Recent research trends for high coherence quantum circuits

Quantum computers could potentially solve problems that are considered intractable using even the fastest conventional supercomputers [1, 2]. The fundamental component of a quantum computer is a quantum bit (qubit) formed by a quantum two-level system (TLS). Two of the key performance metrics include T₁ and T₂ times which are energy relaxation and dephasing times respectively (loosely referred to as coherence times). Both of these times should be as long as possible, in order to reduce the otherwise daunting overhead, to enable practical quantum computing. One of the leading candidates for implementing a quantum computer are superconducting qubits. Superconducting qubits are formed using Josephson junctions (a thin insulator sandwiched by two superconducting layers), inductors and capacitors. Coherence times for superconducting qubits have steadily increased over the years with improvements in our understanding of materials, defects, and the electromagnetic environment in which these qubits are placed. In this preface we briefly review recent developments towards improving coherence times.

Superconducting transmons placed inside a microwave radio-frequency cavity thus far have yielded some of the longest coherence times among superconducting qubits. In this issue Dial et al [3] measure a series of such qubits designed to have varying sensitivities to different surface loss sources. While the results cannot conclusively pinpoint which type of surface loss dominates, it was found that substrate loss even for sapphire can limit coherence times. It is also pointed out that due to the large variations of coherence times across wafers, there is a need to build up sufficient statistical data to reach appropriate conclusions. Similar to other recent work [4], such systematic studies are expected to shed light on the origin of surface loss.

The standard tunneling model for TLS, developed in the 1970s, explains observed differences in thermal properties, and response to strain as well as electric fields between crystalline and amorphous dielectrics (glasses). As discussed by Burnett et al [5], the model fails in one important aspect: explaining the power dependencies of high-Q resonators in the few photon regime. This regime is of immense importance for the superconducting quantum computing community, as this is the operating environment of superconducting quantum bits. To overcome the deficiencies of the standard model a better understanding of the dynamics on the microscopic level is needed. Burnett et al, present a model for the TLS loss where the interaction between coherent and incoherent TLS plays a more significant role. The validity of the model is further tested by subsequently fitting it to the measured noise spectrum and power dependence of loss for high quality factor superconducting resonators. The fit indicates that the suggested model more accurately captures the intra TLS dynamics than the standard model in the regime of very low powers and millikelvin temperatures.

Superconducting microwave resonators and superconducting quantum bits (qubits) are in many aspects closely related. The similarities to qubits, and the multiple uses for these devices as readout and buses in quantum computing networks makes understanding their losses a necessity for improving superconducting quantum circuits. Reaching internal losses much lower than 10⁻⁶ for superconducting planar resonators, at low drive powers and millikelvin temperatures, is a major challenge. Fabricating devices with such minimal level of loss requires that all aspects, from material selection to film growth and patterning, collude in a favorable way. In the paper by Richardson et al [6], a detailed study of the growth and patterning of high quality resonators is presented. The resonators are made from MBE grown aluminum on two substrates, silicon and sapphire, both known for their low dielectric losses. It is found that the aluminum film is relaxed within only a few monolayers of material growth on both substrates. Despite the high degree of control in film growth, significant variation in the internal losses of the resonators is found. This is suggestive that the variation would be related to the patterning process after which accidental corrosion on the sidewalls of the aluminum film and photoresist residues can be observed through careful examination. It is further found that the resonators with the lowest internal loss tend to have little resist residue, however, it is found that the low resist residue does not guarantee low loss behavior.

Superconducting qubits are traditionally made from aluminum films deposited via electron beam evaporation onto sapphire or silicon substrates. In lieu of recent work which highlights the importance of surfaces and interfaces in setting the coherence time of qubits [4, 7], Tournet et al [8] explore aluminum films grown on gallium arsenide substrates by molecular beam epitaxy (MBE). MBE has been explored previously in the superconducting qubit field, but in this case MBE was used to grow aluminum films on a sapphire substrate [9]. However, aluminum, in period III of the periodic table, is a natural candidate for growth on a III–V substrate like gallium arsenide. Tournet et al show that careful control of the growth conditions and the surface reconstruction of the GaAs substrate led to near-atomic smoothness and single crystal (011) aluminum films. Aluminum film quality was confirmed during growth with RHEED, and afterwards examined with Nomarski differential interference contrast microscopy, AFM, and HRXRD.

The authors bring up the valid point that the dielectric loss tangent for bulk GaAs has never been measured at DR temperatures, but offer a mitigating solution: a MBE grown film and the underlying thin GaAs buffer layers can be deposited on bulk silicon. Another major loss mechanism in superconducting qubits is the substrate-vacuum interface. To mitigate this problem, they highlight the prevalence of reactive ion etching for III–V materials which can be used to create trenches in the substrate. The trenches can reduce the amount electric fields interact with lossy TLS at the substrate-vacuum interface.

Typical solid state quantum computing experiments, with quantum dots or superconducting qubits, are performed at 10 mK in a dilution refrigerator (DR). One of the major problems in scaling up these experiments is the sheer number of coaxial cables from room to base temperature required to control and readout each qubit. Tuckerman et al [10] report on a new transmission line interconnect physical platform, based on niobium microstrip structures with polyimide (PI-2611 and HD-4100) dielectrics, which promises high wire density, wide bandwidth, low heat leakage, and mechanical compliance. They fabricate transmission line structures with lengths ranging from 50 to 550 mm. Furthermore, to characterize the loss tangent of the flexible dielectrics in their stack, they fabricate resonators and demonstrate the surprisingly low loss properties at DR temperatures. These experiments indicate the promise of having a transmission line interconnect for delivering high power, high density, low loss signals to and from the base stage of a DR.

The quality factor of superconducting resonators is sensitive to many of the same decoherence mechanisms that superconducting qubits are also sensitive to. In this issue, Kreikebaum et al [11] perform a systematic study using superconducting resonators to test the effects of various shielding mechanisms. In the case of aluminum resonators, the results point towards magnetic and infrared shielding as being important for optimal performance. However in the case of titanium nitride resonators quality factors show no dependence on added shielding. Because both superconductors have a widely differing gap energy the observed difference between the materials could be related to quasiparticles but further tests are necessary to see if the same behavior occurs in the case of qubits coupled to different resonators.

Both surface loss due to TLSs and dissipation from magnetic vortices can limit quality factors in superconducting resonators and superconducting qubits. The inclusion of flux-trapping holes are often used to eliminate magnetic vortices but they can increase dielectric loss. In this issue, Chiaro et al [12] perform a systematic study mapping out the trade space between both mechanisms. The results indicate the proximity of holes to the resonator can influence quality factors, and that a separation of at least $6\,\mu {\rm{m}}$ is sufficient to remove excess dielectric loss for current quality factors. Residual magnetic loss is found to be small suggesting that superconducting resonators can be made insensitive to small magnetic fields.