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Related Concept Videos

Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
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Routh-Hurwitz Criterion II01:19

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the...
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The parallel-axis theorem provides a convenient and quick method of finding the moment of inertia of an object about an axis parallel to the axis passing through its center of mass. Consider a thin rod as an example. There is a striking similarity between the process of finding the moment of inertia of a thin rod about an axis through its middle, where the center of mass lies, and about an axis through its end using the conventional method. In the conventional method, the concept of linear mass...
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Updated: Aug 27, 2025

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Coherence as a Resource for Shor's Algorithm.

Felix Ahnefeld1, Thomas Theurer2, Dario Egloff3

  • 1Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11, D-89081 Ulm, Germany.

Physical Review Letters
|September 30, 2022
PubMed
Summary
This summary is machine-generated.

Coherence is the key quantum resource driving Shor's factoring algorithm's speedup. This study quantifies coherence's role, establishing bounds on the algorithm's success probability and highlighting its fundamental importance in quantum computation.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation
  • Quantum Algorithms

Background:

  • Shor's factoring algorithm offers a significant speedup over classical methods.
  • The specific quantum properties responsible for this advantage require further elucidation.
  • Understanding these properties is crucial for advancing quantum computing.

Purpose of the Study:

  • To quantitatively identify and analyze the role of coherence in a sequential variant of Shor's algorithm.
  • To investigate how coherence acts as a dynamical resource in this specific protocol.
  • To establish bounds on the algorithm's success probability based on coherence measures.

Main Methods:

  • Analysis of a sequential variant of Shor's algorithm with a fixed structure.
  • Application of dynamical resource theories to quantify coherence.
  • Derivation of lower and upper bounds on the protocol's success probability using coherence measures.

Main Results:

  • Coherence was quantitatively identified as the crucial quantum resource.
  • Rigorous bounds on the success probability were derived, dependent on coherence measures.
  • The performance of the quantum protocol was directly linked to the quantified coherence.

Conclusions:

  • Within the considered fixed structure, coherence is the quantum resource that dictates Shor's algorithm performance.
  • This work provides new insights into the fundamental role of coherence in quantum computation.
  • The findings underscore the importance of managing and utilizing coherence for effective quantum algorithms.