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The original version of this Article contained an error in Equation (1), which incorrectly read “Absorbance=log($\frac{I0}{I}$)=εlh”. The correct version reads “Absorbance=log($\frac{I0}{I}$)=εlc”. This has been corrected in both the PDF and HTML versions of the Article.
The original version of this Article contained an error in Fig. 4d, in which the label of the region to the left of the white dashed lines incorrectly read 'Order stripes'. The correct version states 'Disorder stripes'. This has been corrected in both the PDF and HTML versions of the Article.
The original version of this Comment contained errors in the legend of Figure 2, in which the locations of the fifteenth and sixteenth GBA members were incorrectly given as '(15) Australian Genome Foundry, Macquarie University; (16) Australian Foundry for Advanced Biomanufacturing, University of Queensland'. The correct version replaces this with '(15) Australian Foundry for Advanced Biomanufacturing (AusFAB), University of Queensland and (16) Australian Genome Foundry, Macquarie University'. This has been corrected in both the PDF and HTML versions of the Comment.
The original version of this Article contained an error in the second sentence of the Acknowledgements, which incorrectly read: ‘This work was supported by the Quantum Testbed Program of the Advanced Scientific Computing Research for Basic Energy Sciences program, Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231’. The correct version states ‘the Quantum Testbed Program of the Advanced Scientific Computing Research Division’ in place of ‘the Quantum Testbed Program of the Advanced Scientific Computing Research for Basic Energy Sciences program’. This has been corrected in both the PDF and HTML versions of the Article.
The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.
Correction to: Nature Communicationshttps://doi.org/10.1038/s41467-024-45998-2, published online 26 February 2024. In the Acknowledgements section of this article, the grant number relating to National Institutes of Health funding to J.A.D. was incorrectly given as RM1HG009490 and should have been U19NS132303. The grant number 2334028 relating to the National Science Foundation funding to J.A.D. was omitted. Funding from Hampton University Summer Undergraduate Research Program, Mr. Li Ka Shing, Emerson Collective and the Innovative Genomics Institute (IGI) were omitted. The original article has been corrected.
Correction to: Nature Communicationshttps://doi.org/10.1038/s41467-024-47917-x, published online 04 June 2024 In this article the grant number #200020_201096 relating to the Swiss National Science Foundation was omitted. The original article has been corrected.
Correction to: Nature Communicationshttps://doi.org/10.1038/s41467-022-29942-w, published online 02 May 2022 In the version of the article initially published, the text “UCSD has filed a patent application (WO2022072709A1), in which F.P. and A.R.M. are inventors, containing some results regarding the TCF4 correction overexpression strategy described in this paper. The patent was published on 04-07-2022” was missing from the Competing interests section and has now been added to the HTML and PDF versions of the article.
We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ 1 and the engineered dissipation rate κ 2 . Under a practical noise ratio κ 1 /κ 2 = 10 -3 , the repetition-SC scheme can reach a 10 -15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.
In the version of this Article originally published in July 2018, a parallelization coding problem, which meant that a subset of model grid cells were subjected to erroneous updating of atmospheric gas concentrations, resulted in incorrect calculation of atmospheric CO 2 for these grid cells, and therefore underestimation of the carbon uptake by land through vegetation growth and eventual increases to soil carbon stocks. Having re-run the simulations using the corrected code, the authors found that the original estimates of the impact of the natural wetland methane feedback were overestimated. The permafrost and natural wetland methane feedback requires lower permissible emissions of 9–15% to achieve climate stabilization at 1.5 °C, compared with the original published estimate of 17–23%. The Article text, Table 1 and Fig. 3 have been updated online to reflect the revised numerical estimates. The Supplementary Information file has also been amended, with Supplementary Figs 6, 7, 8 and 9 replaced with revised versions produced using the corrected model output. As the strength of feedbacks remain significant, still require inclusion in climate policy and are nonlinear with global warming, the overall conclusions of the Article remain unchanged.
An amendment to this paper has been published and can be accessed via a link at the top of the paper. Correction to: Nature Microbiology https://doi.org/10.1038/s41564-019-0426-5, published online 13 May 2019. In the version of this Article originally published, the name of the author ‘Mathew Robert Brown’ was incorrectly written as ‘Mathew Brown’ in the main author list and as ‘Matthew Brown’ in the Global Water Microbiome Consortium list. In addition, in the Global Water Microbiome Consortium list, the names of the authors ‘Kevin F. Boehnke’, ‘Janeth Sanabria’ and ‘Adalberto Noyola’ were incorrectly written as ‘Kevin Boehnke’, ‘Janeth Sanabria Gómez’ and ‘Adalberto Noyola Robles’, respectively. The names have now been corrected and the author initials in the author contributions section updated accordingly.
