Correction to: Nature Communicationshttps://doi.org/10.1038/ncomms16025, published online 06 July 2017 The original version of this Article included the authors Kun Zuo and Vincent Mourik who wish to be removed from authorship. Consequently, the author affiliations for these authors have been removed from the ‘Authors and Affiliations’ section. The original version of the ‘Contributions’ statement, which read “H.Z. and Ö.G. fabricated the devices, performed the measurements and analysed the data. S.C.-B. performed the TEM analysis. M.P.N. and M.W. performed the numerical simulations. K.Z., V.M., F.K.d.V., J.v.V., M.W.A.d.M., J.D.S.B., D.J.v.W., M.Q.-P., M.C.C. and S.G. contributed to the experiments. D.C., S.P. and E.P.A.M.B. grew the InSb nanowires. S.K. prepared the lamellae for the TEM analysis. K.W. and T.T. synthesized the h-BN crystals. L.P.K. supervised the project. All authors contributed to the writing of the manuscript”, has been amended to read “H.Z. and Ö.G. fabricated the devices, performed the measurements and analysed the data. S.C.-B. performed the TEM analysis. M.P.N. and M.W. performed the numerical simulations. F.K.d.V., J.v.V., M.W.A.d.M., J.D.S.B., D.J.v.W., M.Q.-P., M.C.C. and S.G. contributed to the experiments. D.C., S.P. and E.P.A.M.B. grew the InSb nanowires. S.K. prepared the lamellae for the TEM analysis. K.W. and T.T. synthesized the h-BN crystals. L.P.K. supervised the project. All authors contributed to the writing of the manuscript”. This has been corrected in both the PDF and HTML versions of the article.

Nature Communications is publishing an editorial expression of concern on the article “Ballistic superconductivity in semiconductor nanowires”, by H. Zhang et al. On 09 December 2021, the Editorial Staff was alerted by Vincent Mourik and two other researchers to potential problems in the manner in which raw data have been selected, processed and analysed. In response to these concerns, Nature Communications initiated an investigation by contacting the corresponding authors of the article and consulting with two independent experts. The investigation involved technical scrutiny of the additional analyses provided by the corresponding authors, including supplementary data from the repository https://zenodo.org/records/6851435. Based on the evidence presented, the Reviewers endorsed the publication of the correction note appended below. Readers are urged to take this information into consideration when interpreting the data presented in this article. Kun Zuo and Vincent Mourik also informed the editorial staff that they wished to be removed from authorship because in their opinion, the correction does not address the concerns with respect to the data and they do not endorse the validity of the claims and conclusions of the article. The author list in both the PDF and HTML has now been rectified. All authors,with the exception ofKenjiWatanabe and Takashi Taniguchi, disagreewith the publication of this Editorial Expression of Concern.

The authors of the paper “Epitaxy of advanced nanowire quantum devices”¹ wish to retract this work. When preparing the underlying data for public release², it was discovered that some data had been inappropriately deleted or cropped when preparing the final published figures, and we promptly alerted the editors of Nature. We found unjustified data removal and cropping in Figures 4a and c, and Extended Data Figures 7 and 8, which affect the agreement between the theoretical curves and the experimental data and the claims of ballistic transport. We are accordingly retracting the paper. The authors stand by all the other data, and their contribution to advanced nanowire quantum devices. All authors have agreed to this retraction.

Superconducting coplanar-waveguide resonators that can operate in strong magnetic fields are important tools for a variety of high-frequency superconducting devices. Magnetic fields degrade resonator performance by creating Abrikosov vortices that cause resistive losses and frequency fluctuations or suppress the superconductivity entirely. To mitigate these effects, we investigate lithographically defined artificial defects in resonators fabricated from Nb-Ti-N superconducting films. We show that by controlling the vortex dynamics, the quality factor of resonators in perpendicular magnetic fields can be greatly enhanced. Coupled with the restriction of the device geometry to enhance the superconductors critical field, we demonstrate stable resonances that retain quality factors ≃105 at the single-photon power level in perpendicular magnetic fields up to B⊥ ≃20mT and parallel magnetic fields up to B⥠≃6T. We demonstrate the effectiveness of this technique for hybrid systems by integrating an In-Sb nanowire into a field-resilient superconducting resonator and use it to perform fast charge readout of a gate-defined double quantum dot at B=1T.

Circuit quantum electrodynamics has proven to be a powerful tool to probe mesoscopic effects in hybrid systems and is used in several quantum computing (QC) proposals that require a transmon qubit able to operate in strong magnetic fields. To address this we integrate monolayer graphene Josephson junctions into microwave frequency superconducting circuits to create graphene based transmons. Using dispersive microwave spectroscopy we resolve graphene's characteristic band dispersion and observe coherent electronic interference effects confirming the ballistic nature of our graphene Josephson junctions. We show that the monoatomic thickness of graphene renders the device insensitive to an applied magnetic field, allowing us to perform energy level spectroscopy of the circuit in a parallel magnetic field of 1 T, an order of magnitude higher than previous studies. These results establish graphene based superconducting circuits as a promising platform for QC and the study of mesoscopic quantum effects that appear in strong magnetic fields.

Semiconductor nanowires are ideal for realizing various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles (such as anyons) can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought into contact with a superconductor. To exploit the potential of non-Abelian anyons - which are key elements of topological quantum computing - fully, they need to be exchanged in a well-controlled braiding operation. Essential hardware for braiding is a network of crystalline nanowires coupled to superconducting islands. Here we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks with a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire 'hashtags' reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase-coherent system with strong spin-orbit coupling. In addition, a proximity-induced hard superconducting gap (with vanishing sub-gap conductance) is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens up new avenues for the realization of epitaxial three-dimensional quantum architectures which have the potential to become key components of various quantum devices.

Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.

Ballistic electron transport is a key requirement for existence of a topological phase transition in proximitized InSb nanowires. However, measurements of quantized conductance as direct evidence of ballistic transport have so far been obscured due to the increased chance of backscattering in one-dimensional nanowires. We show that by improving the nanowire-metal interface as well as the dielectric environment we can consistently achieve conductance quantization at zero magnetic field. Additionally we study the contribution of orbital effects to the sub-band dispersion for different orientation of the magnetic field, observing a near-degeneracy between the second and third sub-bands.