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

Phonon engineering of atomic-scale defects in superconducting quantum circuits

Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longest T1 time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.

Blurred interface induced control of electrical transport properties in Josephson junctions

The interfacial microstructures of Josephson junctions are vital for understanding the microscopic mechanism to improve the performance of superconducting qubits further. However, there remain significant concerns about well understanding the correlation between atomic structures and electrical behaviors. Here, we propose a new method to define the interface of the barrier in Josephson junctions, and investigate the factors that affect the electrical properties of junctions using material analysis techniques and first principles. We find that the aluminium-oxygen ratio of the interface contributes greatly to the electrical properties of junctions, which is consistent with the conclusions obtained by utilizing the generative adversarial network for data augmentation. When the aluminium-oxygen ratio of the interface is 0.67-1.1, the model exhibits a lower barrier height and better electrical properties of the junction. Moreover, when the thickness of the barrier is fixed, the impact of the aluminium-oxygen ratio becomes prominent. A detailed analysis of Josephson junctions using a microscopic model has led to identifying of process defects that can enhance the yield rate of chips. It has a great boost for determining the relationship between microstructures and macroscopic performances.

Structure and Formation Mechanisms in Tantalum and Niobium Oxides in Superconducting Quantum Circuits

Improving the qubit's lifetime (T1) is crucial for fault-tolerant quantum computing. Recent advancements have shown that replacing niobium (Nb) with tantalum (Ta) as the base metal significantly increases T1, likely due to a less lossy native surface oxide. However, understanding the formation mechanism and nature of both surface oxides is still limited. Using aberration-corrected transmission electron microscopy and electron energy loss spectroscopy, we found that Ta surface oxide has fewer suboxides than Nb oxide. We observed an abrupt oxidation state transition from Ta2O5 to Ta, as opposed to the gradual shift from Nb2O5, NbO2, and NbO to Nb, consistent with thermodynamic modeling. Additionally, amorphous Ta2O5 exhibits a closer-to-crystalline bonding nature than Nb2O5, potentially hindering H atomic diffusion toward the oxide/metal interface. Finally, we propose a loss mechanism arising from the transition between two states within the distorted octahedron in an amorphous structure, potentially causing two-level system loss. Our findings offer a deeper understanding of the differences between native amorphous Ta and Nb oxides, providing valuable insights for advancing superconducting qubits through surface oxide engineering.

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (n ¯ ≃ 1 - 10 phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

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.

Bounds to electron spin qubit variability for scalable CMOS architectures

Spins of electrons in silicon MOS quantum dots combine exquisite quantum properties and scalable fabrication. In the age of quantum technology, however, the metrics that crowned Si/SiO2 as the microelectronics standard need to be reassessed with respect to their impact upon qubit performance. We chart spin qubit variability due to the unavoidable atomic-scale roughness of the Si/SiO2 interface, compiling experiments across 12 devices, and develop theoretical tools to analyse these results. Atomistic tight binding and path integral Monte Carlo methods are adapted to describe fluctuations in devices with millions of atoms by directly analysing their wavefunctions and electron paths instead of their energy spectra. We correlate the effect of roughness with the variability in qubit position, deformation, valley splitting, valley phase, spin-orbit coupling and exchange coupling. These variabilities are found to be bounded, and they lie within the tolerances for scalable architectures for quantum computing as long as robust control methods are incorporated.

Mechanically induced correlated errors on superconducting qubits with relaxation times exceeding 0.4 ms

Superconducting qubits are among the most advanced candidates for achieving fault-tolerant quantum computing. Despite recent significant advancements in the qubit lifetimes, the origin of the loss mechanism for state-of-the-art qubits is still subject to investigation. Furthermore, the successful implementation of quantum error correction requires negligible correlated errors between qubits. Here, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, averaging 0.2 ms and exceeding 0.4 ms - corresponding to quality factors above 5 million and 10 million, respectively. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of the qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments.

