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Abstract: 

Superconducting quantum processors have a long road ahead to reach fault-tolerant quantum computing. One of the most daunting challenges is taming the numerous microscopic degrees of freedom ubiquitous in solid-state devices. State-of-the-art technologies, including the world's largest quantum processors, employ aluminum oxide (AlOx) tunnel Josephson junctions (JJs) as sources of nonlinearity, assuming an idealized pure sin(phi) current-phase relation (CPR). However, this celebrated sin(phi) CPR is only expected to occur in the unrealistic limit of vanishingly low-transparency channels in the AlOx barrier. Here we show that the standard CPR fails to describe the energy spectra of transmon artificial atoms across various samples and laboratories. 

Instead, a mesoscopic model of tunneling through an inhomogeneous AlOx barrier predicts %-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 reality of Josephson harmonics transforms qubit design and prompts a reevaluation of models for quantum gates, parametric amplification and mixing, Floquet qubits, protected Josephson Rhombus chains, etc. Indeed, we show that engineered Josephson harmonics can reduce the charge dispersion and the associated errors in transmon qubits by an order of magnitude.