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Related Concept Videos

Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

2.0K
Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area...
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Gauss's Law01:07

Gauss's Law

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
739
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
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Ampere's Law: Problem-Solving01:31

Ampere's Law: Problem-Solving

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Ampere's law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the current enclosed in the loop. If the fingers of the right hand curl along the direction of the integration path, the current in the direction of the thumb is considered positive. The current opposite to the thumb direction is considered negative.
Specific steps need to be considered while calculating the symmetric magnetic field distribution...
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Gaussian Amplitude Amplification for Quantum Pathfinding.

Daniel Koch1, Massimiliano Cutugno1, Samuel Karlson2

  • 1Air Force Research Lab, Information Directorate, Rome, NY 13441, USA.

Entropy (Basel, Switzerland)
|July 27, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new quantum oracle operation that, with Grover

Keywords:
amplitude amplificationquantum algorithmsquantum computing

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Area of Science:

  • Quantum computing algorithms
  • Graph theory
  • Optimization problems

Background:

  • Quantum algorithms can offer speedups for complex problems.
  • Finding optimal paths in weighted directed graphs is computationally challenging.
  • Grover's algorithm is a key quantum search technique.

Purpose of the Study:

  • To develop a novel quantum oracle for optimization.
  • To enhance Grover's algorithm for graph-based problems.
  • To explore applications in solving the Traveling Salesman Problem.

Main Methods:

  • Designing a quantum oracle for Gaussian distributions.
  • Integrating the oracle with the Grover diffusion operator.
  • Utilizing amplitude amplification for optimal path finding.
  • Analyzing performance on randomized and Traveling Salesman Problem instances.

Main Results:

  • The combined oracle and Grover operator significantly boost solution finding probability.
  • The approach effectively encodes Gaussian distributions for path optimization.
  • Demonstrated potential for solving randomized weight cases.
  • Theoretical framework established for Traveling Salesman Problem application.

Conclusions:

  • The proposed quantum oracle enhances Grover's algorithm for graph optimization.
  • This method shows promise for solving complex optimization tasks, including the Traveling Salesman Problem.
  • Further research can explore practical implementations and larger-scale problems.