Dynamics of a Quantum System Interacting with White Non-Gaussian Baths: Poisson Noise Master Equation

Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the bath is modeled as an ensemble of harmonic oscillators, which yields Gaussian statistics of the bath influence on the quantum systems. However, there are also phenomena in which the bath consists of two-state systems, spins, or anharmonic oscillators; therefore, the non-Gaussian properties of the bath become important. Nevertheless, a theoretical framework to describe quantum systems under the influence of such non-Gaussian baths is not well established. Here, we develop a theory to describe quantum dissipative systems affected by Poisson noise properties of the bath, because the Lévi-Itô decomposition theorem asserts that Poisson noise is fundamental in describing arbitrary white noise beyond Gaussian properties. We introduce a quantum bath model that allows for the consistent description of dissipative quantum systems. The obtained master equation reveals non-Gaussian bath effects in the white noise regime, and provides an essential step toward describing open quantum dynamics under the influence of generic baths.

Optimizing quantum gates towards the scale of logical qubits

A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures.

Readout-Induced Suppression and Enhancement of Superconducting Qubit Lifetimes

It has long been known that the lifetimes of superconducting qubits suffer during readout, increasing readout errors. We show that this degradation is due to the anti-Zeno effect, as readout-induced dephasing broadens the qubit so that it overlaps "hot spots" of strong dissipation, likely due to two-level systems in the qubit's bath. Using a flux-tunable qubit to probe the qubit's frequency-dependent loss, we accurately predict the change in lifetime during readout with a new self-consistent master equation that incorporates the modification to qubit relaxation due to measurement-induced dephasing. Moreover, we controllably demonstrate both the Zeno and anti-Zeno effects, which can explain both suppression and the rarer enhancement of qubit lifetimes during readout.

Quantum heat valve and diode of strongly coupled defects in amorphous material

The mechanical strain can control the frequency of two-level atoms in amorphous material. In this work, we would like to employ two coupled two-level atoms to manipulate the magnitude and direction of heat transport by controlling mechanical strain to realize the function of a thermal switch and valve. It is found that a high-performance heat diode can be realized in the wide piezo voltage range at different temperatures. We also discuss the dependence of the rectification factor on temperatures and couplings of heat reservoirs. We find that the higher temperature differences correspond to the larger rectification effect. The asymmetry system-reservoir coupling strength can enhance the magnitude of heat transfer, and the impact of asymmetric and symmetric coupling strength on the performance of the heat diode is complementary. It may provide an efficient way to modulate and control heat transport's magnitude and flow preference. This work may give insight into designing and tuning quantum heat machines.

Nonergodic Measurements of Qubit Frequency Noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.

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.

Performance of high impedance resonators in dirty dielectric environments

High-impedance resonators are a promising contender for realizing long-distance entangling gates between spin qubits. Often, the fabrication of spin qubits relies on the use of gate dielectrics which are detrimental to the quality of the resonator. Here, we investigate loss mechanisms of high-impedance NbTiN resonators in the vicinity of thermally grown SiO2 and Al2O3 fabricated by atomic layer deposition. We benchmark the resonator performance in elevated magnetic fields and at elevated temperatures and find that the internal quality factors are limited by the coupling between the resonator and two-level systems of the employed oxides. Nonetheless, the internal quality factors of high-impedance resonators exceed 103 in all investigated oxide configurations which implies that the dielectric configuration would not limit the performance of resonators integrated in a spin-qubit device. Because these oxides are commonly used for spin qubit device fabrication, our results allow for straightforward integration of high-impedance resonators into spin-based quantum processors. Hence, these experiments pave the way for large-scale, spin-based quantum computers.

High-Q trenched aluminum coplanar resonators with an ultrasonic edge microcutting for superconducting quantum devices

Dielectric losses are one of the key factors limiting the coherence of superconducting qubits. The impact of materials and fabrication steps on dielectric losses can be evaluated using coplanar waveguide (CPW) microwave resonators. Here, we report on superconducting CPW microwave resonators with internal quality factors systematically exceeding 5 × 106 at high powers and 2 × 106 (with the best value of 4.4 × 106) at low power. Such performance is demonstrated for 100-nm-thick aluminum resonators with 7-10.5 um center trace on high-resistivity silicon substrates commonly used in Josephson-junction based quantum circuit. We investigate internal quality factors of the resonators with both dry and wet aluminum etching, as well as deep and isotropic reactive ion etching of silicon substrate. Josephson junction compatible CPW resonators fabrication process with both airbridges and silicon substrate etching is proposed. Finally, we demonstrate the effect of airbridges' positions and extra process steps on the overall dielectric losses. The best quality factors are obtained for the wet etched aluminum resonators and isotropically removed substrate with the proposed ultrasonic metal edge microcutting.

