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相关概念视频

Quantum Numbers02:43

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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State Space to Transfer Function01:21

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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使用量子增强特征空间进行监督学习

Vojtěch Havlíček1,2, Antonio D Córcoles3, Kristan Temme4

  • 1IBM T. J. Watson Research Center, Yorktown Heights, NY, USA.

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此摘要是机器生成的。

本研究介绍了机器学习分类的两个量子算法,利用量子计算的潜力克服了大型特征空间和支持向量机 (SVM) 的计算成本高的内核估计. 这些方法利用量子状态空间进行增强的特征表示,为机器学习任务中的量子优势铺平了道路.

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科学领域:

  • 量子计算
  • 机器学习
  • 监督学习

背景情况:

  • 机器学习中的内核方法,如支持向量机 (SVM),面临着大型特征空间和计算上昂贵的内核函数估计的挑战.
  • 量子计算通过纠和干扰利用指数级大的量子状态空间提供了潜在的计算加速度.
  • 量子计算和机器学习之间的联系对于解决复杂的计算问题至关重要.

研究的目的:

  • 为监督学习分类任务提出并实验实施两种新的量子算法.
  • 探索量子增强特征空间在机器学习中的潜在量子优势.
  • 研究噪音中等尺度量子计算机 (NISQ) 在机器学习中的应用.

主要方法:

  • 在超导处理器上实验实施两个量子算法.
  • 使用量子状态空间作为一个增强的特征空间,只能在量子计算机上有效地访问.
  • 一种方法采用使用变量量子电路的量子变量分类器,类似于经典的SVM.
  • 第二种方法涉及量子内核估计器,用于计算量子计算机上的内核函数以优化经典的SVM.

主要成果:

  • 两种用于分类的量子算法的成功实验实施.
  • 展示量子增强特征空间作为获得量子优势的途径.
  • 开发用于将NISQ设备应用于机器学习问题的工具.

结论:

  • 量子算法可以有效地解决经典机器学习的局限性,特别是对于大型特征空间.
  • 量子增强的特征空间为实现机器学习中的量子优势提供了有前途的方法.
  • 开发的方法提供了在机器学习应用中利用NISQ计算机的实用工具.