We perform ab initio calculations of hydrogen-based tunneling defects in alumina to identify deleterious two-level systems (TLS) in superconducting qubits. The defects analyzed include bulk hydrogenated Al vacancies, bulk hydrogen interstitial defects, and a surface OH rotor. The formation energies of the defects are first computed for an Al- and O-rich environment to give the likelihood of defect occurrence during growth. The potential energy surfaces are then computed and the corresponding dipole moments are evaluated to determine the coupling of the defects to an electric field. Finally, the tunneling energy is computed for the hydrogen defect and the analogous deuterium defect, providing an estimate of the TLS energy and the corresponding frequency for photon absorption. We predict that hydrogenated cation vacancy defects will form a significant density of GHz frequency TLSs in alumina.
We perform ab initio calculations of hydrogen-based tunneling defects in alumina to identify deleterious two-level systems (TLS) in superconducting qubits. The defects analyzed include bulk hydrogenated Al vacancies, bulk hydrogen interstitial defects, and a surface OH rotor. The formation energies of the defects are first computed for an Al- and O-rich environment to give the likelihood of defect occurrence during growth. The potential energy surfaces are then computed and the corresponding dipole moments are evaluated to determine the coupling of the defects to an electric field. Finally, the tunneling energy is computed for the hydrogen defect and the analogous deuterium defect, providing an estimate of the TLS energy and the corresponding frequency for photon absorption. We predict that hydrogenated cation vacancy defects will form a significant density of GHz frequency TLSs in alumina.
Dissipative two-level systems (TLS) have been a long-standing problem in glassy solids over the last fifty years, and have recently gained new relevance as sources of decoherence in quantum computing. Resonant absorption by TLSs in the dielectric poses a serious limitation to the performance of superconducting qubits; however, the microscopic nature of these systems has yet to be established. Based on first-principles calculations, we propose that hydrogen impurities in Al2O3 are the main source of TLS resonant absorption. Hydrogen is an ubiquitous impurity and can easily incorporate in Al2O3. We find that interstitial H in Al2O3 forms a hydrogen bond (O-H...O). At specific O-O distances, consistent with bond lengths found in amorphous Al2O3 or near Al2O3 surfaces or interfaces, the H atom feels a double well. Tunneling between two symmetric positions gives rise to resonant absorption in the range of 10 GHz, explaining the experimental observations. We also calculate the expected qubit-TLS coupling and find it to lie between 16 and 20 MHz, consistent with experimental measurements.
Quantum two-level systems (TLSs) are present in the materials of qubits and are considered defects because they limit qubit coherence. For superconducting qubits, the quintessential Josephson junction barrier is made of amorphous alumina, which hosts TLSs. However, TLSs are not generally understood, either structurally or in atomic composition. In this study, we greatly extend the quantitative data available on TLSs by reporting on the physical dipole moment in two alumina types: polycrystalline $\ensuremath{\gamma}$-Al2O3 and amorphous a-AlOx. To obtain the dipole moments pz, rather than the less-structural coupling parameter g, we tune individual TLSs with a known external electric field in a cavity quantum electrodynamic system. We find a clear difference in the dipole moment distribution from the film types, indicating a difference in TLS structures. A large sample of approximately 400 individual TLSs are analyzed from the polycrystalline film type. Their dipoles along the growth direction pz have a mean value of $2.6\ifmmode\pm\else\textpm\fi{}0.3$ debye (D) ($0.54\ifmmode\pm\else\textpm\fi{}0.06\phantom{\rule{0.1em}{0ex}}e$ \AA{}) and standard deviation $\ensuremath{\sigma}=1.6\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($0.33\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.1em}{0ex}}e$ \AA{}). The material distribution fits well to a single Gaussian function. Approximately 200 individual TLSs are analyzed from amorphous films. Both the mean ${p}_{z}=4.6\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($0.96\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.1em}{0ex}}e$ \AA{}) and $\ensuremath{\sigma}=2.5\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($0.52\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.1em}{0ex}}e$ \AA{}) are larger. Amorphous alumina also has very large pz, greater than 8.6D (1.8e \AA{}), in contrast to polycrystalline which has none of this moment. These large moments agree only with oxygen-based TLS models. Based on data and the candidate models (delocalized O and hydrogen-based TLSs), we find polycrystalline alumina has smaller ratio of O-based to H-based TLS than amorphous alumina.