Fabrication of Al/AlOx/Al junctions with high uniformity and stability on sapphire substrates

Tantalum and aluminum on sapphire are widely used platforms for qubits of long coherent time. As quantum chips scale up, the number of Josephson junctions on sapphire increases. Thus, both the uniformity and stability of the junctions are crucial to quantum devices, such as scalable superconducting quantum computer circuit, and quantum-limited amplifiers. By optimizing the fabrication process, especially, the conductive layer during the electron beam lithography process, Al/AlO_x/Al junctions of sizes ranging from 0.0169 to 0.04 µm² on sapphire substrates were prepared. The relative standard deviation of room temperature resistances (R_N) - [Formula: see text] of these junctions is better than 1.7% on 15 mm × 15 mm chips, and better than 2.66% on 2 inch wafers, which is the highest uniformity on sapphire substrates has been reported. The junctions are robust and stable in resistances as temperature changes. The resistances increase by the ratio of 9.73% relative to R_N as the temperature ramp down to 4 K, and restore their initial values in the reverse process as the temperature ramps back to room temperature. After being stored in a nitrogen cabinet for 100 days, the resistance of the junctions changed by1.16% on average. The demonstration of uniform and stable Josephson junctions in large area paves the way for the fabrication of superconducting chip of hundreds of qubits on sapphire substrates.

Thermal conductivity of glasses: first-principles theory and applications

Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem. The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity-the former neglects anharmonicity, the latter misses the quantum Bose-Einstein statistics of vibrations-and require atomistic models that are very challenging for first-principles methods. Here, we present a protocol to determine from first principles the thermal conductivity κ(T) of glasses above the plateau (i.e., above the temperature-independent region appearing almost without exceptions in the κ(T) of all glasses at cryogenic temperatures). The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and accounts comprehensively for the effects of structural disorder, anharmonicity, and Bose-Einstein statistics. We validate this approach in vitreous silica, showing that models containing less than 200 atoms can already reproduce κ(T) in the macroscopic limit. We discuss the effects of anharmonicity and the mechanisms determining the trend of κ(T) at high temperature, reproducing experiments at temperatures where radiative effects remain negligible.

Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100  G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Effect of the Al/AlOx interfacial stacking sequence on the transport properties of alumina tunnel junctions

Superconducting quantum bits based on Al/AlO_x/Al Josephson junction devices are among the most developed quantum bits at present. The microstructure of the device interface critically affects the electrical properties of Josephson junctions, which in turn severely affects the superconducting quantum bits. Further progress towards scalable superconducting qubits urgently needs to be guided by novel analysis mechanisms or methods to improve the performance of junctions. A direct experimental study of the atomic structure of the device is very challenging. Therefore, we simulated three-dimensional Al/α-Al₂O₃/Al Josephson junction devices via first-principles electronic structure and ballistic transport calculations to investigate the relationship between transport properties and the Al/Al₂O₃ stacking sequence. This work elucidates in detail the effects of the aluminum and alumina stacking sequence on the electron transport properties of the Al/Al₂O₃/Al system at the microscopic level by combining first-principles density functional theory and a non-equilibrium Green's function formalism. It is first revealed that the oxygen termination mode exhibits the least sensitivity to conductance changes in the Al/Al₂O₃ stacking sequence, offering useful theoretical guidance for increasing the yield of fixed-frequency multi-qubit quantum chips which require tight control on qubit frequency.

Surface Passivation of Niobium Superconducting Quantum Circuits Using Self-Assembled Monolayers

Superconducting coplanar waveguide (CPW) microwave resonators in quantum circuits are the best components for reading and changing the state of artificial atoms because of their excellent coupling to quantum systems. This coupling forms the basis of the developing circuit quantum electrodynamic architecture. In quantum processors, oscillators are used to store and transmit quantum information using microwave-frequency wave packets. However, the presence of amorphous thin-film defects is deleterious and can result in an irrevocable loss of coherent information with uncontrolled degrees of freedom. Although there has been extensive research into techniques to reduce the coherent loss of such devices, the precise structure of amorphous dielectric layers on surfaces and interfaces and their associated loss mechanism are being actively studied. In particular, planar superconducting resonators are very sensitive to defects on their surfaces, such as two-level systems in oxidized metals and nonequilibrium quasiparticles, making these devices suitable probes for the different loss mechanisms. In this work, we present the design, fabrication, and characterization of Nb CPW resonators with different surface treatments with self-assembled monolayers (SAMs), which mitigate the growth of oxides in superconducting circuits. We demonstrate SAM-passivated resonators having internal quality factors of greater than 10⁶ at a single-photon excitation power (measured at 100 mK), which were probed using scanning electron microscopy, X-ray photoelectron spectroscopy, and transmission electron microscopy to demonstrate the efficiency of our surface treatment. Finally, we compared the improvements in the experimental quality factors to those obtained by numerical simulation.

