This is a book on the mathematical theory of quantum information, focusing on a formal presentation of definitions, theorems, and proofs. It is primarily intended for graduate students and researchers having some familiarity with quantum information and computation, such as would be covered in an introductory-level undergraduate or graduate course, or in one of several books on the subject that now exist. Quantum information science has seen an explosive development in recent years, particularly within the past two decades. A comprehensive treatment of the subject, even if restricted to its theoretical aspects, would certainly require a series of books rather than just one. Consistent with this fact, the selection of topics covered herein is not intended to be fully representative of the subject. Quantum error correction and fault-tolerance, quantum algorithms and complexity theory, quantum cryptography, and topological quantum computation are among the many interesting and fundamental topics found within the theoretical branches of quantum information science that are not covered in this book. Nevertheless, one is likely to encounter some of the core mathematical notions discussed in this book when studying these topics.
Traditional network security situation prediction methods depend on the accuracy of historical situation value. Moreover, there are differences in correlation and importance among various network security factors. In order to solve these problems, a combined prediction model based on the temporal convolution attention network (TCAN) and bi-directional gate recurrent unit (BiGRU) network optimized by singular spectrum analysis (SSA) and improved quantum particle swarm optimization algorithm (IQPSO) was proposed. This model was first decomposed and reconstructed into a series of subsequences through the SSA of network security situation data. Next, a prediction model of TCAN-BiGRU was established for each subsequence, respectively. The TCN with relatively simple structure was used in the TCAN to extract features from the data. Besides, the improved channel attention mechanism (CAM) was used to extract important feature information from TCN. Afterwards, the before-after status of the learning situation value of the BiGRU neural network was used to extract more feature information from sequences for prediction. Meanwhile, an improved IQPSO was proposed to optimize the hyper-parameter of the BiGRU neural network. Finally, the prediction results of subsequence were superimposed to obtain the final predicted value. In the experiment, on the one hand, the IQPSO was compared with other optimization algorithms; and the results showed that the IQPSO has better optimization performance; on the other hand, the comparison with traditional prediction methods was performed through the simulation experiment and the established prediction model; and the results showed that the combined prediction model established has higher prediction accuracy.
Topological physics relies on the existence of Hamiltonian’s eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and – in non- Hermitian systems – exceptional points (EPs), lines or surfaces 1–3 . They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point.
翻译Advances in biomedical sciences are often spurred by the development of tools with enhanced sensitivity and resolution, which allow detection and imaging of signals that are progressively weaker, more localized and/or biologically specific. Improvements in nuclear magnetic resonance (NMR) or magnetoencephalography (MEG) have resulted in tremendous progress in diagnostics and treatment, yet further progress in sensitivity and resolution seems to be challenging with conventional methods. However, a promising direction for a new generation of biomedical sensors with greatly enhanced performance comes from advances in quantum science and technology.
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