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Physical Review Letters

Identification of the Local Sources of Paramagnetic Noise in Superconducting Qubit Devices Fabricated on α−Al2O3 Substrates Using Density-Functional Calculations

Donghwa Lee, Jonathan L. DuBois, Vincenzo Lordi

Published Jan 7, 2014• 45 citations
Publisher

Abstract

Effective methods for decoupling superconducting qubits (SQs) from parasitic environmental noise sources are critical for increasing their lifetime and phase fidelity. While considerable progress has been made in this area, the microscopic origin of noise remains largely unknown. In this work, first principles density functional theory calculations are employed to identify the microscopic origins of magnetic noise sources in SQs on an α-Al2O3 substrate. The results indicate that it is unlikely that the existence of intrinsic point defects and defect complexes in the substrate are responsible for low frequency noise in these systems. Rather, a comprehensive analysis of extrinsic defects shows that surface aluminum ions interacting with ambient molecules will form a bath of magnetic moments that can couple to the SQ paramagnetically. The microscopic origin of this magnetic noise source is discussed and strategies for ameliorating the effects of these magnetic defects are proposed.

DOI
10.1103/physrevlett.112.017001

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Effective methods for decoupling superconducting qubits (SQs) from parasitic environmental noise sources are critical for increasing their lifetime and phase fidelity. While considerable progress has been made in this area, the microscopic origin of noise remains largely unknown. In this work, first principles density functional theory calculations are employed to identify the microscopic origins of magnetic noise sources in SQs on an α-Al2O3 substrate. The results indicate that it is unlikely that the existence of intrinsic point defects and defect complexes in the substrate are responsible for low frequency noise in these systems. Rather, a comprehensive analysis of extrinsic defects shows that surface aluminum ions interacting with ambient molecules will form a bath of magnetic moments that can couple to the SQ paramagnetically. The microscopic origin of this magnetic noise source is discussed and strategies for ameliorating the effects of these magnetic defects are proposed.
Superconducting quantum devices, from qubits and magnetometers to dark matter detectors, are influenced by magnetic flux noise originating from paramagnetic surface defects and impurities. These spin systems can feature complex dynamics, including a Berezinskii-Kosterlitz-Thouless transition, that depend on the lattice, interactions, external fields, and disorder. However, the disorder included in typical models is not materials-specific, diminishing the ability to accurately capture measured flux noise phenomena. We present a first principles-based simulation of a spin lattice consisting of paramagnetic O2_22​ molecules on an Al2_22​O3_33​ surface, a likely flux noise source in superconducting qubits, to elucidate opportunities to mitigate flux noise. We simulate an ensemble of surface adsorbates with disordered orientations and calculate the orientation-dependent exchange couplings using density functional theory. Thus, our spin simulation has no free parameters or assumed functional form of the disorder, and captures correlation in the defect landscape that would appear in real systems. We calculate a range of exchange interactions between electron pairs, with the smallest values, 0.016 meV and -0.023 meV, being in the range required to act as a two-level system and couple to GHz resonators. We calculate the flux noise frequency, temperature, and applied external magnetic field dependence, as well as the susceptibility-flux noise cross-correlation. Calculated trends agree with experiment, demonstrating that a surface harboring paramagnetic adsorbates arranged with materials-specific disorder and interactions captures the various properties of magnetic flux noise observed in superconducting circuits. In addition, we find that an external electric field can tune the spin-spin interaction strength and reduce magnetic flux noise.
Magnetic fluctuation from oxygen deficiency centers on the SiO2_22​ surface
The magnetic stability of oxygen deficiency centers on the surface of α-quartz is investigated with first- principles calculations to understand their role in contributing to magnetic flux noise in superconducting qubits (SQs) and superconducting quantum interference devices (SQUIDs) fabricated on amorphous silica substrates. Magnetic defects on the substrate are likely responsible for some of the 1/f noise that plagues these systems. Dangling-bonds associated with three-coordinated Si atoms allow electron density transfer between spin up and down channels, resulting in low energy magnetic states. Such under-coordinated Si defects are common in both stoichiometric and oxygen deficient silica and quartz and are a probable source of magnetic flux fluctuations in SQs and SQUIDs.
The magnetic stability of E′ centers and the peroxy radical on the surface of α-quartz is investigated with first-principles calculations to understand their role in magnetic flux noise in superconducting qubits (SQs) and superconducting quantum interference devices (SQUIDs) fabricated on amorphous silica substrates. Paramagnetic E′ centers are common in both stoichiometric and oxygen deficient silica and quartz, and we calculate that they are more common on the surface than the bulk. However, we find the surface defects are magnetically stable in their paramagnetic ground state and thus will not contribute to 1/f noise through fluctuation at millikelvin temperatures.
Magnetic flux noise is a dominant source of dephasing and energy relaxation in superconducting qubits. The noise power spectral density varies with frequency as 1/fα, with α1, and spans 13 orders of magnitude. Recent work indicates that the noise is from unpaired magnetic defects on the surfaces of the superconducting devices. Here, we demonstrate that adsorbed molecular O2 is the dominant contributor to magnetism in superconducting thin films. We show that this magnetism can be reduced by appropriate surface treatment or improvement in the sample vacuum environment. We observe a suppression of static spin susceptibility by more than an order of magnitude and a suppression of 1/f magnetic flux noise power spectral density of up to a factor of 5. These advances open the door to the realization of superconducting qubits with improved quantum coherence.
Superconducting qubits are hampered by flux noise produced by surface spins from a number of sources. Recent experiments indicated that hydrogen (H) atoms may be one of the sources. Using density functional theory calculations, we report that H atoms either embedded in or adsorbed on an {\alpha}-Al2O3(0001) surface have sizeable spin moments ranging from 0.81 to 0.87 {\mu}B with extremely shallow energy barriers for spin reorientation as low as ~10 mK. Furthermore, H adatoms on the surface attract gas molecules such as O2 and produce new spin sources. We propose using a protective graphene coating on an {\alpha}-Al2O3(0001) surface to eliminate H-induced surface spins and to screen other adsorbates from the environment.
The performance of superconducting qubits is orders of magnitude below what is expected from theoretical estimates based on the loss tangents of the constituent bulk materials. This has been attributed to the presence of uncontrolled surface oxides formed during fabrication which can introduce defects and impurities that create decoherence channels. Here, we develop an ab initio Shiba theory to investigate the microscopic origin of magnetic-induced decoherence in niobium thin film superconductors and the formation of native oxides. Our ab initio calculations encompass the roles of structural disorder, stoichiometry, and strain on the formation of decoherence-inducing local spin moments. With parameters derived from these first-principles calculations we develop an effective quasi-classical model of magnetic-induced losses in the superconductor. We identify d-channel losses (associated with oxygen vacancies) as especially parasitic, resulting in a residual zero temperature surface impedance. This work provides a route to connecting atomic scale properties of superconducting materials and macroscopic decoherence channels affecting quantum systems.