Microscopic observation of two-level systems in a metallic glass model

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Developing a Chemical and Structural Understanding of the Surface Oxide in a Niobium Superconducting Qubit

Superconducting thin films of niobium have been extensively employed in transmon qubit architectures. Although these architectures have demonstrated improvements in recent years, further improvements in performance through materials engineering will aid in large-scale deployment. Here, we use information retrieved from secondary ion mass spectrometry and electron microscopy to conduct a detailed assessment of the surface oxide that forms in ambient conditions for transmon test qubit devices patterned from a niobium film. We observe that this oxide exhibits a varying stoichiometry with NbO and NbO₂ found closer to the niobium film/oxide interface and Nb₂O₅ found closer to the surface. In terms of structural analysis, we find that the Nb₂O₅ region is semicrystalline in nature and exhibits randomly oriented grains on the order of 1-3 nm corresponding to monoclinic N-Nb₂O₅ that are dispersed throughout an amorphous matrix. Using fluctuation electron microscopy, we are able to map the relative crystallinity in the Nb₂O₅ region with nanometer spatial resolution. Through this correlative method, we observe that the highly disordered regions are more likely to contain oxygen vacancies and exhibit weaker bonds between the niobium and oxygen atoms. Based on these findings, we expect that oxygen vacancies likely serve as a decoherence mechanism in quantum systems.

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.

O-terminated interface for thickness-insensitive transport properties of aluminum oxide Josephson junctions

Alumina Josephson junction has demonstrated a tremendous potential to realize superconducting qubits. Further progress towards scalable superconducting qubits urgently needs to be guided by novel analysis mechanisms or methods to reduce the thickness sensitivity of the junction critical current to the tunnel barrier. Here, it is first revealed that the termination mode of AlOx interface plays a crucial role in the uniformity of critical current, and we demonstrate that the O-terminated interface has the lowest resistance sensitivity to thickness. More impressively, we developed atomically structured three-dimensional models and calculated their transport properties using a combination of quantum ballistic transport theory with first-principles DFT and NEGF to examine the effects of the Al2O3 termination mode and thickness variations. This work clarifies that O-terminated interface can effectively improve the resistance uniformity of Josephson junction, offering useful guidance for increasing the yield of fixed-frequency multi-qubit quantum chips which require tight control on qubit frequency.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Open quantum systems coupled to finite baths: A hierarchy of master equations

An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium but it induces a dynamical evolution of the bath state. In this paper, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy, we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which not only is more realistic but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular noninteracting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model.

High coherence and low cross-talk in a tileable 3D integrated superconducting circuit architecture

We report high qubit coherence as well as low cross-talk and single-qubit gate errors in a superconducting circuit architecture that promises to be tileable to two-dimensional (2D) lattices of qubits. The architecture integrates an inductively shunted cavity enclosure into a design featuring nongalvanic out-of-plane control wiring and qubits and resonators fabricated on opposing sides of a substrate. The proof-of-principle device features four uncoupled transmon qubits and exhibits average energy relaxation times T₁ = 149(38) μs, pure echoed dephasing times T_ϕ,e = 189(34) μs, and single-qubit gate fidelities F = 99.982(4)% as measured by simultaneous randomized benchmarking. The 3D integrated nature of the control wiring means that qubits will remain addressable as the architecture is tiled to form larger qubit lattices. Band structure simulations are used to predict that the tiled enclosure will still provide a clean electromagnetic environment to enclosed qubits at arbitrary scale.

