Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlO_x) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current–phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlO_x barrier. Here we show that the standard current–phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlO_x barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlO_x-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.

In this letter, we propose a heterostructure design for tunnel field effect transistors with two low direct bandgap group IV compounds, GeSn and highly tensely strained Ge in combination with ternary SiGeSn alloy. Electronic band calculations show that strained Ge, used as channel, grown on Ge_1−xSn_x (x > 9%) buffer, as source, becomes a direct bandgap which significantly increases the tunneling probability. The SiGeSn ternaries are well suitable as drain since they offer a large indirect bandgap. The growth of such heterostructures with the desired band alignment is presented. The crystalline quality of the (Si)Ge(Sn) layers is similar to state-of-the-art SiGe layers.