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

Observation of Discrete Charge States of a Coherent Two-Level System in a Superconducting Qubit

We report observations of discrete charge states of a coherent two-level system (TLS) that is strongly coupled to an offset-charge-sensitive superconducting transmon qubit. We measure an offset charge of 0.072e associated with the two TLS eigenstates, which have a transition frequency of 2.9 GHz and a relaxation time exceeding 3 ms. Combining measurements in the strong dispersive and resonant regime, we quantify both transverse and longitudinal coupling of the TLS-qubit interaction. We further perform joint tracking of TLS transitions and quasiparticle tunneling dynamics but find no intrinsic correlations. This Letter demonstrates microwave-frequency TLS as a source of low-frequency charge noise.

Giant Two-Level Systems in a Granular Superconductor

Disordered thin films are a common choice of material for superconducting, high impedance circuits used in quantum information or particle detector physics. A wide selection of materials with different levels of granularity are available, but, despite low microwave losses being reported for some, the high degree of disorder always implies the presence of intrinsic defects. Prominently, quantum circuits are prone to interact with two-level systems (TLS), typically originating from solid state defects in the dielectric parts of the circuit, like surface oxides or tunneling barriers. We present an experimental investigation of TLS in granular aluminum thin films under applied mechanical strain and electric fields. The analysis reveals a class of strongly coupled TLS having electric dipole moments up to 30  eÅ, an order of magnitude larger than dipole moments commonly reported for solid state defects. Notably, these large dipole moments appear more often in films with a higher resistivity. Our observations shed new light on granular superconductors and may have implications for their usage as a quantum circuit material.

Avoided Level Crossing and Entangled States of Interacting Hydrogen Molecules Detected by the Quantum Superposition Microscope

Pump-probe measurements by ultrashort THz pulses can be used to excite and follow the coherence dynamics in the time domain of single hydrogen molecules (H2) in the junction of a scanning tunneling microscope (STM). By tailoring the resonance frequency through the sample bias, we identified two spectral signatures of the interactions among multiple H2 molecules. First, the avoided level crossing featured by energy gaps ranging from 20 to 80 GHz was observed because of the level repulsion between two H2 molecules. Second, the tip can sense the signal of H2 outside the junction through the projective measurement on the H2 inside the junction, owing to the entangled states created through the interactions. A dipolar-type interaction was integrated into the tunneling two-level system model of H2, enabling accurate reproduction of the observed behaviors. Our results obtained by the quantum superposition microscope reveal the intricate quantum mechanical interplay among H2 molecules and additionally provide a 2D platform to investigate unresolved questions of amorphous materials.

Experimentally revealing anomalously large dipoles in the dielectric of a quantum circuit

Quantum two-level systems (TLSs) intrinsic to glasses induce decoherence in many modern quantum devices, such as superconducting qubits. Although the low-temperature physics of these TLSs is usually well-explained by a phenomenological standard tunneling model of independent TLSs, the nature of these TLSs, as well as their behavior out of equilibrium and at high energies above 1 K, remain inconclusive. Here we measure the non-equilibrium dielectric loss of TLSs in amorphous silicon using a superconducting resonator, where energies of TLSs are varied in time using a swept electric field. Our results show the existence of two distinct ensembles of TLSs, interacting weakly and strongly with phonons, where the latter also possesses anomalously large electric dipole moment. These results may shed new light on the low temperature characteristics of amorphous solids, and hold implications to experiments and applications in quantum devices using time-varying electric fields.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Reduction of charge offset drift using plasma oxidized aluminum in SETs

Aluminum oxide ([Formula: see text])-based single-electron transistors (SETs) fabricated in ultra-high vacuum (UHV) chambers using in situ plasma oxidation show excellent stabilities over more than a week, enabling applications as tunnel barriers, capacitor dielectrics or gate insulators in close proximity to qubit devices. Historically, [Formula: see text]-based SETs exhibit time instabilities due to charge defect rearrangements and defects in [Formula: see text] often dominate the loss mechanisms in superconducting quantum computation. To characterize the charge offset stability of our [Formula: see text]-based devices, we fabricate SETs with sub-1 e charge sensitivity and utilize charge offset drift measurements (measuring voltage shifts in the SET control curve). The charge offset drift ([Formula: see text]) measured from the plasma oxidized [Formula: see text] SETs in this work is remarkably reduced (best [Formula: see text] over [Formula: see text] days and no observation of [Formula: see text] exceeding [Formula: see text]), compared to the results of conventionally fabricated [Formula: see text] tunnel barriers in previous studies (best [Formula: see text] over [Formula: see text] days and most [Formula: see text] within one day). We attribute this improvement primarily to using plasma oxidation, which forms the tunnel barrier with fewer two-level system (TLS) defects, and secondarily to fabricating the devices entirely within a UHV system.

