Graph Representation of Topological Stabilizer States

Topological quantum states, especially these in topological stabilizer quantum error correction codes, are currently the focus of intense activity because of their potential for fault-tolerant operations. While every stabilizer state maps to a graph state under local Clifford operations, the graphs associated with topological stabilizer codes remain unknown. In this thesis, I show that the toric code graph is composed of only two kinds of subgraphs: star graphs and half graphs. The topological order of the toric code is identified with the existence of multiple star graphs, which reveals a nice connection between repetition codes and the toric code. The graph structure readily yields a log-depth and a constant-depth (including ancillae) circuit for state preparation. Next, I derive the necessary and sufficient conditions for a family of graph states to be in TQO-1, a class of quantum error correction code states whose code distance scales macroscopically with the number of physical qubits. Using these criteria, I consider a number of specific graph families, including the star and complete graphs, and the line graphs of complete and completely bipartite graphs, and discuss which are topologically ordered and how to construct the codewords. The formalism is then employed to construct several codes with macroscopic distance, including a three-dimensional topological code generated by local stabilizers that also has a macroscopic number of encoded logical qubits. Last, the connection between the characterization of topological order using graph theory and the hierarchy of topological order is analyzed

Topological graph states and quantum error correction codes

Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph states to be in TQO-1, which is a class of quantum error correction code states whose code distance scales macroscopically with the number of physical qubits. Using these criteria, we consider a number of specific graph families, including the star and complete graphs, and the line graphs of complete and completely bipartite graphs, and discuss which are topologically ordered and how to construct the codewords. The formalism is then employed to construct several codes with macroscopic distance, including a three-dimensional topological code generated by local stabilizers that also has a macroscopic number of encoded logical qubits. The results indicate that graph states provide a fruitful approach to the construction and characterization of topological stabilizer quantum error correction codes.Comment: 21 pages, 7 figures

SCARA: Scalable Graph Neural Networks with Feature-Oriented Optimization

Recent advances in data processing have stimulated the demand for learning graphs of very large scales. Graph Neural Networks (GNNs), being an emerging and powerful approach in solving graph learning tasks, are known to be difficult to scale up. Most scalable models apply node-based techniques in simplifying the expensive graph message-passing propagation procedure of GNN. However, we find such acceleration insufficient when applied to million- or even billion-scale graphs. In this work, we propose SCARA, a scalable GNN with feature-oriented optimization for graph computation. SCARA efficiently computes graph embedding from node features, and further selects and reuses feature computation results to reduce overhead. Theoretical analysis indicates that our model achieves sub-linear time complexity with a guaranteed precision in propagation process as well as GNN training and inference. We conduct extensive experiments on various datasets to evaluate the efficacy and efficiency of SCARA. Performance comparison with baselines shows that SCARA can reach up to 100x graph propagation acceleration than current state-of-the-art methods with fast convergence and comparable accuracy. Most notably, it is efficient to process precomputation on the largest available billion-scale GNN dataset Papers100M (111M nodes, 1.6B edges) in 100 seconds

Clustered microRNAs' coordination in regulating protein-protein interaction network

<p>Abstract</p> <p>Background</p> <p>MicroRNAs (miRNAs), a growing class of small RNAs with crucial regulatory roles at the post-transcriptional level, are usually found to be clustered on chromosomes. However, with the exception of a few individual cases, so far little is known about the functional consequence of this conserved clustering of miRNA loci. In animal genomes such clusters often contain non-homologous miRNA genes. One hypothesis to explain this heterogeneity suggests that clustered miRNAs are functionally related by virtue of co-targeting downstream pathways.</p> <p>Results</p> <p>Integrating of miRNA cluster information with protein protein interaction (PPI) network data, our research supports the hypothesis of the functional coordination of clustered miRNAs and links it to the topological features of miRNAs' targets in PPI network. Specifically, our results demonstrate that clustered miRNAs jointly regulate proteins in close proximity of the PPI network. The possibility that two proteins yield to this coordinated regulation is negatively correlated with their distance in PPI network. Guided by the knowledge of this preference, we found several network communities enriched with target genes of miRNA clusters. In addition, our results demonstrate that the variance of this propensity can also partly be explained by protein's connectivity and miRNA's conservation.</p> <p>Conclusion</p> <p>In summary, this work supports the hypothesis of intra-cluster coordination and investigates the extent of this coordination.</p

