantum computing devices, photon detectors, parametric amplifiers and quantum memories. Here we describe the fabrication and measurement of superconducting coplanar waveguide microwave resonators on silicon substrates with internal quality factors over 2 millions at low powers, corresponding to single-photon regime. These quality factors are achieved by careful optimization of resonators geometry, measurement setup and key TLS-containing interfaces: metal-air, metal-substrate, and substrate-air. We provide a detailed analysis of the design and technological factors impact on resonators quality, including multi-step substrates cleaning, aluminum films crystalline structure, low-damage dry etching, design features and air-bridges application. Finally, using the same process flow we fabricate and characterize superconducting tunable X-mon qubits with the coherence over 100 us, confirming well-known correlations between resonators and qubits quality.

*Devices were fabricated at the BMSTU Nanofabrication Facility (Functional Micro/Nanosystems, FMNS REC, ID 74300).   

Long Relaxation Times of a C-shunt Flux Qubit Coupled to a 3D Cavity

We present measurements of relaxation times of a capacitively shunted flux qubit embedded in a 3D microwave cavity. Qubit energy-relaxation times T₁ were found to be in the range of 60-90 μs, and Hahn-echo coherence time T_2E was about 80 μs. Using the CPMG dynamical decoupling sequence, the T₁-limited coherence time T_2CPMG of 160 μs was reached. Qubit energy relaxation could be attributed to quasiparticle tunneling, while dephasing times were limited by charge and critical-current noises at the optimal flux bias point and by 1/f flux noise elsewhere. With their relaxation times being comparable or exceeding previously reported values for other types of flux qubits, 3D c-shunt flux qubits can be utilized for quantum annealing, quantum magnetometry and spin sensing.   

Coplanar silicon/aluminum resonators with internal quality factor above 2M: measurements*

High quality factor superconducting coplanar waveguide microwave resonators provide a well established technique for qubits control and readout in quantum processors based on circuit QED and hybrid devices. Along with many fabrication issues in such devices, packaging, electromagnetic shielding and filtering, as well as advanced cryogenic setup play crucial role. In this work, we focused on sample holders design and materials simulations, verified by superconducting resonators quality factor and qubits lifetime cryogenic measurements. The impact of cryogenic setups with various shielding and filtering techniques is considered. As the result of packaging and cryogenic setup optimization we demonstrate the robust measurements of superconducting coplanar waveguide resonators with internal quality factor over 2 millions and tunable X-mon qubits with coherence up to 100 us.

*Devices were fabricated at the BMSTU Nanofabrication Facility (Functional Micro/Nanosystems, FMNS REC, ID 74300).