Two-level systems (TLSs) are the dominant source of decoherence in superconducting qubits, a leading platform for quantum computing. While TLSs are believed to arise from atomic-scale tunneling defects, their precise structural origins, particularly at complex and disordered interfaces in real devices, have remained elusive. Conventional structural characterization is extremely challenging because these interfaces are non-periodic, containing steps and roughness, and device-relevant TLS defects involve only atomic motions with small energy differences. We have determined the atomic character of candidate TLSs at the Al-Si interface of a superconducting qubit using aberration-corrected scanning transmission electron microscopy (STEM) combined with experiment-constrained 3D structure modeling and computational defect searching. High-angle annular dark-field (HAADF) STEM images were obtained from a disordered interface containing a prominent step defect and localized strain. Structure modeling started with 3D models created in the Ingrained framework to match the experimental projections, accounting for mistilt and uniform strain. These models were then refined using FANTASTX (Fully Automated Nanoscale To Atomistic Structure from Theory and eXperiments), a multi-objective optimizer that simultaneously minimizes disagreement with the experimental image via structural similarity and the ab initio (DFT) total system energy. Transition-state searches with the activation relaxation technique nouveau (ARTn) on the refined models identified many atomic configurations occupying double-well potentials corresponding to TLS. Statistical analysis of over 1500 TLSs shows that candidate TLS with tunneling energies and asymmetries in the range relevant to superconducting qubits (∼5 GHz) predominantly involve Al atoms located near the interface. These atoms exhibit smaller median tunneling displacements (∼0.44 Å) than the non-candidate TLS and reside in locally disordered environments with marginally longer and less dense first-neighbor shells than those of non-candidate TLSs. The most probable candidate TLSs feature cooperative motion of one or two Al atoms, and sometimes with Si, in directions largely parallel to the interface. This work provides the first direct atomic-scale insight into the structural defects that may be responsible for decoherence at a realistic, device-relevant interface. It also demonstrates a scalable, generalizable workflow for solving the atomic structure of complex, disordered interfaces by integrating aberration-corrected STEM with advanced computational refinement and defect searching. The methodology is directly applicable to other materials systems and heterointerfaces critical to quantum devices [5].
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
Interstitial hydrogen and deuterium in body-centered-cubic metals constitute archetypal quantum tunneling systems. Their relevance has been renewed by the connection between hydrogenic tunneling in Nb and defect-induced decoherence in superconducting qubits, motivating a predictive microscopic theory. Existing theoretical treatments invoke an adiabatic separation between the light interstitial and the host lattice, an assumption whose validity has not been rigorously established for hydrogenic species. Here, we show that the experimentally measured tunnel splittings of O-trapped H and D in bcc Nb are quantitatively well-described within a five-dimensional (5D) Lattice-Renormalized Born-Oppenheimer (LRBO) framework. This approach treats three interstitial modes and two judiciously selected lattice modes, which includes a transition-state mode, on equal quantum footing. By recasting nested Born-Oppenheimer hierarchies within this same formalism and benchmarking against modern \textit{ab initio} potential energy surfaces, we show that adiabatic separation of the light particle from lattice dynamics is satisfied only in the positive-muon (μ+) mass limit. In contrast, tunneling for H and D is fundamentally a collective, nonadiabatic process mediated by anharmonic lattice couplings. Finally, we show that the breakdown of adiabaticity can be anticipated from simple energy estimates involving the ground-state light-particle energy evaluated at a small number of fixed lattice configurations, providing a practical criterion for assessing the validity of adiabatic tunneling theories in other systems.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.