Profile of immunoglobulin G N-glycome in COVID-19 patients: A case-control study

Coronavirus disease 2019 (COVID-19) remains a major health challenge globally. Previous studies have suggested that changes in the glycosylation of IgG are closely associated with the severity of COVID-19. This study aimed to compare the profiles of IgG N-glycome between COVID-19 patients and healthy controls. A case-control study was conducted, in which 104 COVID-19 patients and 104 age- and sex-matched healthy individuals were recruited. Serum IgG N-glycome composition was analyzed by hydrophilic interaction liquid chromatography with the ultra-high-performance liquid chromatography (HILIC-UPLC) approach. COVID-19 patients have a decreased level of IgG fucosylation, which upregulates antibody-dependent cell cytotoxicity (ADCC) in acute immune responses. In severe cases, a low level of IgG sialylation contributes to the ADCC-regulated enhancement of inflammatory cytokines. The decreases in sialylation and galactosylation play a role in COVID-19 pathogenesis via the activation of the lectin-initiated alternative complement pathway. IgG N-glycosylation underlines the complex clinical phenotypes of SARS-CoV-2 infection

Spatiotemporal transcriptomic atlas of mouse organogenesis using DNA nanoball-patterned arrays.

Spatially resolved transcriptomic technologies are promising tools to study complex biological processes such as mammalian embryogenesis. However, the imbalance between resolution, gene capture, and field of view of current methodologies precludes their systematic application to analyze relatively large and three-dimensional mid- and late-gestation embryos. Here, we combined DNA nanoball (DNB)-patterned arrays and in situ RNA capture to create spatial enhanced resolution omics-sequencing (Stereo-seq). We applied Stereo-seq to generate the mouse organogenesis spatiotemporal transcriptomic atlas (MOSTA), which maps with single-cell resolution and high sensitivity the kinetics and directionality of transcriptional variation during mouse organogenesis. We used this information to gain insight into the molecular basis of spatial cell heterogeneity and cell fate specification in developing tissues such as the dorsal midbrain. Our panoramic atlas will facilitate in-depth investigation of longstanding questions concerning normal and abnormal mammalian development.This work is part of the ‘‘SpatioTemporal Omics Consortium’’ (STOC) paper package. A list of STOC members is available at: http://sto-consortium.org. We would like to thank the MOTIC China Group, Rongqin Ke (Huaqiao University, Xiamen, China), Jiazuan Ni (Shenzhen University, Shenzhen, China), Wei Huang (Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai, China), and Jonathan S. Weissman (Whitehead Institute, Boston, USA) for their help. This work was supported by the grant of Top Ten Foundamental Research Institutes of Shenzhen, the Shenzhen Key Laboratory of Single-Cell Omics (ZDSYS20190902093613831), and the Guangdong Provincial Key Laboratory of Genome Read and Write (2017B030301011); Longqi Liu was supported by the National Natural Science Foundation of China (31900466) and Miguel A. Esteban’s laboratory at the Guangzhou Institutes of Biomedicine and Health by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA16030502), National Natural Science Foundation of China (92068106), and the Guangdong Basic and Applied Basic Research Foundation (2021B1515120075).S

Corrigendum to: The TianQin project: current progress on science and technology

In the originally published version, this manuscript included an error related to indicating the corresponding author within the author list. This has now been corrected online to reflect the fact that author Jun Luo is the corresponding author of the article