Integration of Topological Insulator Josephson Junctions in Superconducting Qubit Circuits

The integration of semiconductor Josephson junctions (JJs) in superconducting quantum circuits provides a versatile platform for hybrid qubits and offers a powerful way to probe exotic quasiparticle excitations. Recent proposals for using circuit quantum electrodynamics (cQED) to detect topological superconductivity motivate the integration of novel topological materials in such circuits. Here, we report on the realization of superconducting transmon qubits implemented with (Bi_0.06Sb_0.94)₂Te₃ topological insulator (TI) JJs using ultrahigh vacuum fabrication techniques. Microwave losses on our substrates, which host monolithically integrated hardmasks used for the selective area growth of TI nanostructures, imply microsecond limits to relaxation times and, thus, their compatibility with strong-coupling cQED. We use the cavity-qubit interaction to show that the Josephson energy of TI-based transmons scales with their JJ dimensions and demonstrate qubit control as well as temporal quantum coherence. Our results pave the way for advanced investigations of topological materials in both novel Josephson and topological qubits.

On the nature of decoherence in quantum circuits: Revealing the structural motif of the surface radicals in α-Al2O3

Quantum information technology puts stringent demands on the quality of materials and interfaces in the pursuit of increased device coherence. Yet, little is known about the chemical structure and origins of paramagnetic impurities that produce flux/charge noise that causes decoherence of fragile quantum states and impedes the progress toward large-scale quantum computing. Here, we perform high magnetic field electron paramagnetic resonance (HFEPR) and hyperfine multispin spectroscopy on α-Al₂O₃, a common substrate for quantum devices. In its amorphous form, α-Al₂O₃ is also unavoidably present in aluminum-based superconducting circuits and qubits. The detected paramagnetic centers are immanent to the surface and have a well-defined but highly complex structure that extends over multiple hydrogen, aluminum, and oxygen atoms. Modeling reveals that the radicals likely originate from well-known reactive oxygen chemistry common to many metal oxides. We discuss how EPR spectroscopy might benefit the search for surface passivation and decoherence mitigation strategies.

Computational study of oxide stoichiometry and variability in the Al/AlOx/Al tunnel junction

Aluminium tunnel junctions are key components of a wide variety of electronic devices. These superconducting tunnel junctions, known as Josephson Junctions (JJ's) are one of the main components of superconducting qubits, a favourite qubit technology in the race for working quantum computers. In this simulation study our JJ configurations are modelled as two aluminium electrodes which are separated by a thin layer of amorphous aluminium oxide. There is limited understanding of how the structure of the amorphous oxide barrier affects the performance and shortcomings of JJ systems. In this paper we present a computational study which combines molecular dynamics, atomistic semi-empirical methods (Density Functional Tight Binding) and non-equilibrium Green's function to study the electronic structure and current flow of these junction devices. Our results suggest that the atomic nature of the amorphous barrier linked to aluminum-oxygen coordination sensitively affects the current-voltage (IV) characteristics, resistance and critical current. Oxide stoichiometry is an important parameter that can lead to variation in resistance and critical currents of several orders of magnitude. The simulations further illustrate the variability that arises due to small differences in atomic structure across amorphous barriers with the same stoichiometry, density and barrier length. Our results also confirm that the charge transport through the barrier is dominated by metallic conduction pathways.

Hexagonal boron nitride as a low-loss dielectric for superconducting quantum circuits and qubits

Dielectrics with low loss at microwave frequencies are imperative for high-coherence solid-state quantum computing platforms. Here we study the dielectric loss of hexagonal boron nitride (hBN) thin films in the microwave regime by measuring the quality factor of parallel-plate capacitors (PPCs) made of NbSe₂-hBN-NbSe₂ heterostructures integrated into superconducting circuits. The extracted microwave loss tangent of hBN is bounded to be at most in the mid-10^-6 range in the low-temperature, single-photon regime. We integrate hBN PPCs with aluminium Josephson junctions to realize transmon qubits with coherence times reaching 25 μs, consistent with the hBN loss tangent inferred from resonator measurements. The hBN PPC reduces the qubit feature size by approximately two orders of magnitude compared with conventional all-aluminium coplanar transmons. Our results establish hBN as a promising dielectric for building high-coherence quantum circuits with substantially reduced footprint and with a high energy participation that helps to reduce unwanted qubit cross-talk.

Emergence of two-level systems in glass formers: a kinetic Monte Carlo study

Using a distinguishable-particle lattice model based on void-induced dynamics, we successfully reproduce the well-known linear relation between heat capacity and temperature at very low temperatures. The heat capacity is dominated by two-level systems formed due to the strong localization of voids to two neighboring sites, and can be exactly calculated in the limit of ultrastable glasses. Similar but weaker localization at higher temperatures accounts for glass transition. The result supports the conventional two-level tunneling picture by revealing how two-level systems emerge from random particle interactions, which also cause glass transition. Our approach provides a unified framework for relating microscopic dynamics of glasses at room and cryogenic temperatures.

