Simulating alternating bias assisted annealing of amorphous oxide tunnel junctions

TL;DR

This work tackles TLS-induced decoherence in amorphous oxide barriers of superconducting qubits by computationally reproducing the alternating bias assisted annealing (ABAA) protocol using Car-Parrinello MD and machine-learned interatomic potentials. By generating an Al–a-Al2O3–Al barrier, applying $0.5$ V bias pulses at $30$ K with aging, and analyzing the energy landscape and vibrational modes via Phonopy and the MACE potential, the authors demonstrate that ABAA drives the system toward deeper energetic minima and reduces low-frequency soft modes. The results indicate a reduction of TLS-related vibrational density of states below $0.5$ THz, though TLSs are not eliminated and may be shifted to higher frequencies outside the qubit coupling window. These findings support ABAA as a viable strategy to enhance qubit coherence and offer computational guidance for optimizing bias strength, temperature, and pulse count.

Abstract

Amorphous oxide tunneling barriers, primarily formed from aluminum, represent one of the most widely adopted platforms for superconducting quantum bits (qubits). To overcome challenges associated with defects and sample variance among the tunneling barriers, the methodology of alternating bias assisted annealing (ABAA) was introduced in Pappas et. al[1]. The process of applying alternating bias to the barrier and subsequently aging before use was shown to reduce defects in the barrier. Namely, defects that give rise to two-level systems, coupling to the qubit and expediting decoherence. In this work we replicate an expedited ABAA process through a combination of ab-initio molecular dynamics and machine-learned potentials, illuminating how ABAA effects the energy landscape of the barrier.

Figures (4)

• Figure 1: Schematic of alternating bias assisted annealing (ABAA) protocol, wherein an electrical bias of alternating magnitude is applied to the amorphous oxide tunneling barrier, depicted on the right. The number of two-level systems (TLSs) in the qubit frequency range before ABAA, labeled X, has been observed to decrease relative to the TLS number following ABAA, labeled Y in experimental studiespappas2024alternating.
• Figure 2: Left: Amorphous aluminum oxide tunneling barrier with Al atoms in blue and O atoms in red. Bottom: Enhanced view of oxide where an oxygen atom can be seen to exhibit the features of a dangling bond, isolated in real-space. The spatial isolation of this atom gives rise to a rotational degree of freedom. Recomputing the energy along a path in this rotational degree of freedom yields the anharmonic potential well shown in the top right. These wells can give rise to two-level systems which couple to the qubit, expediting decoherence.
• Figure 3: Total energy of the amorphous oxide tunneling barrier as a function of time at 300K. The molecular dynamics simulation begins by applying a positive bias (Pulse I) to the barrier after it has been relaxed within density functional theory. Pulse I is terminated when the energy plateaus at $\sim 2ps$, after which two subsequent simulations are initiated. In the first, the system is allowed to age in the absence of the bias simulating aging, shown in red. Following this process the structure is then relaxed at 0K to compare the final and initial energy, shown in green. In the second, a bias of opposite sign and equal magnitude is applied, shown in magenta. The bias is again terminated when the energy begins to plateau and allowed to age in the absence of an applied field, shown in cyan. Following this process the structure is then relaxed at 0K to compare the final and initial energy, shown in black. Each pulse is found to lower the total energy of the system upon aging and relaxation.
• Figure 4: Spatially resolved vibrational density of states in the pure aluminum, aluminum-aluminum oxide interface, and oxide regions of the tunneling barrier before the ABAA protocol (blue lines), as well as after the aging and relaxation process following a single pulse (green lines) or two pulses (red lines). In each region the VDOS below $0.5$THz is reduced following two pulses. In the aluminum and interface we find this is compensated by an increased VDOS in the vicinity of 1THz. The oxide shows a reduced VDOS across the full examined frequency range.