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This chapter introduces the fundamental concepts of quantum computation, such as quantum states, quantum circuits, and quantum measurements, along with key topics in quantum machine learning, including quantum read-in, quantum read-out, and quantum linear algebra. These foundational elements are essential for understanding quantum machine learning algorithms and will be repeatedly referenced throughout the subsequent chapters. This chapter is organized into six sections: Sect. 2.1 introduces quantum bits and their mathematical representations; Sect. 2.2 covers quantum circuits, including quantum gates, quantum channels, and quantum measurements; Sect. 2.3 discusses how to encode classical data into quantum systems and extract classical information from quantum states; Sect. 2.4 explores concepts in quantum linear algebra; Sect. 2.5 provides practical coding exercises to reinforce these concepts; and finally, Sect. 2.6 presents recent advancements in efficient quantum read-in and read-out techniques, as well as developments in quantum linear algebra for further exploration.

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Basics of Quantum Computing

  • 章节

  • 发表日期：

    2025年

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  • Yuxuan Du,
  • Xinbiao Wang,
  • Naixu Guo,
  • Zhan Yu,
  • Yang Qian,
  • Kaining Zhang,
  • Min-Hsiu Hsieh,
  • Patrick Rebentrost,
  • Dacheng Tao

摘要

This chapter introduces the fundamental concepts of quantum computation, such as quantum states, quantum circuits, and quantum measurements, along with key topics in quantum machine learning, including quantum read-in, quantum read-out, and quantum linear algebra. These foundational elements are essential for understanding quantum machine learning algorithms and will be repeatedly referenced throughout the subsequent chapters. This chapter is organized into six sections: Sect. 2.1 introduces quantum bits and their mathematical representations; Sect. 2.2 covers quantum circuits, including quantum gates, quantum channels, and quantum measurements; Sect. 2.3 discusses how to encode classical data into quantum systems and extract classical information from quantum states; Sect. 2.4 explores concepts in quantum linear algebra; Sect. 2.5 provides practical coding exercises to reinforce these concepts; and finally, Sect. 2.6 presents recent advancements in efficient quantum read-in and read-out techniques, as well as developments in quantum linear algebra for further exploration.