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Scientific Reports

Hydrogen bonds in Al2O3 as dissipative two-level systems in superconducting qubits

Luke Gordon, Hazem Abu‐Farsakh, Anderson Janotti, Chris G. Van de Walle

Published Dec 23, 2014• 63 citations
Publisher

Abstract

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.

DOI
10.1038/srep07590

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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.
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.
Hydrogen contamination in Josephson junctions may contribute to device-to-device variability in superconducting qubits, yet its incorporation, location, and bonding in tunnel barriers remain poorly understood. We combine molecular dynamics simulations of aluminum oxidation in dense O2 and H2O environments with atomistic quantum transport calculations. The simulations produce amorphous AlOx barriers with experimentally relevant hydrogen concentrations. Analysis of 400 statistically independent samples shows that the number of incorporated H atoms follows a beta-binomial distribution, reflecting correlations arising from self-limiting oxidation. Most H atoms reside near the AlOx surface, primarily in Al-OH and Al-OH-Al motifs. Quantum transport calculations for Al/Al2O3/Al junctions reveal that hydrogen enhances transmission near the Fermi level by creating an interface dipole that shifts the oxide bands relative to the electrode Fermi level. Combining hydrogen-number statistics with calculated transmission coefficients yields a probability distribution for the Josephson energy. At an average hydrogen content of 2.56 at.%, we predict E_J/h = 10.23 GHz with a standard deviation of 3.6 MHz. Hydrogen shifts the mean Josephson energy by approximately 11%, proportionally to its concentration, but contributes far less to device-to-device variability than observed in state-of-the-art fabricated junctions. These findings provide an atomistic understanding of hydrogen incorporation and its impact on Josephson energy.
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.
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.
While several experiments claim that two-level system (TLS) defects in amorphous surfaces and interfaces are responsible for energy relaxation in superconducting resonators and qubits, none can provide quantitative explanation of their data in terms of the conventional noninteracting TLS model. Here a model that interpolates between the interacting and noninteracting TLS loss tangent is proposed to perform numerical analysis of experimental data and extract information about TLS parameters and their distribution. As a proof of principle, the model is applied to TESLA cavities that contain only a single lossy material in their interior, the niobium-niobium oxide interface. The best fits show interacting TLSs with a sharp modulus of electric dipole moment for both thin (5nm5\phantom{\rule{0.2em}{0ex}}\mathrm{nm}5nm) and thick (100nm100\phantom{\rule{0.2em}{0ex}}\mathrm{nm}100nm) oxides, indicating that the TLSs are ``atomic'' instead of ``glassy.'' The proposed method can be applied to other devices with multiple material interfaces and substrates, with the goal of elucidating the nature of TLSs causing energy loss in resonators and qubits.
Identification of Soft Modes in Amorphous Al2O3Al2O3{\rm Al}_{2}{\rm O}_{3}Al2​O3​ via First‐Principles
Abstract Amorphous is a fundamental component of modern superconducting qubits. While amorphous oxides offer distinct advantages, such as directional isotropy and a consistent bulk electronic gap, in realistic systems these compounds also support two‐level systems (TLSs) which couple to the qubit, expediting decoherence. In this work, a first‐principles study of amorphous is performed and low‐energy modes are identified in the electronic and vibrational spectra as a possible origin for TLSs.