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While preparing a follow-up manuscript, we found an error in one of the orbital reduction factors used in our crystal field models, given in Scheme 2. The third equation in that scheme was published as ka2t2 = 1 - 12 N2 2 a'p ; however, the correct formula is k a2t2 = 1 - 12 N'a'p2. (Table Presented).
Localized projections of 21st‐century hydroclimate variables obtained from downscaling Global Climate Model (GCM) output are central to informing regional impact assessments and infrastructure planning. Regional GCM biases can be significant and, for dynamical downscaling, can be addressed either before (a priori) or after (a posteriori) downscaling. However, a priori bias correction (APBC) has generally unexplored effects on climate change signals. Here we analyze dynamically downscaled solutions of CMIP6 GCMs over the Western U.S., with and without APBC, and quantify APBC's impact on climate change signals relative to other irreducible uncertainty sources. For temperature and precipitation, the uncertainty introduced by APBC is negligible compared to that arising from GCM choice or internal variability. Furthermore, APBC greatly reduces regional models' unrealistically high snow‐water‐equivalent (SWE) biases that result directly from GCM errors. We leverage this finding to encourage the dynamical downscaling community to adopt APBC as a standard operating procedure.
Correction to: Nature Communications https://doi.org/10.1038/s41467-019-12723-3, published online 18 October 2019.
Correction to: Nature Communications https://doi.org/10.1038/s41467-019-10257-2, published online 20 June 2019.
An amendment to this paper has been published and can be accessed via a link at the top of the paper. The original version of this Article incorrectly omitted the received/accepted dates of Received: 05 June 2018; Accepted: 10 October 2018. This has now been corrected in the PDF and HTML versions of the Article.
The current Figs. 1 and 2 have incorrect numbers shown on the purple bars. The source data was also incorrect in the original version of the Article. This has been corrected in both the PDF and HTML versions of the Article.
Correction to: Nature Communications https://doi.org/10.1038/s41467-020-19237-3, published online 2 November 2020. The original version of this Article contained an error in the author affiliations.
The original version of this Article omitted the following from the Acknowledgements: This research was partially conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. This has now been corrected in both the PDF and HTML versions of the Article.
The original version of this Article omitted DMR-1420570 from the Acknowledgements. This has now been corrected in both the PDF and HTML versions of the Article.
In this article the affiliation ‘State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, Nanjing 210008, China’ for Xinhua Peng was missing. The original article has been corrected.
In the Acknowledgements section of this article the grant number relating to NSF was incorrectly given as DMR 2045826 and should have been DMR-2045826. The original article has been corrected.
Correction to: Nature Communicationshttps://doi.org/10.1038/s41467-024-54578-3, published online 27 November 2024. The original version of this Article omitted a line in the Acknowledgements section: Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This has been now added into the last line of the acknowledgements section in both the PDF and HTML versions of the Article.
The original version of this Article contained discrepancies in numbering several equations and chemical reactions and referring to them in the main text. Here, corrections are listed.
Abstract High-fidelity and rapid readout of a qubit state is key to quantum computing and communication, and it is a prerequisite for quantum error correction. We present a readout scheme for superconducting qubits that combines two microwave techniques: applying a shelving technique to the qubit that reduces the contribution of decay error during readout, and a two-tone excitation of the readout resonator to distinguish among qubit populations in higher energy levels. Using a machine-learning algorithm to post-process the two-tone measurement results further improves the qubit-state assignment fidelity. We perform single-shot frequency-multiplexed qubit readout, with a 140 ns readout time, and demonstrate 99.5% assignment fidelity for two-state readout and 96.9% for three-state readout–without using a quantum-limited amplifier.
Abstract Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin–Knill theorem, which forbids the existence of QEC codes that admit transversal continuous symmetry actions (transformations). Here, we systematically study the competition between continuous symmetries and QEC in a quantitative manner. We first define a series of meaningful measures of approximate symmetries motivated from different perspectives, and then establish a series of trade-off bounds between them and QEC accuracy utilizing multiple different methods. Remarkably, the results allow us to derive general quantitative limitations of transversally implementable logical gates, an important topic in fault-tolerant quantum computation. As concrete examples, we showcase two explicit types of quantum codes, obtained from quantum Reed–Muller codes and thermodynamic codes, respectively, that nearly saturate our bounds. Finally, we discuss several potential applications of our results in physics.
Abstract One of the most promising routes toward scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner even in the presence of substantial noise along their connecting interface. We quantify analytically and numerically the combined effect of errors across the interface and bulk. We show that the system can tolerate 14 times higher noise at the interface compared to the bulk, with only a small effect on the code’s threshold and subthreshold behavior, reaching threshold with ~1% bulk errors and ~10% interface errors. This implies that fault-tolerant scaling of error-corrected modular devices is within reach using existing technology.
We study quantum networks with tree structures, in which information propagates from a root to leaves. At each node in the network, the received qubit unitarily interacts with fresh ancilla qubits, after which each qubit is sent through a noisy channel to a different node in the next level. Therefore, as the tree depth grows, there is a competition between the irreversible effect of noise and the protection against such noise achieved by the delocalization of information. In the classical setting, where each node simply copies the input bit into multiple output bits, this model has been studied as the broadcasting or reconstruction problem on trees, which has broad applications. In this work, we study the quantum version of this problem. We consider a Clifford encoder at each node that encodes the input qubit in a stabilizer code, along with a single qubit Pauli noise channel at each edge. Such noisy quantum trees describe a scenario in which one has access to a stream of fresh (low-entropy) ancilla qubits, but cannot perform error correction. Therefore, they provide a different perspective on quantum fault tolerance. Furthermore, they provide a useful model for describing the effect of noise within the encoders of concatenated codes. We prove that above certain noise thresholds, which depend on the properties of the code such as its distance, as well as the properties of the encoder, information decays exponentially with the depth of the tree. On the other hand, by studying certain efficient decoders, we prove that for codes with distance d ≥ 2 and for sufficiently small (but non-zero) noise, classical information and entanglement propagate over a noisy tree with infinite depth. Indeed, we find that this remains true even for binary trees with certain 2-qubit encoders at each node, which encodes the received qubit in the binary repetition code with distance d = 1.
On macroevolutionary timescales, extensive mutations and phylogenetic uncertainty mask the signals of genotype–phenotype associations underlying convergent evolution. To overcome this problem, we extended the widely used framework of non-synonymous to synonymous substitution rate ratios and developed the novel metric ω C , which measures the error-corrected convergence rate of protein evolution. While ω C distinguishes natural selection from genetic noise and phylogenetic errors in simulation and real examples, its accuracy allows an exploratory genome-wide search of adaptive molecular convergence without phenotypic hypothesis or candidate genes. Using gene expression data, we explored over 20 million branch combinations in vertebrate genes and identified the joint convergence of expression patterns and protein sequences with amino acid substitutions in functionally important sites, providing hypotheses on undiscovered phenotypes. We further extended our method with a heuristic algorithm to detect highly repetitive convergence among computationally non-trivial higher-order phylogenetic combinations. Our approach allows bidirectional searches for genotype–phenotype associations, even in lineages that diverged for hundreds of millions of years.