Miniaturizing Transmon Qubits Using van der Waals Materials

Quantum computers can potentially achieve an exponential speedup versus classical computers on certain computational tasks, recently demonstrated in superconducting qubit processors. However, the capacitor electrodes that comprise these qubits must be large in order to avoid lossy dielectrics. This tactic hinders scaling by increasing parasitic coupling among circuit components, degrading individual qubit addressability, and limiting the spatial density of qubits. Here, we take advantage of the unique properties of van der Waals (vdW) materials to reduce the qubit area by >1000 times while preserving the capacitance while maintaining quantum coherence. Our qubits combine conventional aluminum-based Josephson junctions with parallel-plate capacitors composed of crystalline layers of superconducting niobium diselenide and insulating hexagonal boron nitride. We measure a vdW transmon T₁ relaxation time of 1.06 μs, demonstrating a path to achieve high-qubit-density quantum processors with long coherence times, and the broad utility of layered heterostructures in low-loss, high-coherence quantum devices.

Spatial Correlation between Fluctuating and Static Fields over Metal and Dielectric Substrates

We report spatially resolved measurements of static and fluctuating electric fields over conductive (Au) and nonconductive (SiO_{2}) surfaces. Using an ultrasensitive "nanoladder" cantilever probe to scan over these surfaces at distances of a few tens of nanometers, we record changes in the probe resonance frequency and damping that we associate with static and fluctuating fields, respectively. We find static and fluctuating fields to be spatially correlated. Furthermore, the fields are of similar magnitude for the two materials. We quantitatively describe the observed effects on the basis of trapped surface charges and dielectric fluctuations in an adsorbate layer. Our results are consistent with organic adsorbates significantly contributing to surface dissipation that affects nanomechanical sensors, trapped ions, superconducting resonators, and color centers in diamond.

A macroscopic object passively cooled into its quantum ground state of motion beyond single-mode cooling

The nature of the quantum-to-classical crossover remains one of the most challenging open question of Science to date. In this respect, moving objects play a specific role. Pioneering experiments over the last few years have begun exploring quantum behaviour of micron-sized mechanical systems, either by passively cooling single GHz modes, or by adapting laser cooling techniques developed in atomic physics to cool specific low-frequency modes far below the temperature of their surroundings. Here instead we describe a very different approach, passive cooling of a whole micromechanical system down to 500 μK, reducing the average number of quanta in the fundamental vibrational mode at 15 MHz to just 0.3 (with even lower values expected for higher harmonics); the challenge being to be still able to detect the motion without disturbing the system noticeably. With such an approach higher harmonics and the surrounding environment are also cooled, leading to potentially much longer mechanical coherence times, and enabling experiments questioning mechanical wave-function collapse, potentially from the gravitational background, and quantum thermodynamics. Beyond the average behaviour, here we also report on the fluctuations of the fundamental vibrational mode of the device in-equilibrium with the cryostat. These reveal a surprisingly complex interplay with the local environment and allow characteristics of two distinct thermodynamic baths to be probed.

Compared to active techniques, passive cooling of mechanical modes allows to work with devices in equilibrium with their environment without excess damping. Here, the authors demonstrate passive cooling and thermalisation of a 15 μm drum-head device with MHz fundamental flexure to its quantum ground state.

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.

Propagating Wigner-Negative States Generated from the Steady-State Emission of a Superconducting Qubit

We experimentally demonstrate the steady-state generation of propagating Wigner-negative states from a continuously driven superconducting qubit. We reconstruct the Wigner function of the radiation emitted into propagating modes defined by their temporal envelopes, using digital filtering. For an optimized temporal filter, we observe a large Wigner logarithmic negativity, in excess of 0.08, in agreement with theory. The fidelity between the theoretical predictions and the states generated experimentally is up to 99%, reaching state-of-the-art realizations in the microwave frequency domain. Our results provide a new way to generate and control nonclassical states, and may enable promising applications such as quantum networks and quantum computation based on waveguide quantum electrodynamics.

