Observation of Josephson harmonics in tunnel junctions

Authors:
raw_author_name: Willsch, Dennis
raw_affiliation_string: JSC - Jülich Supercomputing Centre (Wilhelm-Johnen-Straße, 52425 Jülich - Germany)
raw_author_name: Rieger, Dennis
raw_affiliation_string: KIT - Karlsruhe Institute of Technology (Campus North, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen / Campus South, Kaiserstraße 12, 76131 Karlsruhe - Germany)
raw_author_name: Winkel, Patrick
raw_affiliation_string: KIT - Karlsruhe Institute of Technology (Campus North, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen / Campus South, Kaiserstraße 12, 76131 Karlsruhe - Germany); Yale Quantum Institute (United States); Yale University [New Haven] (157 Church Street, New Haven, CT 06510-2100 - United States)
raw_author_name: Willsch, Madita
raw_affiliation_string: JSC - Jülich Supercomputing Centre (Wilhelm-Johnen-Straße, 52425 Jülich - Germany)
raw_author_name: Krause, Jonas
raw_affiliation_string: Physikalisches Institut [Köln] (Zülpicher Straße 77, 50937 Köln - Germany)
raw_author_name: Ando, Yoichi
raw_affiliation_string: Physikalisches Institut [Köln] (Zülpicher Straße 77, 50937 Köln - Germany)
raw_author_name: Lescanne, Raphaël
raw_affiliation_string: Alice & Bob (53 Bd du Général Martial Valin
75015 Paris - France); LPENS - Laboratoire de physique de l'ENS - ENS Paris (24, rue Lhomond
75005 Paris - France)
raw_author_name: Leghtas, Zaki
raw_affiliation_string: CAS - Centre Automatique et Systèmes (35 rue Saint-Honoré 77305 Fontainebleau cedex - France); QUANTIC - QUANTum Information Circuits (France)
raw_author_name: Bronn, Nicholas T.
raw_affiliation_string: IBM T. J. Watson Research Centre (United States)
raw_author_name: Lanes, Olivia
raw_affiliation_string: IBM T. J. Watson Research Centre (United States)
raw_author_name: Minev, Zlatko K.
raw_affiliation_string: IBM T. J. Watson Research Centre (United States)
raw_author_name: Günzler, Simon
raw_affiliation_string: KIT - Karlsruhe Institute of Technology (Campus North, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen / Campus South, Kaiserstraße 12, 76131 Karlsruhe - Germany)
raw_author_name: Paluch, Patrick
raw_affiliation_string: KIT - Karlsruhe Institute of Technology (Campus North, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen / Campus South, Kaiserstraße 12, 76131 Karlsruhe - Germany)
raw_author_name: Morari, Cristian
raw_affiliation_string: INCDTIM - National Institute for Research and Development of Isotopic and Molecular Technologies (Str. Donat nr. 67-103 PO 5 Box 700
400293 Cluj-Napoca
Romania
 - Romania)
raw_author_name: Wernsdorfer, Wolfgang
raw_affiliation_string: KIT - Karlsruhe Institute of Technology (Campus North, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen / Campus South, Kaiserstraße 12, 76131 Karlsruhe - Germany)
raw_author_name: DiVincenzo, David P.
raw_affiliation_string: FZJ - Forschungszentrum Jülich GmbH | Centre de recherche de Jülich | Jülich Research Centre (Wilhelm-Johnen-Straße, 52428 Jülich - Germany); RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH Aachen

Templergraben 55
52062 Aachen (Hausanschrift)
52056 Aachen (Postanschrift) - Germany)
raw_author_name: Michielsen, Kristel
raw_affiliation_string: JSC - Jülich Supercomputing Centre (Wilhelm-Johnen-Straße, 52425 Jülich - Germany)
raw_author_name: Catelani, Gianluigi
raw_affiliation_string: FZJ - Forschungszentrum Jülich GmbH | Centre de recherche de Jülich | Jülich Research Centre (Wilhelm-Johnen-Straße, 52428 Jülich - Germany)
raw_author_name: Pop, Ioan M.
raw_affiliation_string: KIT - Karlsruhe Institute of Technology (Campus North, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen / Campus South, Kaiserstraße 12, 76131 Karlsruhe - Germany)

Abstract: Abstract 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.