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相关概念视频

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

89
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
89
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

81
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
81
Linear Circuits01:17

Linear Circuits

402
A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...
402
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

883
A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
883
Transient and Steady-state Response01:24

Transient and Steady-state Response

176
In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
176
Classification of Systems-I01:26

Classification of Systems-I

183
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
183

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High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water
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对于NISQ友好的线性响应配方,有哪些选择?

Karl Michael Ziems1, Erik Rosendahl Kjellgren2, Peter Reinholdt2

  • 1Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark.

Journal of chemical theory and computation
|April 25, 2024
PubMed
概括
此摘要是机器生成的。

本研究介绍了一种资源高效的量子线性响应 (qLR) 理论,用于在近期量子计算机上模拟复杂的化学系统. 两个新的qLR方法",proj LRSD"和"all-proj LRSD"显示出准确的激发状态计算的希望.

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科学领域:

  • 量子化学是一种量子化学.
  • 计算物理学的计算物理.
  • 频谱学是一种光谱学.

背景情况:

  • 线性反应 (LR) 理论对于理解光诱导过程至关重要.
  • 模拟大型系统和与LR理论的强电子相关性在计算上具有挑战性.
  • 量子计算为这些复杂的模拟提供了潜在的解决方案.

研究的目的:

  • 开发一种资源效率高的量子线性响应 (qLR) 理论,适用于近期量子计算机.
  • 为了适应超出最小基础集的系统,使用活动空间近似来调整qLR.
  • 为了确定效率高的qLR形式来模拟激发状态属性.

主要方法:

  • 引入了多配置自相一致场 LR 替代的截断的活动空间版本.
  • 开发了用于在近期量子硬件上执行qLR方程的新型运算符转换.
  • 研究了八种不同的短期qLR形式.

主要成果:

  • 成功模拟了兴奋状态潜在能量曲线和吸收光谱.
  • 确定了两个有前途的qLR形式:"proj LRSD"和"all-proj LRSD".
  • 通过节约资源的方法,证明了将qLR应用于更大的系统的可行性.

结论:

  • 开发的资源效率高的qLR理论使近期量子设备上的精确兴奋状态计算成为可能.
  • "proj LRSD"和"all-proj LRSD"被确定为实际量子模拟的主要候选者.
  • 这项工作推进了量子计算在化学和生物学中的应用,用于光诱导过程.