Logarithmic Entanglement Growth from Disorder-Free Localization in the Two-Leg Compass Ladder

We explore the finite-temperature dynamics of the quasi-1D orbital compass and plaquette Ising models. We map these systems onto a model of free fermions coupled to strictly localized spin-1/2 degrees of freedom. At finite temperature, the localized degrees of freedom act as emergent disorder and localize the fermions. Although the model can be analyzed using free-fermion techniques, it has dynamical signatures in common with typical many-body localized systems: Starting from generic initial states, entanglement grows logarithmically; in addition, equilibrium dynamical correlation functions decay with an exponent that varies continuously with temperature and model parameters. These quasi-1D models offer an experimentally realizable setting in which natural dynamical probes show signatures of disorder-free many-body localization.

Ultrahigh vacuum packaging and surface cleaning for quantum devices

We describe design, implementation, and performance of an ultra-high vacuum (UHV) package for superconducting qubit chips or other surface sensitive quantum devices. The UHV loading procedure allows for annealing, ultra-violet light irradiation, ion milling, and surface passivation of quantum devices before sealing them into a measurement package. The package retains vacuum during the transfer to cryogenic temperatures by active pumping with a titanium getter layer. We characterize the treatment capabilities of the system and present measurements of flux tunable qubits with an average T₁ = 84 µs and T₂ ^echo=134μs after vacuum-loading these samples into a bottom loading dilution refrigerator in the UHV-package.

Demonstration of non-Markovian process characterisation and control on a quantum processor

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated — or non-Markovian — noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of 10⁻³. Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.

As quantum computing devices become more complex, they enter the realm of correlated noise, which is difficult to characterise and mitigate. Here, the authors demonstrate, over a range of superconducting devices, a method for non-Markovian dynamics characterisation based on the process tensor framework.

Asymptotically Exact Theory for Nonlinear Spectroscopy of Random Quantum Magnets

We study nonlinear response in quantum spin systems near infinite-randomness critical points. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms for the distribution functions of relaxation times that result from realistic channels for dissipation in random magnets. We argue that our results capture the scaling of relaxation times and nonlinear response in generic random quantum magnets in any spatial dimension.

Two-level systems in superconducting quantum devices due to trapped quasiparticles

A major issue for the implementation of large-scale superconducting quantum circuits is the interaction with interfacial two-level system (TLS) defects that lead to qubit parameter fluctuations and relaxation. Another major challenge comes from nonequilibrium quasiparticles (QPs) that result in qubit relaxation and dephasing. Here, we reveal a previously unexplored decoherence mechanism in the form of a new type of TLS originating from trapped QPs, which can induce qubit relaxation. Using spectral, temporal, thermal, and magnetic field mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a highly coherent subset of the general TLS population with a low reconfiguration temperature ∼300 mK and a nonuniform density of states. These properties can be understood if the TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter. This implies that even very rare QP bursts will affect coherence over exponentially long time scales.

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.

Resolving the positions of defects in superconducting quantum bits

Solid-state quantum coherent devices are quickly progressing. Superconducting circuits, for instance, have already been used to demonstrate prototype quantum processors comprising a few tens of quantum bits. This development also revealed that a major part of decoherence and energy loss in such devices originates from a bath of parasitic material defects. However, neither the microscopic structure of defects nor the mechanisms by which they emerge during sample fabrication are understood. Here, we present a technique to obtain information on locations of defects relative to the thin film edge of the qubit circuit. Resonance frequencies of defects are tuned by exposing the qubit sample to electric fields generated by electrodes surrounding the chip. By determining the defect's coupling strength to each electrode and comparing it to a simulation of the field distribution, we obtain the probability at which location and at which interface the defect resides. This method is applicable to already existing samples of various qubit types, without further on-chip design changes. It provides a valuable tool for improving the material quality and nano-fabrication procedures towards more coherent quantum circuits.

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.

Near-Field Scanning Microwave Microscopy in the Single Photon Regime

The microwave properties of nano-scale structures are important in a wide variety of applications in quantum technology. Here we describe a low-power cryogenic near-field scanning microwave microscope (NSMM) which maintains nano-scale dielectric contrast down to the single microwave photon regime, up to 109 times lower power than in typical NSMMs. We discuss the remaining challenges towards developing nano-scale NSMM for quantum coherent interaction with two-level systems as an enabling tool for the development of quantum technologies in the microwave regime.