In the version of this article originally published, the present address for Petr Popov was incorrectly listed as ‘Koltech Institute of Science & Technology, Moscow, Russia’. The correct present address is ‘Skolkovo Institute of Science and Technology, Moscow, Russia’. The error has been corrected in the HTML and PDF versions of the paper.
Correction to: Nature Methods 14, 909–914, https://doi.org/10.1038/nmeth.4388 (2017), published online 7 August 2017. In the version of this article initially published, the authors erroneously reported the search mode that was used for ProSightPC 3.0 in the Online Methods and in Supplementary Table 3. The results presented in Fig. 5 were obtained with ‘absolute mass’ search mode, not ‘biomarker discovery’ search mode. The ‘biomarker discovery’ search mode of ProSightPC 3.0 looks for subsequences of those contained in the annotated proteoform database (e.g., truncated forms from degradation and/or cleavage). This search mode is expected to generate similar numbers of identifications as Informed-Proteomics, but is also expected to take dramatically longer (~480 CPU hours). Unfortunately, because of these heavy computational requirements, the authors were unable to complete an analysis using this search mode. They chose to use ‘absolute mass’ mode to illustrate the effect of search mode and database choice on the results. ‘Absolute mass’ mode is the most restrictive of the search modes illustrated in Fig. 5, as it searches only for proteoforms explicitly listed in the proteoform database within a user-defined mass tolerance. In addition, in the supplementary information originally published online, Supplementary Table 3 incorrectly stated that ProSightPC v3.0 was used in ‘biomarker discovery’ mode. ‘Absolute mass’ mode was the mode actually used in this comparison. These errors have been corrected in the HTML and PDF versions of this article and in the associated supplementary information.
Correction to: Nature Methodshttps://doi.org/10.1038/s41592-025-02660-z, published online 12 May 2025. This article was originally published under standard Springer Nature license (© The Author(s), under exclusive licence to Springer Nature America, Inc.). It is now available as an open-access paper under a Creative Commons Attribution 4.0 International license, © The Author(s). The error has been corrected in the HTML and PDF versions of the article.
Correction to: Scientific Data, published online 25 May 2022 The order of the column headings was incorrect in Table 1, meaning values were listed under the wrong descriptions. This has been corrected in the pdf and HTML versions of the article.
Correction to: Scientific Datahttps://doi.org/10.1038/s41597-024-03319-8, published online 23 May 2024 In this article the author’s name Marcelo Salles Olinger was incorrectly given as Marcello Salles Olinger. The original article has been corrected.
Particle tracking, which is an essential tool in many fields of scientific research, uses algorithms that retrieve the centroid of tracked particles with sub-pixel accuracy. However, images in which the particles occupy a small number of pixels on the detector, are in close proximity to other particles or suffer from background noise, show a systematic error in which the particle sub-pixel positions are biased towards the center of the pixel. This “pixel locking” effect greatly reduces particle tracking accuracy. In this report, we demonstrate the severity of these errors by tracking experimental (and simulated) imaging data of optically trapped silver nanoparticles and single fluorescent proteins. We show that errors in interparticle separation, angle and mean square displacement are significantly reduced by applying the corrective Single-Pixel Interior Filling Function (SPIFF) algorithm. Our work demonstrates the potential ubiquity of such errors and the general applicability of SPIFF correction to many experimental fields.
Abstract To investigate long length scale structures using neutron scattering, real space techniques have shown certain advantages over the conventional methods working in reciprocal space. As one of the real space measurement techniques, spin echo modulated small angle neutron scattering (SEMSANS) has attracted attention, due to its relaxed constraints on sample environment and the possibility to combine SEMSANS and a conventional small angle neutron scattering instrument. In this report, we present the first implementation of SEMSANS at a pulsed neutron source and discuss important corrections to the data due to the sample absorption. These corrections allow measurements made with different neutron wavelengths and SEMSANS configurations to be overlaid and give confidence that the measurements provide an accurate representation of the density correlations in the sample.