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.

Materials loss measurements using superconducting microwave resonators

The performance of superconducting circuits for quantum computing is limited by materials losses. In particular, coherence times are typically bounded by two-level system (TLS) losses at single photon powers and millikelvin temperatures. The identification of low loss fabrication techniques, materials, and thin film dielectrics is critical to achieving scalable architectures for superconducting quantum computing. Superconducting microwave resonators provide a convenient qubit proxy for assessing performance and studying TLS loss and other mechanisms relevant to superconducting circuits such as non-equilibrium quasiparticles and magnetic flux vortices. In this review article, we provide an overview of considerations for designing accurate resonator experiments to characterize loss, including applicable types of losses, cryogenic setup, device design, and methods for extracting material and interface losses, summarizing techniques that have been evolving for over two decades. Results from measurements of a wide variety of materials and processes are also summarized. Finally, we present recommendations for the reporting of loss data from superconducting microwave resonators to facilitate materials comparisons across the field.

Towards understanding two-level-systems in amorphous solids: insights from quantum circuits

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered-what are these two-level defects (TLS)? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to TLS within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects-observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.

Correlating Decoherence in Transmon Qubits: Low Frequency Noise by Single Fluctuators

We report on long-term measurements of a highly coherent, nontunable superconducting transmon qubit, revealing low-frequency burst noise in coherence times and qubit transition frequency. We achieve this through a simultaneous measurement of the qubit's relaxation and dephasing rate as well as its resonance frequency. The analysis of correlations between these parameters yields information about the microscopic origin of the intrinsic decoherence mechanisms in Josephson qubits. Our results are consistent with a small number of microscopic two-level systems located at the edges of the superconducting film, which is further confirmed by a spectral noise analysis.

Possible Hundredfold Enhancement in the Direct Magnetic Coupling of a Single-Atom Electron Spin to a Circuit Resonator

We report on the challenges and limitations of direct coupling of the magnetic field from a circuit resonator to an electron spin bound to a donor potential. We propose a device consisting of a trilayer lumped-element superconducting resonator and a single donor implanted in enriched 28Si. The resonator impedance is significantly smaller than the practically achievable limit obtained with prevalent coplanar resonators. Furthermore, the resonator includes a nanoscale spiral inductor to spatially focus the magnetic field from the photons at the location of the implanted donor. The design promises an increase of approximately 2 orders of magnitude in the local magnetic field, and thus the spin-to-photon coupling rate g , compared with the estimated rate of coupling to the magnetic field of coplanar transmission line resonators. We show that by use of niobium (aluminum) as the resonator's superconductor and a single phosphorous (bismuth) atom as the donor, a coupling rate of g / 2 π = 0.24 MHz ( 0.39 MHz ) can be achieved in the single-photon regime. For this hybrid cavity-quantum-electrodynamic system, such enhancement in g is sufficient to enter the strong-coupling regime.

Suppression of low-frequency charge noise in superconducting resonators by surface spin desorption

Noise and decoherence due to spurious two-level systems located at material interfaces are long-standing issues for solid-state quantum devices. Efforts to mitigate the effects of two-level systems have been hampered by a lack of knowledge about their chemical and physical nature. Here, by combining dielectric loss, frequency noise and on-chip electron spin resonance measurements in superconducting resonators, we demonstrate that desorption of surface spins is accompanied by an almost tenfold reduction in the charge-induced frequency noise in the resonators. These measurements provide experimental evidence that simultaneously reveals the chemical signatures of adsorbed magnetic moments and highlights their role in generating charge noise in solid-state quantum devices.